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MathGeniusLab is a premier mathematics learning centre that has a strong track record in helping many primary school children score top grades in PSLE math. We are able to help each child use their various approaches.
mindset through
1. We make learning math fun through games and activities. 2. We teach our students heuristics to solve challenging problems. 3. We use higher order thinking to help our students learn different strategies to solve the same type of problems, thereby improving their understanding of the concept. We are conveniently located at Bishan and Marine Parade. For more information, please visit www.mathgeniuslab.com or email
[email protected].
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About PSLE Math Series 2013 PSLE Math Series is a must-have resource guide for any student who is preparing for PSLE Math in 2013. It consists of examination questions that appeared in top schools’ examination papers in the past 5 years from 2007 to 2011. All questions are carefully categorized to ensure every learner understand and apply all the concepts necessary to solve the most challenging problems. It follows the MOE syllabus closely to help every child score well in school exams and PSLE. Please register at www.pslemathseries.com for product updates. Please email
[email protected] for any query.
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How to Use PSLE Math Series 1. Self study 2. Use it with the support of your tutor/teacher 3. Attend lessons at any centre that uses PSLE Math Series To gain maximum benefits from PSLE Math Series, download the ‘PSLE Math Series’ app from App Store. The ‘PSLE Math Series’ app can be used on both the iPhone and the iPad. The app will auto check your answers and generate a report which will be sent to your registered email. More information can be found at www.pslemathseries.com.
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Volume 1 Contents
PSLE Math Series
Unit 1 Whole Numbers
1
Unit 2 Patterns
31
Unit 3 Algebra
73
Unit 4 Data Analysis
87
Unit 5 Fractions
126
Unit 6 Percentage
147
Unit 7 Ratio
172
Unit 8 Speed
230
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Unit 1 Whole Numbers
PSLE Math Series
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
Four Operations Pairing/Grouping Concept Multiple Differences Factors and Multiples Bonus/Free Concept Equal Intervals Guess and Check Unit/Model Method Before-after Difference pslemathseries.com
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PSLE Math Series
Unit 1.1 Whole Numbers Four Operations
2007 1. Gerald received 10 hongbaos during Chinese New Year. Five of them contained $20 each and three of them contained $12 each. He used the money in the remaining 2 hongbaos to buy 4 t-shirts at $12.50 each. How much money was there in all the hongbaos Gerald received? PH07C37 2. A total of 36 kg of butter is packaged into boxes each containing 4 kg of butter. Each box is then sold for $1.85. What is the total selling price of all the boxes of butter? NH07C40 3. Emily was twice as old as Jimmy 5 years ago. In 10 years’ time, Jimmy will be 32 years old. How old is Emily now? RY07C40 4. The entrance fee to an amusement park was $4.50 for an adult and $2.50 for a child. Mr Lee took some children to the park and paid a total of $19.50 as entrance fee. How many children did he take to the park? HK07P36 5. James used 12 litres of syrup to make fruit punch. For every litre of syrup, he added 3.5 litres of water. The fruit punch was then poured into cups of 200 mℓ for sale. (a) How many cups of fruit punch did he get? (b) If each cup of fruit punch was sold for $0.50, how much money would James collect? RG07P39 2008 6. Mary had $50. She can buy either exactly 3 similar wallets and 5 similar combs or exactly 10 such wallets. How many such combs can she buy with $210? NH08C38 7. A necklace cost $160 more than a bracelet. 2 such bracelets cost as much as 3 rings. If each ring cost $100, what was the cost of the necklace? TN08S36 8. Mary and Eliza went shopping. Mary bought 2 compact discs at $8.50 each and a key chain for $6. Eliza spent $3.80 less than Mary. If Eliza bought a story book for $5.40 and 3 similar markers, how much did she pay for each marker? MB08S38
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9. The table shows the sales of flour at ABC’s supermarket. Type of packet Price per packet Number of packets sold Small $2 48 Medium $3 30
Total mass of packets sold 48 kg 45 kg
How much money did the supermarket collect from the total sale of all the flour? AT08S37 10. A box weighs 0.55 kg. When 7 packets of salt were placed into it, the total mass became 3.35 kg. When 3 packets of salt were taken out and a tin of milk powder was placed into the box, the mass of the box became 3.65 kg. Find the mass of a tin of milk powder. RY08P37 11. There are 2500 children in a school. 1400 of them enjoy Music lessons. 1500 of them enjoy Art lessons. 450 of them do not enjoy both Music and Art lessons. How many of them enjoy both Music and Art lessons? RY08S36 2009 12. A bar of chocolate is sold at $3.50 each or in packets of 4 at $12 per packet. Alice wants to buy exactly 38 bars of chocolate for a party. What is the least amount of money that Alice could have spent on the chocolate? AC09P07 13. Dennis wanted to buy a toy aeroplane which cost $44.10. He decided to save $2.10 a day to buy it. If the price of the toy aeroplane decreased to $39.90 at a sale, how much did he need to save each day so that he could buy the toy aeroplane after saving for the same number of days? HK09P06 14. In a school science fair, there were exhibits from Primary 4 to Primary 6. Altogether 25 exhibits came from Primary 5 and 6. If 16 exhibits were not from Primary 6 and 15 exhibits were not from Primary 5, how many exhibits were there altogether? HK09P17 15. At a party, a box of candies was divided equally among 114 children. 38 of these children gave up their candies. As a result, there were 228 more candies shared among the remaining children. How many candies were there in the box at first? RS09P06 16. A Chinese medical shop had 50 jars containing the same number of herbs in each jar. During renovation, 15 jars were removed and their herbs were distributed equally amongst the remaining jars. As a result, there were 12 more herbs in each jar than before. How many herbs were in each jar before the renovation? RY09C10
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2010 17. A box contained a total of 506 ten-cent coins and five-cent coins. All the ten-cent coins were worth $15. If all the five-cent coins were removed from the box and replaced by twenty-cent coins of the same value as the five-cent coins, how many twenty-cent coins would replace the five-cent coins? SN10C05 18. During a sale, Shop X and Shop Y were selling similar blouses at $28 and $21 respectively. Before this sale, the price of blouses was the same in both shops. A sum of $170 could be saved by buying 2 blouses from each shop during the sale. How much was the discount per blouse in Shop X? AT10C12 19. Carrie had $210. During a moving-out sale, she paid $54 for 3 dresses and 5 T-shirts. She bought another 10 T-shirts and a few dresses with all the remaining money. If each dress cost $6, how many dresses did she buy in all? RY10S07 20. Nancy and Jane baked 1800 muffins altogether. After Nancy sold 680 of her muffins, Nancy still had 20 muffins more than Jane. How many muffins did Nancy bake? NH10S10 21. After giving 22 cards away, Peter put the rest of the cards equally into boxes. He found that he had 7 cards left after putting 25 cards into each box. How many boxes of cards did Peter have if he had 154 cards at first? AT10S07 22. There is a block of 100 flats. Ah Huat, a painter, paints one flat each month from January to November. The flats are painted in the same order and Ah Huat takes a holiday every December. If my flat was painted in May 2004, which month and year will it be painted next? AT10S11 23. A courier company charged $25 for every large parcel and $15 for every small parcel delivered safely. However, a penalty of $50 was charged for every damaged parcel, regardless of size. 𝟏
This month, the company delivered 120 parcels of which of them were small parcels. 𝟒
It collected a total of $2000 after paying a penalty for an equal number of large and small parcels. How many large parcels were delivered safely? NY10S12 24. There are some 10-cent coins and 50-cent coins in the piggy bank. The amount of money in the box is $3.40. If the number of 10-cent coins is less than 5, find the total number of coins in the piggy bank. RG10S09
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25. The table below shows the number of mobile phones per family in a particular block of flats. Number of mobile phones 0 1 2 3 4 Number of families 2 24 49 67 28 What is the total number of mobile phones in that block of flats? AC10P08 26. Lindsay and Johanna went shopping. Lindsay bought 7 dresses at $88.90 each and a pair of shoes for $45.70. Johanna bought a camera which was 0.6 of what Lindsay spent altogether. Then she had $22.85 left. How much money did Johanna have originally? SN10P07 27. There are 2 teams of workers at a fast food restaurant. Team G has 30 more members than Team H. Each member in Team G prepares 4 burgers in 1 minute while each member in Team H only prepares 3 burgers in 1 minute. In 1 hour, both teams prepare 36 600 burgers altogether. How many members are there in each team? SN10S15 28. 5 friends were playing Wii games on a Friday afternoon from 3 pm to 6 pm. As there were only 4 consoles, they took turns to play. At any time, 3 of them played while the other 2 friends watched. If each of them had the same amount of playing time, how many minutes did each child play that afternoon? SN10S09 29. At a factory, Jane could assemble 8 toys in a day while Mary could assemble 5 more toys than her in a day. If Mary was absent for 4 days, how many days would she need to assemble 18 more toys than Jane? CH10P10 30. A condominium unit was sold at $810 000, when rounded off to the nearest ten thousand dollars. What was the lowest possible selling price? NY10S02 31. A lemon costs 30₵ more than a lime. Kayee bought 56 limes at 35₵ each. If she were to use the same amount of money to buy only lemons, how many fewer lemons could she buy? SN10P02 32.
Wendy wants to make icy-pop to serve 10 people. Using the recipe above, how much strawberries does she need? HK10P03
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33. During an Art lesson, Mrs Choo gave each group 17 pieces of cardboards as shown below on the left to make a structure. John’s group decided to fold each pieces into a prism as shown below on the right:
His group glued all the 17 prisms together to form the structure shown below.
(a) What is the length of the base of the prism? (b) What is the height of the structure? MB10P08 34. The school conducted a survey with some pupils on how they travelled to school. There 1
were twice as many boys as girls who travelled to school by MRT. of those who 5
travelled by bus were girls. The table below shows the findings. Study the table and find the number of boys who went to school by MRT. HP10P05 Walk MRT Car Bus Total Boys 5 ? 24 ? 107 Girls 10 ? 12 8 53 35. Mr Tseng bought a new car. He paid a down payment of $20 000. After paying monthly 1
instalments of $1200 for 4 years, he still had $4000 more to pay. What was the cost of 2
the car? AT10S04
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36. During a basketball match, the teacher promised the team of 8 pupils an equal playing time during the 40 minutes match. Given that only 5 players can play at any one time, what is the average playing time for each pupil? CH10P05 37. A number is between 50 and 70. When it is divided by 3, the answer is a whole number. When it is divided by 8, it has a remainder of 5. What is the number? RY10C03 2011 38. Darren used 14 litres of syrup to make fruit punch.
He added 2.35 litres of water. The fruit punch was then poured into cups of 250 mℓ for sale. (a) How many full cups of fruit punch did he get? (b) Each cup of fruit punch was sold for $0.95. How much would Darren collect if he sold all the full cups of fruit punch? RG11S11 39. Tammy packed 46 kg of chicken wings into 8 packets of equal mass. What was the mass of 1 packet of chicken wings? Round off your answer to 1 decimal place. NY11C02 40. A factory produced a total of 5000 toy cars for the first 4 days. With the improved productivity of the workers subsequently, the factory managed to produce 1750 toy cars per day. How many days did the factory take to produce 22500 toy cars? NY11C05 41. The sum of 2 numbers is 121. One of the numbers is a multiple of 9, while the other number is a factor of 12. Find the two numbers. RY11C01 42. Lauren and Jude went shopping and they spent the same amount of money. Lauren bought 6 dresses at $68.90 each and a pair of jeans for $56.60. Jude spent 0.6 of the amount spent by Lauren on a DVD player. After paying for a mobile phone, Jude had $23.85 left. How much did he pay for the mobile phone? SN11C13 43. Kasey needed to make 120 bows for prize giving. She used 12.4 cm to make a bow. She bought 3 rolls of ribbon, each 5 m long. Find the length of ribbon she had left. HK11P03 44. The total mass of a crate and 16 similar bottles of juice is 29.5 kg. If the mass of 5 such bottles of juice is 8.75 kg. Find the mass of the crate. TN11S05 45. Andre, Benny, Chris share a total of $1144. Andre and Benny have $778 and Benny and Chris have $649. How much money does Benny have? HP11P04 46. The number of children in Twinkle Tots Childcare Centre is less than 80. If they are divided into groups of 14, 3 children will be left out. If they are divided into groups of 16, 9 children will be left out. How many children are there in the childcare centre? SN11C01
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47. Ray has more than 10 but less than 60 cards. If he packs them into packets of 6 cards, he will have 3 cards left over. If he packs them into packets of 7 cards, he will be short of 5 cards. How many cards does Ray have? NH11S03 48. Devi bought 2 identical rulers, 3 identical pens and 2 identical notebooks from Pop Bookstore. Her pen leaked and some ink smudge on her receipt. If the cost of each pen was $2 after rounding off to the nearest dollar, what was the highest possible cost of each notebook? NY11C07
49. The table below shows the number of books borrowed by pupils in the month of July. Number of pupils 4 5 ? 8 3 0 Number of books borrowed by 0 1 2 3 4 5 each pupil The total number of books borrowed by the pupils is 65. How many pupils borrowed 2 books? CH11P05 50. The table shows the number of pets owned by a class of pupils. If the total number of pets owned by the pupils is 82, how many pupils owned 2 pets? NH11P02 Number of pets Number of pupils
0 4
1 12
2 ?
3 10
4 6
51. Fill in the boxes below with different operators (+ − × ÷) to make the expression correct. (You are allowed to use the same operator twice) RG11P04
52. Write down the decimal that is exactly halfway between 0.36 and 0.94. NH11P05 53. Ann is 8 years old. When she reaches her mother's present age, her mother would be 62 years old. How old is Ann's mother now? MG11P06 54. A 2-digit number when divided by 9 gives a remainder of 5. What is the largest possi ble number? RS11P01
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PSLE Math Series
Unit 1.2 Whole Numbers Pairing/Grouping
2007 1. One day, during a pet show-and-tell session in class, 8 pupils brought a dog each while the rest of the pupils brought a cat each. If there were 174 legs altogether in the classroom, (a) how many pupils were there? (b) how many more cats than dogs were there? RY07C42 2. Andy bought 20 books and pens for $118. One week later, he sold 4 pens. Then he had the same number of pens and books left. Each book cost $1.00 more than each pen. How much did he pay for the books? NH07C43 3. Each time Ann deposits $4 into her bank account, her father deposits thrice as much as Ann in her account. When Ann has $208 in her bank account, how much did her father deposit in her account? AC07S38 4. Mr. Lee worked out a saving plan for Janet. For every $4 Janet saved, he would top up $2 into her bank account. After some time, the amount saved in Janet’s account was $252. How much of this amount was contributed by Mr. Lee? NH07P40 5. A grocer packed 252 kg of rice into bags of 5-kg and 2-kg. He has an equal number of 5kg bags and 2-kg bags of rice. How many bags of rice does he have in all? SC07P37 2008 6. Rafi receives $2 from his mother for every $10 he saves. He also receives $3 from his father for every $20 he saves. He has $174 altogether after some time. (a) How much of the money is from his mother? (b) How much of it is from his savings? MG08C48 7. The cost of 0.5 kg of lady’s fingers is the same as 1.5 kg of carrots. Mrs Devi spent $41.25 for 2 kg of lady’s fingers and 10.5 kg of carrots. What was the cost of 1 kg of carrots? RG08S44
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8. John saves a fixed amount of money every week. For the amount that he saves each week, his father will contribute 0.6 of that amount to his savings. How much does John save every week if he saves a total of $192 in 15 weeks? NY08P37 9. Wayne had five more 50₵ coins than 20₵ coins. After he used eight 50₵ coins, the value of 50₵ coins became $1.50 more than that of 20₵ coins. How many coins did he have at first? NY08S42 2010 10. Curry puff is sold at 80 cents each. For every 3 curry puffs, Mrs Lim can buy 1 more curry puff at a discount of 50%. If Mrs Lim has $50, how many curry puff can she buy? NH10C15 11. The usual selling price of a bottle of vitamins is $63. During the Great Singapore Sale, for every 2 bottles bought, the second bottle can be purchased at a 50% discount. Mrs Lee paid $567 for the vitamins during the sale. How many bottles of vitamins did she buy? MG10S07 12. John has $34 in his piggy bank. There was a mixture of 20-cent and 50-cent coins. There were 5 more 50-cent coins than 20-cent coins in the piggy bank. How many 50-cent coins are there in his piggy bank? CH10S06 13. Rabiah bought a total of 80 stools and chairs for $1780. When 20 stools were removed, there was an equal number of stools and chairs left. If each chair cost $6 more than each stool, find the cost of each chair. AT10S10 14. At a bakery, muffins are sold at $1 each. When a customer buys 5 muffins, she can buy one more at half the price. What is the greatest number of muffins that a customer can buy with $20? HK10P05 15. At a sale, wet tissues are sold at $1 per packet or 4 packets for $3.50. What is the maximum number of packets you can buy for $100? CH10P04 16. Siva needed to buy some furniture for his new company. He could buy 4 tables and 6 bookshelves with $490. With the same amount of money, he could buy 14 bookshelves too. (a) How many sets of 4 tables and 6 bookshelves could he buy with $2000? (b) Siva decided to buy tables only, how many tables could he buy with $1960? RY10S13
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2011 17. For every $8 Julie saved, Mrs Tang would top up $3 into her bank account. After some time, the amount saved in Julie’s account was $528. How much did Mrs. Tang contribute? AT11C03 18. Jessica and Joe were buying sports gear at a mall where a discount of $8 was given for every $80 spent. (a) Jessica picked up $572 worth of sports gear. How much did she pay for them after the discount? (b) If Joe paid the cashier $864, how much discount did he get? AT11C12 19. The table below shows the admission fees to a circus for an adult and a child. There were 50 more children than adults at the circus. If a total of $5614 was collected, how many children were at the circus? CH11S09 Adult Child
$25 $8
20. The price of one egg tart is $0.90 from Delicious Bakery. For every 3 egg tarts a customer buys, he can buy the fourth one at half the price. What is the greatest number of egg tarts that a customer can buy with $72? AC11P11
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PSLE Math Series
Unit 1.3 Whole Numbers Multiple Differences
2007 1. Eddy gets $4 more pocket money than Sam each week. They each spend $11 per week on food and save the rest. After a few weeks, Eddy managed to save $65 and Sam only managed to save $45. How much pocket money does Sam get each week? RY07C46 2. For every $20 Jason saved, his brother saved $35. If his brother had saved $90 more than Jason, find out how much Jason had saved. RG07S41 3. Terrence earns $350 less than Leslie every month. They each spend $800 every month and save the rest of their money. (a) How long does it take for Terrence to save $2100 and Leslie to save $4550? (b) What is Terrence’s monthly salary? HP07P45 2008 4. Alvin’s monthly income is $250 more than Clayton but their monthly expenditures are the same. Over a certain period of time, Alvin has saved $1350 but Clayton has only saved $600. Given that each of them spends $500 a month, (a) How long does Clayton take to save the $600? (b) What is Alvin’s monthly income? AC08S42 5. Meili received $2.50 more than Sandy in their daily allowance. Each of them spent the same amount each day and saved the rest. When Meili saved $31.50, Sandy saved only $24. How much was Meili’s daily savings? NY08S39 2010 6. Both Joanne and Joseph had an equal amount of money at first. Every month, Joanne spent $850 and Joseph spent $912. After a few months, Joanne was left with $1550 𝟒
while Joseph had as much as Joanne. How much money did Joseph have at first? 𝟓
AC10S15 7. Darren saves $1.40 daily and Sonia saves $1.10 more than him daily. Although Sonia started saving one week later than Darren, she now saved $2.30 more than him. How many days has Darren been saving? NY10S06
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2011 8. Macy and Kathdu were given equal amount of pocket money each day. Macy and Kathdu started saving on the same day. After saving for a certain number of days, Macy and Kathdu had $11.20 and $12.80 in their savings respectively. Macy spent $0.20 more than Kathdu every day. How many days had they been saving? NY11S01 9. Jeanne earns $22 more than Caleb every week. Each of them spends $110 per week and saves the rest. When Jeanne has saved $1056, Caleb has only saved $880. (a) How long does Jeanne take to save $1056? (b) How much does Caleb earn in a week? RY11C13
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Unit 1.4 Whole Numbers
PSLE Math Series
Factors and Multiples
2008 1. Mrs Ming has some party lights. The red light flashes every 4 seconds, the blue light flashes every 5 seconds while the purple light flashes every 6 seconds. If all 3 colour lights flash together at 9 p.m. what is the very next time on the clock that they will flash together again? AT08S40 2. Mrs Smith has drawn up a schedule to have her home cleaned by 3 part-time workers. The cleaner goes to her home once every 3 days, the sweeper once every 4 days, and the gardener once every 6 days. If the 3 workers first met on 28 July, when was the earliest date (in July) the cleaner had to start work? NY08P36 3. Mrs Wong bought an equal number of toy dinosaurs and teddy bears at a fun fair. The toy dinosaurs were sold at 3 for $2 and the teddy bears were sold at 4 for $3. She paid $4 more for the teddy bears than for the toy dinosaurs. How much did she pay for all the items? RY08P44 4. There was a total of 200 blue, red and green balls. There were twice as many red balls as blue balls. There were fewer green balls than red balls. The number of blue balls and red balls in each group was less than 100 and divisible by 3 and 4. How many green balls were there? NY08P41 5. 390 marbles were placed into 3 boxes according to their colours. The number of blue marbles is twice the number of red marbles, and the number of green marbles is less than the number of blue marbles. The number of marbles in each box is less than 200. The number of marbles in each box is divisible by both 6 and 5. How many green marbles were there? MG08P40 2009 6. There are three bulbs in a shop. One lights up every 4 minutes, another bulb lights up every 8 minutes and the third bulb lights up every 11 minutes. All the bulbs light up together when Ali walked into the shop. How many times will he see at least 2 bulbs 𝟑
light up together if he was in the shop for hour? SC09S13 𝟒
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2010 7. Once a computer program is executed, 3 chipmunks will appear on the screen. One minute later, the 3 chipmunks will yawn at the same time. After that, Chipmunk Alwin will yawn at intervals of 60 seconds, Chipmunk Simmon will yawn at intervals of 75 seconds and Chipmunk Tadore will yawn at intervals of 100 seconds. When the 3 chipmunks yawned at the same time for the third time, how many minutes has the program been running? NY10P02 2011 8. Mrs Ronald has 3 sacks of coffee beans weighing 56 kg, 96 kg and 120 kg. She wants to repack all the coffee beans into smaller packets of equal mass. Without mixing the coffee beans from the three sacks and without any leftover or wastage, (a) what is the greatest possible mass of each packet? (b) How many packets of coffee beans will she get in all? SN11C06 9. There are two metal bars of length 72 cm and 96 cm. Short bars of equal length are cut from the two metal bars without any remainders. What is the largest possible length of each short bar? NH11P04 10. One side of a garden was double-fenced. The outer fencing had 3 wooden spokes along a length of 0.4 m and the inner fencing had 9 metal spokes along a length of 180 cm as shown in the diagram below.
There were 198 more wooden than metal spokes. How many wooden and metal spokes were there altogether? HP11P11
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PSLE Math Series
Unit 1.5 Whole Numbers Bonus/Free Concept
2007 1. Mr Lim earned $3 for each gift hamper he sold. For every 12 hampers sold, he earned an extra $5. (a) How much money would Mr Lim earn if he sold 85 hampers? (b) How many hampers must he sell in order to earn $194? NY07C43 2. Wendy bought CDs at $3 each and sold them at $8 each. To promote sales, all customers who bought two CDs were given one free CD. After she had sold all the CDs, Wendy made a gain of $1235 despite giving away 150 CDs to her customers. How many of Wendy's customers bought only one CD? HP07S48 3. Mrs Durai wants to buy bookmarks for 3 classes of pupils. There are 35 pupils in each class. For every 4 bookmarks she buys, she gets another one free. (a) How many bookmarks does she need if each pupil gets 1 bookmark? (b) 4 bookmarks cost $2. What is the least amount she needs to pay? PC07P(1)37 2008 4. John is paid $3 for every file he sells. He receives a bonus of $20 for every 75 files he sells. How many files must he sell to earn $1249? RG08S38 2009 5. For every 200 books Johnson sells, he earns $8. He will receive an additional bonus of $20 for every 3000 books sold. How many books must he sell to earn $700? AT09C14 6. John earns a commission of $2.20 for every magazine he sells. He also receives an additional bonus of $5 for every dozen magazines he sells. How many magazines must he sell to earn $325? SN09C16 2010 7. One box of greeting cards costs $3.75. Mandy needs 120 boxes of such cards. For every 4 boxes of cards she buys, she gets 1 box free of charge. How much does Mandy have to pay for 120 boxes of such cards? SN10S10
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8. A shopkeeper sells a packet of 10 candies for $4. He gives away 2 free candies for every 2 packets of candies purchased. Diana needs 131 candies for her birthday party. What is the least amount of money that she has to pay? NH10P09 9. Mr Lim bought 320 doughnuts for a party at a shop with the following promotions:
What was the least amount of money that Mr Lim could have paid for the doughnuts? NY10P07
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PSLE Math Series
Unit 1.6 Whole Numbers Equal Interval
2007 1. Mr Lim planted some cherry trees in a circle with the same distance apart. The distance between the first and the fourth tree was 60 m. (a) Find the distance between the first and the tenth tree. (b) If 50 trees were planted and Mr Lim tied a rope to fence up the area, find the length of the rope needed. PH07C48
2. Emily had a rod. She marked it in three different ways. First, she marked the rod into ten equal parts. Without erasing the first set of markings, she then marked the rod into 12 equal parts. Finally, she added another set of markings by marking the rod into 15 equal parts. If she cut the rod according to the markings she had made, how many parts would she get? PH07S48 2008 3. There were 9 chairs in each row. 8 rows of chairs were rearranged, equally spaced, to form the perimeter of a square. There were same numbers of chairs on each side of the square. How many chairs were there on each side of the square? SC08P43 2009 4. Jason planted 20 mango trees in a row at equal distance apart. The distance between the first and the fifth tree was 28.4 m. Find the distance between the first and the last tree. HP09S06
2010 5. The Tampines Expressway (TPE) measures 13 892 metres long. Trees were planted from the beginning to the end along the expressway at an equal distance of 4 m apart. How many trees were planted along the expressway? (Assume the width of the tree is insignificant.) RY10P05
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6. Mary arranged some round buttons in a straight line at equal intervals. The distance between the centre of the 1 st button and the centre of the 4 th button was 24 cm. What was the distance between the centre of the 1 st and the centre of the 40 th button? NH10P03
7. 125 sticks are placed at equal distance apart along one side of a straight road. The distance between the first stick and the last stick is 1550 m. What is the distance between the 4th and 8th stick? RS10P02
2011 8. One part of a car wheel was stained with paint of its surface. The diagram below showed the tyre marks made by the car wheel when the vehicle moved through a certain distance. Find the circumference of the car wheel. RG11P14a
9. It takes Mr. Adams 20 minutes to saw a pole into 5 equal pieces. How many minutes would it take him to saw another similar pole into 10 equal pieces? HK11P02 10. 35 pupil leaders from a primary school were asked to welcome visitors during the school's opening ceremony. They were stationed in a row from one end of the school's entrance to the other end at an equal spacing of 1.3 m apart. On the day of the opening ceremony, 8 pupils did not turn up. As a result, the remaining pupil leaders were restationed at a new equal spacing. What was the new spacing between 2 pupil leaders? RY11S13 11. In a hall, there are 16 rows of 19 chairs each. Mr Wong wishes to rearrange these chairs into a square with the same number of chairs on each side. There are no chairs inside the square. How many chairs will there be on each side of the square? AC11P13
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PSLE Math Series
Unit 1.7 Whole Numbers Guess & Check
2007 1. There are 30 problem sums in a test. 4 marks are given for each correct answer and 1 mark will be deducted for each incorrect answer. Joshua obtained 85 marks. How many problem sums did he answer incorrectly? AC07S39 2. There were 20 questions in a Mathematics Quiz. 5 marks were given for each correct answer. 2 marks were deducted for each wrong answer. Cindy answered all the questions and scored 65 marks. How many questions did she answer correctly? NH07S43 3. There were 10 word problems in a Mathematics Competition. 5 points were awarded for each correct answer and 3 points were deducted for each incorrect answer. If Amy answered all 10 word problems and scored 26 points, how many word problems did she answer correctly? NH07P39 4. Mrs Samy made a deal with her son, Raju, that for every night he spent reading, he would get 2 stickers. For every night that he did not read, he would give her back 1 sticker. The deal lasted 30 days and Raju collected 24 stickers in all. How many nights did Raju spend reading? NY07P41 5. Debra played a computer game in which she fired rockets at planes. For every rocket that hits an enemy plane, she gets 7 points. For every rocket that hits one of her own planes, she loses 2 points. When a rocket does not hit any plane, she does not get or lose any point. Debra fired 392 rockets. 65 of them did not hit any plane. At the end of the game, she scored a total of 1650 points. How many enemy planes did she hit? PC07P(2)45 6. In Semester One, Kelly earned a total of 150 silver and gold stars. Ali earned 55 silver stars and 15 gold stars. Each silver star was worth 3 points. Each gold star was worth 5 points each. Kelly scored 390 more points than him. (a) How many points did Kelly score? (b) How many silver stars did Kelly earn? RY07C45 7. A boy bought 20 stamps. Some were 50-cent stamps and some were 40-cent stamps. The cost of the 50-cent stamps was $4.60 more than the 40-cent stamps. How many 50-cent stamps did he buy? NH07C37
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8. There are 60 shirts and pants in a stall. Each shirt costs $9 and each pair of pants costs $7. If the total cost of the shirts is $188 more than the total cost of the pants, how many shirts are there in the stall? RY07S41 2008 9. A salesman delivered 30 vases to his customers. On the way, he had a minor accident and broke some of the vases. For every unbroken vase delivered, the salesman was paid $40. As a penalty, he had to pay the customer $10 for every broken vase. In the end, the salesman earned $1000 for the sale of the vases. How many vases were not broken? NH08S43 10. Mr Loo had to deliver 800 hampers in May. He received $4 for every hamper that was delivered successfully and $7 would be deducted from his salary for every hamper that was damaged. If his salary in May was $2430, how many hampers did Mr Loo deliver successfully? NY08S43 11. A small egg cost 10₵ while a large egg cost 5₵ more. Mrs Lee paid $6.70 for 50 eggs. How many large eggs did she buy? MB08S39 12. Ann bought 10 magazines from the news stand. She paid $5 each for some of the magazines and $7 each for the rest. If Ann spent $56 altogether, how many magazines cost $5? MG08S42 13. A baker puts cupcakes into boxes of two different sizes. 5 cupcakes fill one small box while 12 cupcakes fill one big box. If the baker has 99 cupcakes, how many boxes of each size does he need to contain all the cupcakes with no leftover? AT08S36 2009 14. Wei Qing played with Ravi in a game of chess for twelve rounds. In each round, the winner scored 5 points while the loser scored 2 points. At the end of the game, Ravi’s total score was 45 points. How many rounds did Wei Qing win? HP09P09 15. The table below shows the scoring system at a basketball tournament. A team is awarded 5 points for a win, 2 points for a draw and no point for a loss. Win Draw Loss 5 points 2 points 0 point At the end of the tournament, Team Alpha played a total of 36 matches (won, drew or lost) and accumulated 120 points. How many matches did Team Alpha win if they had lost 9 matches? RS09P18
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16. Jeneen sat for a quiz that had 70 questions. 3 marks were awarded for each correct answer and 1 mark was deducted for each wrong answer. Jeneen answered all the questions and scored 146 marks for the quiz. How many questions did he answer correctly? SC09S08 17. Mr Lim paid $134.40 for some jackfruits and pomeloes. The cost of the pomelo was 0.8 that of a jackfruit. A pomelo cost $5.60. If all the pomeloes cost $22.40 more than the jackfruits, how many fruits did he buy? NY09C14 2010 18. On a farm, there are some chickens and goats. A boy counts the animals and finds that they have 220 eyes and 360 legs. What fraction of the total animals are goats? NH10C14 19. Grandpa had a farm. He kept 89 goats and chickens. The total number of legs the animals had was 264 legs. How many chickens did Grandpa have? RG10P07 20. In an online quiz, 30 points are awarded for every correct answer. For each wrong answer, 10 points are deducted. Muthu was awarded 2570 points after answering 103 questions. (a) How many points will be awarded if all 103 questions are answered correctly? (b) How many questions did Muthu answer wrongly? PC10P07 21. Joanne had a total of 36 wires and strings. Each wire is 4 cm long and each string is 3 cm long. The total length of the wires is 25 cm longer than the total length of the strings. How many more wires than strings did she have? AT10C13 2011 22. A test consists of 25 questions. A correct answer is worth 4 marks. An incorrect answer will result in a deduction of 2 marks. Li Meng scored 70marks. How many questions did Li Meng answer incorrectly? MGS11P01 23. A farm has some ducks and cows. The ratio of the number of animals to the total number of legs is 8 : 23. Express the number of ducks as a fraction of the cows. Give your answer in the simplest form. NH11C15 24. In a game, you will score 200 points if you win but will have 150 points deducted if you lose. Muthu played 10 games and scored 950 points. How many games did he lose? TN11S08
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25. Letchmi attempted all the 70 questions in an online game and scored 224 marks. Given that 5 marks were awarded for each correct answer but 2 marks were deducted for each wrong answer, how many questions did Letchmi answer correctly? RY11S06 26. David bought 120 purple and green pencil cases. Each green pencil case cost $2.50 and each purple pencil case cost $1.75 each. If the total cost of the pencil cases was $246, how many green pencil cases did he buy? MG11S10
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PSLE Math Series
Unit 1.8 Whole Numbers Unit/Model Method
2007 1. Shirley paid $120 for 8 bags and 6 T-shirts. Each bag cost 3 times as much as a T-shirt. Find the difference in price between a bag and a T-shirt. NH07C36 2. Baker Tan and Baker Lim bought the same number of eggs. Baker Tan used 240 eggs and Baker Lim used 165 eggs. After that, Baker Lim had four times as many eggs as Baker Tan. How many eggs did each of them have at first? PH07C43 3. Anne and Sally had 1436 beads altogether. After receiving 376 beads from Anne, Sally had thrice as many beads as Anne. How many beads did Sally have at first? RY07C39 4. Deming had $100 more than Ali at first. After Deming spent $120 and Ali received $200, Ali had 3 times as much money as Deming. How much did Deming have at firs t? AT07S37 5. The total mass of three boxes X, Y and Z is 16 kg. X is 0.7 kg heavier than Y and 0.25 kg heavier than Z. (a) How much heavier is Z than Y? (b) What is Y’s mass? AT07S38 6. Alan and Benny had equal number of stamps. Alan lost 36 of his stamps. Then Benny had 5 times as many stamps as Alan. How many stamps had Alan at first? NH07S36 7. Alex has $1.50 more money than Betty, and three times as much money as Colin. The 3 of them have $9.70 altogether. How much does Colin have? AC07P41 8. When Mrs Lee was 40 years old, her son was twice her daughter’s age. Mrs Lee will be twice her son’s age when her daughter is 28 years old. How old will Mrs Lee be when her daughter is 20 years old? SC07P45 2008 9. Each pen cost $1.50 more than each eraser. Each file cost $2.40 more than each pen. Hassan bought 2 of each item and paid $14.40. How much did he pay for each file? MB08C38
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10. Mandy, Nancy and Oliver have a total height of 5.08 m. Nancy is 7 cm taller than Mandy. Oliver is 0.21 m taller than Mandy. Find the height of Oliver. AT08C41 11. There are 1928 red and green buttons in a box. The number of red buttons is 246 fewer than the number of green buttons. How many green buttons are there? HK08P36 12. The total cost of a chicken pie is thrice the cost of a muffin. Mrs Seetho paid a total of $40 for 20 muffins and 10 chicken pies. Find the cost of a chicken pie. NY08C41 13. Mr Thomas bought 5 note books and 2 exercise books. Each note book cost twice as much as each exercise book. The total cost of a note book and an exercise book was $2.40. How much did Mr Thomas pay altogether? SN08C37 14. A fruit seller started his day with the same number of apples and oranges. After he sold 435 apples and 120 oranges, the number of oranges was 4 times the number of apples. What was the total number of apples and oranges at first? MB08S36 15. A box containing 3 files weighed 8.8 kg. Later, Keith added 2 more files and 2 books into the box and the mass of the box with the contents became 16 kg. If the mass of one file was 3 times the mass of a book, (a) find the mass of the book. (b) Keith could only carry up to a mass of 13 kg. What was the least number of files that he should remove from the box so that he would be able to carry the box and files? MB08S46 16. A box and 4 similar files weighed 7.6 kg. Tom added 2 more such files and 5 identical books into the box and the total weight became 14.2 kg. Each file weighed 3 times as much as a book. (a) What was the weight of the empty box in kg? (b) If Tom could only lift 12 kg, what was the least number of files that he should remove from the box so that he could lift the box and its contents? AC08P42 17. Matthew, Neena and Osman shared $157. Matthew had $8 less than Neena and Osman had three times as much as Neena. How much did Osman have? MG08S39 18. Mother bought a total of 12 books and files for $93. She bought 2 more books than files. A book cost $3 more than a file. How much did she pay for the files? SC08P38
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19. An equal number of men and women turned up for an audition. After 74 men and thrice as many women were rejected, the number of men was 5 times that of the women. How many people turned up for the audition? SN08P39 2009 20. 12 athletes ran a total of 21600 m. Each male athlete ran 300 m more than each female athlete. There were 4 more male athletes than female athletes. What was the total distance ran by the male athletes? RY09C18 21. Alex, Ben and David went for a run but none of them completed the run. Ben ran 5 times as far as Alex before he stopped. David stopped 1 km before the finishing line and he ran 3 km less than twice the distance Ben ran. The three of them ran 21 km. How long was the run? RG09S12 22. Alice, Beth and Claire had 600 stamps altogether. After Beth had given 30 stamps to Alice, Beth had twice as many stamps as Claire and Alice had 20 stamps more than Claire. How many stamps did Claire have? RG09P06 23. The mass of a box containing 3 files was 10.2 kg. Later, Ali added 2 more files and 3 books into the box and the mass of the box and its contents became 19 kg. If the mass of one file was four times the mass of a book, find the mass of the box when empty (leave your answer in kg). HP09S10 24. Jason had $78 and Ben had $25. After Jason and Ben spent $53 altogether on some games, Jason had 3 times as much money as Ben. How much did Ben spend on the games? RG09S08 25. At present, Ronald is 3 times as old as his sister. In 22 years’ time, Ronald’s age will be 19 years less than twice his sister’s age. How old is Ronald now? HP09S08 3
26. Mrs Sim bought 15 handbags for $267.30. of these handbags cost the same price. Each 5
of the remaining handbags cost 3 times as much. Find the difference in the price of the 2 types of handbags. HP09P07 2010 27. At first, Joe had $177 and Chris had $129. Each of them bought a pair of jeans and a shirt at the same price. The shirt cost three times as much as the jeans. In the end, Joe had 3 times as much money as Chris. What was the cost of the shirt? AC10P07
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28. A company paid a total of $23 600 in salaries to 17 female and some male employees. Each male employee received $500 more than each female employee. There were 14 more female employees than male employees. Find the difference in the total amount of money received by the male employees and the female employees. AT10C18 29. In a fun fair, Matthew and John sold 368 balloons. John and Keith sold 112 balloons altogether. Matthew sold 9 times as many balloons as Keith. How many balloons did the three boys sell altogether? RY10C10 30. Casey and Sherman went to the Information Technology Fair with the same amount of money each. Casey spent $900 on a computer while Sherman spent $300 on a printer. After that, Sherman had thrice as much as money as Casey. How much money did each of them bring to the Information Technology Fair? AT10S06 31. At a sale, Lydia paid $350.40 for 3 blouses, a pair of pants and 3 T-shirts. A blouse cost 1
twice as much as a T-shirt and a pair of pants cost 1 times as much as a blouse. How 2
much money would Lydia have saved if she were to buy 2 blouses, a pair of pants and a T-shirt instead? SN10S12 2011 32. There were 76 more apples than oranges in a fruit stall. After 68 apples and 227 oranges were sold, the number of apples left was 6 times that of the number of oranges left. What was the total number of apples and oranges at the fruit stall at the start? HP11P06 33. Minah paid $2 more for a chocolate cookie than a strawberry cookie. She paid $17 for 4 chocolate cookies and 2 strawberry cookies. How much did she pay for a strawberry cookie? TN11S06 34. A jacket cost 4 times as much as a skirt. The skirt cost $12.60 more than a shawl. If Susie paid $171 for these 3 items, how much did the shawl cost? AC11S02 35. Alan and Dave spent a total of $462. Dave and Martin spent $288 altogether. Alan spent thrice as much as Martin. How much did Dave spend? TN11S10 36. In a game, Parisse scored 240 more points than Max at first. After Parisse lost 332 points to her friend, Fendi, Max had 3 times as many points as Parisse. How many points did Parisse have at first? SN11S08
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37. Rubber hose X is 3.5 m longer then Rubber hose Y. Rubber hose Z is 8.74 m shorter than Rubber hose X. The total length of the three hoses is 168.66 m. Mr Garden buys Rubber hose Y at 40⊄ per metre. How much must he pay for Rubber hose Y? SN11C03 38. There were a total of 4540 passengers onboard 4 ships, labelled A, B, C and D. All the ships were travelling on different sea routes. Ship A had the most number of passengers onboard and Ship D had the least. The difference in the number of passengers onboard Ship A and the other three ships was 139, 363 and 618. (a) How many passengers were on board Ship D? (b) Each ship was required to load sufficient lifeboats to carry all its passengers onboard in case of emergency. Each lifeboat could take up to 30 passengers. Find the total minimum number of lifeboats to be loaded on Ship A and Ship D. NY11S16 39. A confectionery factory baked a total of 3 123 cupcakes in 4 different flavours, Strawberry, Chocolate, Vanilla and Blackforest. The Blackforest flavour was the most popular and Vanilla was the least popular flavour with a difference of 528. The difference in the number of cupcakes between Strawberry flavour and
Blackforest flavour was 351. The difference in the number of cupcakes
between the Chocolate flavour and Blackforest flavour was 190. (a) How many Blackforest-flavour cupcakes were baked? (b) The cupcakes were packed into boxes for delivery. Each box can hold up to 20 cupcakes. What is the minimum number of boxes needed to pack all the Strawberry-flavour and Vanilla-flavour cupcakes? RY11P13 40. Mary and Ben took 49 hours to complete their Science project. They worked separately on their own project. If Mary had worked 5 hours less and Ben had worked 6 hours more, Mary would have put in 2 hours more than Ben. How many hours did Mary put in for the Science project? RG11S13
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PSLE Math Series
Unit 1.9 Whole Numbers Before-After Difference
2007 1. Andrew has 70 more stamps than Basil. If Basil gives Andrew 40 stamps, the number of stamps Andrew has will be 6 times that of Basil’s. (a) How many stamps does Andrew have? (b) How many stamps does Basil have? AC07S42 2. In a Mathematics Test, the number of passes is 164 more than the number of failures. If 6 more pupils passed the test, the number of passes will be 9 times the number of failures. Find the total number of pupils who took the test. SC07S37 3. There were 30 more members in the IT club than in the Art Club. 15 members left the Art Club for the IT club. It was then found that the number of members in the IT club was 5 times as many as the number of members in the Art Club. How many members were there in both clubs altogether? HP07P40 2008 4. Amy, Beth and Carrie have some money. If Amy gives $3.50 to Beth, the two girls will have an equal amount of money. If Beth gives $3.50 to Amy, Amy will have thrice as much money as Beth. Carrie’s share is the sum of the other two girls. How much money do they have altogether? NH08P44 2009 5. Container A has 150 more marbles than Container B. If 30 marbles are being transferred from Container B to Container A, there will be thrice as many marbles in Container A as Container B. How many marbles are there in Container A in the beginning? AC09P11 6. Cathy has 1250 more stamps than John. After John gave Cathy 68 stamps, she had 4 times as many stamps as John. How many stamps did John have at first? PL09P07
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2010 7. Ashley has 120 more stamps than Brandon. If Brandon gives 25 stamps to Ashley, the ratio of the number of stamps he has to the number of stamps Ashley has will be 3 : 5. How many stamps do they have altogether? RV10P02 8. Xavier, Yati and Zul each had a certain number of stamps. At first, Yati had 200 stamps 𝟑
𝟏
𝟒
𝟖
more than Xavier and Zul had the number of stamps Yati had. After Yati gave away of her stamps to Xavier, she had 60 fewer stamps than Xavier. What was the ratio of the number of stamps Xavier had to the number of stamps Yati had to the number of stamps Zul had at first? Give your answer in the simplest form. RY10P18 2011
9. Bee Leng had $960 less than Kerri. After Bee Leng gave $2400 to Kerri, the ratio of Bee Leng’s money to to Kerri’s money became 1 : 3. How much did BeeLeng have in the end? AT11C01 10. Valerie has 1764 more stickers than Mark. After Mark gave Valerie 128 stickers, she had five times as many stickers as Mark. How many stickers did Mark have at first? RY11C09 11. Velu and Rosie had some stamps. If Velu gave Rosie 52 stamps, she would have the same number of stamps as Rosie, If Rosie gave Velu 34 stamps, the ratio of the number of stamps Rosie had to the number of stamps Velu had will be 3 : 7. How many stamps did Velu have at first? RY11P06 12. Packet A, Packet B and Packet C each contained some salt. At first, there were 200g 𝟑
more salt in Packet A than Packet B. Packet C had of the amount of salt in Packet A. 𝟒
𝟏
After of the amount of salt in Packet A was transferred to Packet B, there was 82.15g 𝟖
of salt in Packet B. How many percent less salt were there in Packet C than Packet A at first? NY11P17 13. Eugene, Freddy and George had some playing cards. Freddy had 200 more playing 𝟑
𝟏
𝟒
𝟔
cards than Eugene. George had the number of cards Freddy had. After George lost
of his cards to Eugene, he had 320 fewer cards than Eugene. What was the ratio of the number of cards Eugene had to the number of cards Freddy had to the number of cards George had in the end? RS11P15
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PSLE Math Series
2.1 2.2 2.3 2.4 2.5 2.6
Unit 2 Patterns
Multiple and Constant Square Numbers Triangle Numbers Sum of Numbers Number Puzzles Number Patterns
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Unit 2.1 Patterns Multiple and Constant
PSLE Math Series
2007 1. The figure below shows the number of toothpicks used to form different number of triangles. Study it carefully and answer the following questions:
(a) Complete the following table: Number of triangles 1 Number of toothpicks
3
2
3
4
5
6
…
10
5
7
9
11
(i)____
…
(ii) ____
(b) How many toothpicks are needed to form 100 triangles? (c) How many triangles can you form with 101 toothpicks? AC07S48 2. Look at the patterns shown below. They are made up of 2-cm coloured and plain tiles.
Complete Pattern 5 in the table below. Pattern Number of coloured tiles 1 8 2 12 3 16 5 (a)
Total area of coloured tiles 32 cm2 48 cm2 64 cm2 (b)
(c) Which pattern number will have 176 cm2 as the total area of coloured tiles? HP07S37
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3. In the following figures, the area of the biggest equilateral triangle is 64 cm 2 as shown in Figure 1. A new triangle is formed by connecting the midpoints of the sides of the previous triangle. If the pattern continues, find the area of the smallest triangle in Figure 4. HP07P41
4. Study the following sequence of patterns consisting of triangles and circles. The first three patterns are shown below.
(a) Complete the table below. Pattern 1 Number of triangles 1 Number of circles 4
2 2 6
3 3 (
)
4 4 10
5 5 12
6 6 (
)
7 7 16
(b) How many circles are there in the Pattern 15? (c) Find the number of triangles in a pattern which has 40 circles.NH07C46
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5. Chun Ying used 2-cm square tiles to make rectangles as shown below.
The table shows the number of tiles used for each pattern. Pattern Number of tiles 1 2 2 8 3 18 4 5 (a) Complete the table above for Pattern 4 and Pattern 5. (b) The length of the rectangle of a certain pattern is made up of 50 tiles. Find the perimeter of this rectangle. (c) What is the area of the rectangle formed in Pattern 96? PC07P(2)48
6. The patterns below consist of shaded and unshaded rectangles. Study the patterns carefully before answering the following questions.
(a) What is the total number of rectangles in Pattern 10? (b) If the pattern has 127 rectangles, how many unshaded rectangles are there? RG07S38
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7. The figures below are made up of squares and triangles formed by lines. Study the table below carefully and then answer the questions that follow.
Figure 1 Figure Number of lines
Figure 2
Figure 3 1 9
2 17
3 25
Figure 4 4 33
5 (a)
…
20 (b)
(a) How many lines are there in Figure 5? (b) How many lines are there in Figure 20? (c) How many lines would there be in the figure that has 150 squares? RG07P42
8. The shapes in the table are made up of 1-cm squares. Study the pattern carefully and answer the questions that follow.
2
Area (cm ) Perimeter (cm)
Shape 1 5 12
Shape 2 9 20
Shape 3 13 28
(a) What is the perimeter of Shape 15? (b) What is the area of the shape when its perimeter is 172 cm? SC07P42
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2008 9. To pin up 1 poster on the board, 4 pins are required. To pin up 2 posters, 6 pins are needed.
(a) How many pins are needed to pin up 50 posters? (b) How many posters are pinned up if Mary uses 86 pins? RG08S43
10. The pattern below is made up of circles and sticks.
Fig. 1 (a) Complete the following table. Figure Number 1 2 3 4 (i) 100
Fig. 2
Number of circles 1 2 3 4 10 100
Fig. 3
Number of sticks 4 6 8 10 22 (ii)
(b) How many circles are needed to complete a pattern if the number of sticks used is 502? AC08S46
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11. Study the series of figures below and answer the questions that follow.
(a) How many dots will there be in Figure 5? (b) How many dots will there be in Figure 31? (c) Which figure will have 221 dots? NY08S48
12. Some 1 cm squares are arranged in the following pattern as shown in the table. (Diagrams are not drawn to scale) (a) Study the pattern carefully and complete the table. Pattern Figure Number of Perimeter squares (cm) 1
1
2
2
3
3
4
4
. . .
. . .
10
4
(
8
(
. . . (
)
) . . .
)
(
)
(b) How many squares are needed to form a figure with a perimeter of 142 cm? NH08S45
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13. The figure is made up of identical triangles.
(a) Following this pattern, how many triangles will there be in the 5 th layer and 10th layer? (b) If each small triangle has a base of 3 cm and a perpendicular height of 4 cm, find the area of all the triangles in the 30 th layer. HK08P45
2009 14. The shapes in the table are made up of circles, triangles and straight lines. Study the pattern carefully and answer the questions that follow.
Pattern number Number of triangles Number of straight lines
1 4 4
2 6 7
3 8 10
… … …
25
100 202
76
(a) How many triangles are needed to form the shape in Pattern 25? (b) Which pattern has a shape that is made up of 109 straight lines? SC09P10
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15. Each of the figures in the table below is made up of 3-cm squares. Study the pattern carefully and answer (a) and (b).
Area (cm2) Perimeter (cm)
Figure 1
Figure 2
Figure 3
45
81
117
36
60
84
(a) What is the area of Figure 9? (b) Find the perimeter of the figure which has an area of 405 cm 2. SN09P14
16. The diagrams below show tiling patterns. Each tile is a square of side 1 cm.
Pattern Number Number of squares Perimeter (cm)
1 4 10
2 9 16
3 16 22
… … …
10 121 ?
What is the perimeter of Pattern 10? AT09C10
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17. The table below shows the number of matchsticks used to make the following patterns. Figure Pattern Number of matchsticks
1st
6
2nd
11
3rd
?
(a) How many matchsticks are needed to make the 3 rd pattern? (b) How many matchsticks are needed to make the 10 th pattern? (c) How many matchsticks are needed to make the n th pattern? RY09C12
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2010 18. A series of figures is formed by using 1-cm squares as shown in the table below. Figure Perimeter of figure Area of figure (cm) (cm2)
6
Figure 1
18
10
22
16
26
24
Figure 2
Figure 3
Figure 4 (a) Draw Figure 1 in the table above. (b) Write down the perimeter of Figure 1 in the table above. (c) Find the area of Figure 100. HK10P12
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19. Study the pattern below carefully and complete the table below.
Figure Number
1
2
3
…
1
2
3
…
4
7
10
…
5
9
13
…
8
…
(b)____
Number of rectangles Number of triangles
(a) ___
Total number of rectangles and
193
triangles (a) Find the number of triangles in Figure 8. (b) Find the Figure Number that would require a total number of 193 rectangles and triangles altogether. RY10P12
20. Observe the patterns carefully.
(a) How many dots are there in Pattern 5? (b) Which pattern in the series has 1052 dots? RG10S08
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2011 21. Each of the figures below is made up of 1-cm sticks.
The table below shows the number of sticks used for each figure and the perimeter of each figure. Figure Number Number of 1-cm sticks Perimeter (cm) 1 12 6 2 23 10 3 34 14 4 (a) Complete the table for Figure 4. (b) Which Figure Number will have a perimeter of 1298 cm? HP11P08 22. David used coins to form a series of L-shaped patterns. The first three patterns are shown below.
(a) Complete the table below. L-shaped pattern Number of coins st 1 3 nd 2 5 rd 3 7 th 4 5th 6th (b) Write down the number of coins that David would need to form the 100 th pattern? (c) A pattern is formed by 601 coins. Which pattern would it be? AC11S15
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23. The sequence of patterns is formed with squares. The first three patterns are shown below.
(a) How many squares are needed in Pattern 10? (b) Which pattern number contains 669 squares? CH11S13 24. Study the figures carefully. Each figure is made up of sticks, circles and triangles.
(a) How many circles will there be in Figure 38? (b) In which figure will there be in 123 triangles? (c) How many sticks will be needed to form Figure 150? SN11C18
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25. Jake used sticks to form cubes and arranged them to form a pattern as shown below. How many sticks are required to form Figure 5? Which figure will require a total of 145 sticks to form?
Figure 1 2 3 4 5
Number of cubes 1 2 3 4 5
Number of sticks 12 20 28 33 (a) __________
(a) How many sticks are required to form Figure 5? (b) Which Figure will require a total of 145 sticks to form? AT11S13 26. The following figures are made up of sticks. Look at the figures below and answer the following questions.
Figure number
Number of sticks
1 2 3 4
9 14 19
Number of rectangular faces 3 5 7
(a) Complete the table for figure 4. (b) Which figure is formed using 219 sticks? CH11P13
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27. Each pattern in the sequence below is made up of square tiles. Look at the patterns below and answer the following questions.
(a) How many square tiles are there in the 25 th pattern? (b) In which pattern would 399 square tiles be used? RS11S14 28. The rhombuses below are formed by using matchsticks. Each rhombus has an equal number of matchsticks on its sides.
(a) Complete the following table. Pattern Number of matchsticks
1
2
3
4
5
30
4
12
20
( )
( )
( )
(b) Which pattern number will you get if 1004 matchsticks are used? RY11S18
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Unit 2.2 Patterns Square Numbers
PSLE Math Series 2007
1. Look at the patterns below. They are made up of shaded and plain tiles.
(a) Complete Pattern 4 in the table. Pattern Number of shaded tiles Number of plain tiles 1 8 1 2 12 4 3 16 9 4 (b) What is the total number of shaded and plain tiles in Pattern 9? AT07S44 2. Study the patterns formed by black and white tiles below and answer the following questions.
(a) Using the series of patterns above, complete the table below. Pattern No. of Black Tiles No. of White Tiles Total No. of Tiles 1 3 1 4 2 6 3 9 3 9 7 16 4 12 13 25 5 (b) Find the total number of tiles in Pattern 10. NH07P47 pslemathseries.com
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3. The figure below shows a multi-level pyramid. Each level is formed by identical small triangles.
(a) How many small triangles are needed to form Level 6? (b) If 1137 small triangles are needed to form a particular level, which level would that be? (c) What is the total number of small triangles that are needed to build a 25-level pyramid? NY07C46 2008 4. Nathan saved one 20-cent coin on the first day. The next day he put aside two more 20cent coins as his savings. Each day, he saved two 20-cent coins more than the previous day. (a) Complete the following table. Day Number of coins saved each day
Total number of coins
1
1
1
2
3
4
3 4 5 6
(b) How many days did Nathan take to save 121 coins? SC08S42
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5. Matthew put aside one 20-cent coin as his savings on the first day. The next day, he put aside three 20-cent coins as his savings. Each day he put aside two 20-cent coins more than the previous day. (a) Complete the table below. Day Number of coins saved each day
Total number of coins
1
1
1
2
3
4
3
5
9
4 5
(b) How many 20-cent coins did Matthew save by the 25 th day? (c) When Matthew had saved 121 coins altogether, what day would it be? NH08P47
2009 6. Study the patterns formed by black and white tiles below and answer the following questions.
(a) Using the series of patterns above, complete the table below. Pattern 1 2 3 4 5
No of Black Tiles 3 6 9 12 15
No of White Tiles 1 3 7 13
Total No. of Tiles 4 9 16 25 36
(b) Find the total number of tiles in Pattern 110. (c) In which pattern will there be 9313 white tiles? SN09C18
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7. Study the pattern below. Line 1 2 3 4 5 … (c)
(a) (b) (c) (d)
Numbers 1 1+3 1+3+5 1+3+5+7 (a) _________________
Sum 1 4 9 16 (b)
…
6400
Write down number sequence for the 5th line in the box above. Write down the sum of all the numbers in the 5 th line in the box above. Which line has a sum of 6400? The sum of all the numbers on two consecutive lines is 221. Which are the two lines? NH09C18
8. Ashley used dots and sticks to make the following pattern below. Complete the table. Pattern Number
Number of Dots
Pattern 1
4
Pattern 2
9
16 Pattern 3 Pattern 4
(a)
Pattern 128
(b)
(c) If Ashley counted 256 dots in her final pattern, which pattern number had she made? AT09S13
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9. The figures below are made up of coloured dots. Look at the figures below and answer the following questions.
Figure 1
Figure 2
Figure 3
(a) Calculate the number of dots in figure 4. (b) Calculate the number of dots in figure 20. (c) Which figure contains 1123 coloured dots? CH09P14 2010 10. The following figures are made of ovals.
Figure Number of ovals 1 1 2 5 3 13 4 25 5 (a) Complete the table above for Figure 5. (b) How many ovals will there be in Figure 87? (c) Which figure will have 5305 ovals? PC10P18
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11. The following figures are made up of dots. Look at the figures below and answer the following questions.
Figure Number Number of dots
1 3
2 7
3 13
4 21
(a) How many dots are there in the Figure 50? (b) In which figure can 651 dots be found? CH10P12
12. The following figures are made up of small squares and dots. Look at the figures below and answer the following questions.
Figure 1
Figure 2
Figure 3
Figure Number
Number of small squares 1 4 9
Number of dots
1 2 3
4 9 16
(a) Calculate the number of small squares for figure 4. (b) Calculate the number of dots for figure 10. (c) Which figure contains 256 dots? CH10S18
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2011 13. The sequence of figures below is made up of 2-cm cubes.
Study the patterns carefully and answer questions (a), (b) and (c).
(a) How many 2-cm cubes are there in Figure 5? Write your answer in the table below. Figure No. of 2-cm cubes No. of layers of cubes 1 1 1 2 5 2 3 14 3 4 30 4 5 5 (b) What is the total volume of the cubes in Figure 3? (c) Given that a figure has 285 cubes, how many layers of cubes will there be? NY11S14 14. The pattern below is made up of circles and triangles. Study the pattern carefully and answer the questions below.
(a) How many circles are needed to form pattern 5? (b) How many triangles are needed to form pattern 10? (c) The number of circles used in Pattern X is exactly the same number of triangles used to form Pattern 32. What is X? RG11P10
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15. Study the pattern carefully and answer the questions that follow. Show your workings clearly in the space provided and write your answers in the blanks. RY11C11
Pattern Number
Number of patterned circles
Number of white circles
Total number of circles
1
1
0
1
2
5
4
9
3
9
16
25
4
13
36
49
(a) ___________
(b) ____________
7
12
(c) _____________
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pslemathseries.com 16. The series of figures below are made up of unit squares and unit triangles. In the figure below, a unit square is represented by and a unit triangle is represented by . Study the patterns carefully and answer the questions that follow.
(a) Complete the following table. Figure Number Number of Unit Squares (Shaded and Unshaded)
1 2 3 4
Total Number of Shaded Unit Squares and Shaded Unit Triangles
1 4 9
2 5 8
Total Number of Unit Squares and Unit Triangles (Shaded and Unshaded) 2 8 18
(b) Find the number of unit squares in Figure 20. (c) Find the figure that has a total of 101 shaded unit squares and shaded unit triangles. (d) Find the total number of unit squares and unit triangles in Figure 25. NH11P17
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Unit 2.3 Patterns Triangle Numbers
PSLE Math Series
2007 1. Ahmad formed the following patterns using toothpicks.
(a) How many toothpicks would Ahmad need to form Pattern 4? (b) If the last pattern formed by Ahmad had 165 toothpicks, what was the pattern number? HK07P47 2008 2. Study the pattern carefully and answer questions (a), (b) and (c).
Pattern Number of dots
1 1
2 3
3 6
4 10
(a) How many dots will Pattern 7 have? (b) Which pattern will have 120 dots? (c) How many dots will Pattern 100 have? MB08C48
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3. The patterns below start with a single square. At each stage new squares are added all around the outside.
(a) Complete the table below: Stage 1 Number of 1 squares
2 5
3 13
4 25
5
(b) How many small squares are there by the time you get to the 10th stage? (c) How many squares are there by the time you get to the 100th stage? AT08C47 4. Some beads and matchsticks are arranged in the following pattern as shown below.
(a) Complete the table to show the number of beads and matchsticks in pattern 6 and 7. Pattern
1
2
3
…
Beads
1
2
3
…
Matchsticks
2
4
6
…
6
7
(b) How many more matchsticks are there in pattern 99 than in pattern 88? (c) Find the total number of matchsticks needed to form pattern 1 to pattern 50. SN08C48
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2009 5. The series of figures below are made of cubes. Study the diagram below and answer the following questions.
Figure 1 2 3
Number of cubes 1 4 10
(a) How many cubes will there be in Figure 6? (b) Which figure will have 120 cubes? NY09S15 6. The diagram below shows a series of patterns formed using some tiles
Figure 1
Figure Number of Tiles
Figure 2
1 1
2 3
.
Figure 3
3 6
… …
(a) How many tiles were used to form Figure 6? (b) How many more tiles were used to form Figure 10 than Figure 6? (c) Which figure was formed with 171 tiles? NY09P15
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7. (a) Study the pattern below carefully and complete the table below by filling in the brackets:
Pattern 1
Number of points, N 1
Number of lines, L 0
Pattern 2
2
1
Pattern 3
3
3
Pattern 4
4
6
Pattern 5
5
10
Pattern 6 Pattern … Pattern 10 Pattern … Pattern 12
6 …. 10 …. (
(
) ….
( )
) …. 66
(b) Which 2 patterns have a difference of 25 number of lines (L)? NH09S15
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8. The diagram below shows the seating arrangement in an auditorium. The rest of the seats follow the same pattern. The black boxes represent the space between the seats. Row 1 1 Row 2 2 3 Row 3 4 5 6 Row 4 7 8 9 10 Study the above pattern carefully and answer all the questions that follow. (a) How many seats are there in Row 10? (b) In which row can we find Seat number 28? (c) The first seat number on the left of Row 4 is 7 and the last seat number on the right is 10. If Linda is in the last seat on the right of a secret row and her seat number is 120, in which row will she be? HP09P17
9. The equilateral triangles below are formed using 2 cm sticks.
(a) How many sticks are needed to form pattern 5? (b) In which pattern will each side of the triangle measure 30 cm? (c) Calculate the number of shaded triangles in Pattern 100. RG09P15
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10. Observe the pattern below. Each new stage is constructed by drawing squares around the sides of the squares in the previous stage.
(a) Complete the figure for Stage 5. (b) Fill in the blanks in the table below. Write your answer in the space provided. RY09P12 Stage Number 1 2 3 4 5 … 10
No. of squares in the middle row 1 3 5 7 9 … (ii)
No. of squares added 0 4 8 12 (i) … 36
Total number of squares 1 5 13 25 41 … (iii)
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2011 11. The sequence of the figures below formed by unit squares. Study the patterns carefully and answer questions (a), (b) and (c).
(a) How many unit squares are there in Figure 5? Write your answer in the table below. Figure No. of unit squares 1 3 2 6 3 10 … … 5 (b) Which figure has a total of 36 unit squares? (c) How many unit squares are there in Figure 50? NY11C15 12. The pattern below is made up of hexagons and dots. Look at the pattern and answer the following questions.
(a) How many hexagons are required to build Figure 9? (b) How many dots will be needed to build Figure 6? (c) Which figure will need 108 dots to build? TN11S18
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PSLE Math Series
Unit 2.4 Patterns Sum of Numbers
2007 1. In a hall, there are rows of chairs. The first row has one chair fewer than the second row. The second row has one chair fewer than the third row. This pattern carries on and there are 40 chairs in the 25 th row. How many chairs are there in the first row? PH07C41 2. Mr Koh sold some peaches on Saturday. For each day from Sunday to Friday, he sold 15 peaches fewer than the day before. He sold a total of 595 peaches. How many peaches did he sell on Saturday? SC07S42 3. Fara started collecting stamps in January. In each month from February to May, she collected 30 stamps more than the month before. She saved a total of 750 stamps from January to May. How many stamps did she collect in January? AC07P40 4. A toy robot is programmed to travel in a straight line and to stop after moving a certain distance in the pattern as shown below:
(a) How far is the 5th stop from the 1st stop? (b) What is the distance between the 1 st stop and the 100th stop? RY07S46 2008 5. Nelly has 1000 beads. She puts them in a box with 40 holes. She puts 1 bead in the first hole, 2 beads in the second hole, 3 beads in the third hole and so on until all the 40 holes are filled with beads. How many beads are left when she has filled all the holes? SC08P45 6. Six teams compete in a netball tournament. The teams are A, B, C, D and E. Each team will play against every other team once. How many matches are there? SC08S41
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2009 7. A snail fell into a well that is 300 cm deep. In the first hour, it climbed 80 cm up the well. In the second hour, it climbed 70 cm up the well. Each hour, it managed to climb 10 cm less than the hour before. How many hours did it take to climb out of the well? AT09C09 8. Find the value of 3 + 5 + 7 + ⋯ + 21 40 + 60 + 80 + ⋯ + 360
NH09P09
9. The diagram below shows a triangle with 7, 8 and 9 at its corners. Fill in the numbers 1, 2, 3, 4, 5 and 6 such that the sum on each side adds up to 23. RY09P07
2011 10. Two marbles were released at the same time and they started to roll towards each other from the opposite ends of a straight plank that was 380 cm long. Marble A travelled 70 cm while Marble B travelled 40 cm in the first second. Both marbles travelled 5 cm less than previous distance in each subsequent second. How long did it take for the two marbles to meet? NY11C08 11. The sum of 5 consecutive numbers is 465. What is the smallest number? NH11C09 12. Kerry took an empty container and filled it with 185 mℓ of oil. The next day, she filled the container with as much oil as the amount that was in it the day before. Everyday she repeated this and after the 5 th day, the container was 80% full. What was the capacity of the container in litres? SN11S10
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Unit 2.5 Patterns Number Puzzles
PSLE Math Series
2008 1. In the addition sum below, each letter represents a different digit. Find the digit that each letter represents. RG08S37
+
X
Y
Z
X
Y
Z
Y
Y
X
2. Annie wrote her mother’s age followed by her own age to form a 4-digit number. She used the difference between their ages to subtract from the 4-digit number. Then Annie obtained the number 4489. What was Annie’s age? RG08P47 2009 3. Jane was thinking of a fraction. The sum of its numerator and denominator was 34. After I added 98 to its denominator, the fraction became
𝟏
. What was the fraction
𝟏𝟏
that Jane was thinking of? RG09S11 4. John shifted the decimal point of a number twice to the left to obtain a new number. The difference between the new number and the original number was 136.62. (a) How many times of the new number is the original number? (b) What is the sum of the 2 numbers? RG09P14 2010 5. On the reverse side of a card is a number. The decimal point of this number is shifted to the right twice. The difference between the new number and the initial numbe r is 544.5. What is the number written on this card? MG10P06
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6. There are 4 nursery classes, A, B, C and D, in Healthikidz School. The product of the number of children in Class A and Class C is 168. There are a total of 23 children in Class B and Class C, and a total of 25 children in Class B and Class A. The number of 𝟓
children in Class D is of the number of children in Class A. How many children are 𝟕
there in Healthikidz School altogether? SN10C16 2011 7. If Jason adds 1 to the numerator of fraction, the fraction becomes one whole. If he adds 1
4 to the denominator, the fraction becomes . What is the fraction? AT11C18a 2
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Unit 2.6 Patterns Number Patterns
PSLE Math Series 2007
1. On Day 1, Alvin had $18. After that day, he was given $10 daily. He gives his brother $2 every 3 days. On which day will Alvin have exactly $280? PH07C47 2. Study the following number patterns: 8 # 2 = 8 + 9 = 17 6 # 3 = 6 + 7 + 8 = 21 3 # 4 = 3 + 4 + 5 + 6 = 18 (a) Find the value of 10 # 4. (b) # 3 = 66. Find the missing number in the box. PH07P42 2008 3. Study the number pattern carefully.
(a) What is the missing number X in the 4th pattern? (b) What is the missing number Y in the 12th pattern? (c) If this number pattern continues and you get 285, which number pattern is it? RS08P47
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4. Study the number pattern below. Position Number
1st 2
2nd 3
3rd 4
4th 3
5th 4
6th 5
7th 4
8th 5
9th 6
What is the number in the 100th position? AT08S46 5. Study the number pattern below. Row 1 2 Row 2 2 2 Row 3 2 4 2 Row 4 2 6 6 2 Row 5 2 8 12 8 2 Row 6 2 10 20 20 10 2 Row 7 2 12 30 40 30 12 2 Row 8 2 __ __ 70 70 42 14 2 (a) Write down the 2nd and 3rd number in the blanks above for Row 8 to complete the number pattern. (b) Study the table below. If the 2nd number of a particular row is 30, how many numbers are there in that row? RS08S48 Row Number of numbers 2nd number in the row in the row 2 2 2 3 3 4 4 4 6 5 5 8 6 6 10 7 7 12 … … … … ? 30
2009 6. Study the number pattern below. 52 = 5 × 5 = 25 53 = 5 × 5 × 5 = 125 54 = 5 × 5 × 5 × 5 = 625 55 = 5 × 5 × 5 × 5 × 5 = 3125 (a) In 56 what is the sum of the digits in the ones and tens place? (b) What is the sum of the last three digits in 5 15? (c) What is the sum of the last four digits in 5 210? PL09P15
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7. Study the number pattern carefully. Pattern 1st 2nd 3rd 4th 5th Number 5 8 13 ? 29
6th
7th
8th
9th
10th 11th 12th ?
… …
? 445
(a) What is the missing number in the 4 th pattern? (b) What is the missing number in the 12 th pattern? (c) If this number pattern goes on, which pattern number will give you 445? HP09S18 2010 8. Hiroshi collects gamecards. Every day, he gets 10 additional new gamecards. On every third day, he gives three cards to his friend, Miki. If Hiroshi starts with eight cards on the first day, on which day will he have exactly 180 cards? SN10P18 9. Study the number pattern below. A B Row 1
1 3 5
4
7 9
Total 3
6
Row 4 Row 5
D
2
Row 2 Row 3
C
7 11
8 10
15 19
(a) What is the sum of the two numbers in Row 100? (b) What are the two numbers in Row 100? (c) Under which column, A, B, C or D, will the number 587 appear? NY10S15 10. 1 2 3 4 5
1+(
)+(
1+1 1+2+2+1 1+2+3+3+2+1 1+2+3+4+4+3+2+1 )+( )+( )+( )+( )+(
)+(
)+1
(a) Complete the pattern of the 5th line by writing your answers in the brackets provided above. (b) What is the sum of the numbers in the 5 th line? (c) What is the sum of the numbers in the 50 th line? NH10C17
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11. The table below shows the day of the week that 1 st January falls on from the year 1981 to 2000. Note that Day 1 of a week is a Monday and Day 7 is Sunday. There are 31 days in the month of January. Year 1st Jan falls on Day…
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
4
5
6
7
2
3
4
5
7
1
Year 1st Jan falls on Day…
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2
3
5
6
7
1
3
4
5
6
Year 1st Jan falls on Day…
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
A
B
C
D
E
F
G
H
I
J
(a) What number does the letter C represent? (b) What number does the letter F represent? (c) Which day of the week will 1 st February 2012 fall on? NY10P15 12. A number sequence is shown below. 3, 7, 3, 5, 2, 3, 7, 3, 5, 2, 3, 7, 3, 5, 2, … (a) What is the sum of the first 99 numbers? (b) What is the 128th number? NH10S14 13. Study the number pattern below. Pattern 1 Pattern 2 Pattern 3 Pattern 4 1 3 2 4 2 12 6 5
Pattern 5 5 ??
… …
(a) In Pattern 5, what is the missing number in the box? (b) Find the missing numerator and denominator in Pattern 20. NH10P06 14. Study the pattern carefully. What number should be written in the shaded block? MG10P01
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15. Complete number pattern below. RY10P01 1
,
2
,
3
, …,
5×6 6×7 7×8
9
,
10
(𝑎) (𝑏)
16. Study the following numbers carefully. What is the value of N? SC10P03
2011 17. The number 1 to 500 are written in columns as shown: A B C D E 1 2 3 4 5 9 8 7 6 10 11 12 13 17 16 15 14 18 19 20 21 25 24 23 22 26 … … … If this pattern continues, in which column will the number 500 be written? AT11C18b 18. Study the number pattern. A B C 1 7 6 8 … … …
D 2
E
F 3
5 9
4 10
… …
G
… …
If the pattern continues, in which column will the number 80 appear? HK11P05
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19. Observe the following number pattern.
(a) What are the numbers in the boxes? (b) What is the first number in line 5? (c) How many numbers are there in line 99? NH11C16 20. In the village of Happipeople, the villagers built their houses underground as shown in the figure below. (a) Fill in the House Numbers of Basement Level 6 in the figure below. (b) Miss Sunshine stays in the house on the extreme right of Basement Level 10. What is her House Number? (c) Mr Beam, stays at Basement Level 100. What is the smallest House Number on Mr Beam's level? NY11P14
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PSLE Math Series
3.1 3.2 3.3 3.4
Unit 3 Algebra
Four Operations Model Method Average Miscellaneous Problems pslemathseries.com
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PSLE Math Series
Unit 3.1 Algebra Four Operations
2007 1. Mr Loh bought 5 durians and 3 pineapples for $2y. Each durian cost $5. (a) Find the cost of 1 pineapple. Express your answer in terms of y in its simplest form. (b) Given that y = 17, how much would it cost to buy 6 pineapples? NY07C36 2. Meiyi has $y and Cindy has twice as much as Meiyi. (a) Express their total amount in terms of y. (b) If Cindy has $38, how much do they have altogether? RY07C37 3. A pen costs $2m and 6 magazines cost $8m. How much would 3 such pens and 9 such magazines cost? AC07S36 4. Mr Mohan is 16k years old. He is now 4 times as old as his son. How old will he be when his son is 25 years old? HP07S41 5. A water-melon cost $n. Mother paid $15 for 3 water-melons and 2 pineapples. What was the cost of (a) 3 water-melons? (b) 1 pineapple? NH07S39 6. Frank had $30. He bought 5 pencils which cost k cents each. How much money had he left? Give your answer in dollars. PH07S36 7. Mdm Tong mixes 24 mℓ of rose syrup, 12 mℓ of condensed milk and 44 mℓ of water to prepare ‘bandung’ drink. If she needs 3c litres of ‘bandung’ drink, what is the amount of condensed milk required? SC07S41 8. Ali had y stamps. His father gave him 20 more stamps. He then shared all his stamps equally with his 2 brothers. (a) How many stamps did each boy get in terms of y? (b) If y = 28, how many stamps did each boy get? HK07P41
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9. Joseph has $m. Kenny has 3 times as much money as Joseph. Leo has half the amount of money Joseph and Kenny have altogether. How much money do the 3 boys have altogether? HP07P36 10. (a) Jane is 4k years old. Her sister is 3 years older than her. Express their total age in terms of k. (b) What is the ratio of Jane’s age to her sister’s when k = 9? (Express your answer in the simplest form.) SC07P36 2008 11. (a) The sum of three numbers is 9m. One of the numbers is m and the other number is 4. Express the third number in terms of m. (b) If m = 3, find the value of the third number. MB08C40 12. An eraser costs x cents and a pen costs 80 cents more than an eraser. (a) What is the cost of 3 erasers and 1 pen in terms of x? (b) Jerome wants to buy 3 erasers and 1 pen but is short of 20 cents. If the eraser costs 70 cents, how much money does Jerome have? RS08C42 13. A slice of cake costs $m. Yi Ling bought n such slices of cake. Find the smallest possible sum of m and n if Yi Ling paid a total of $24. NY08C40 14. A book costs $m and a file costs $6 less than a book. (a) What is the cost of 1 book and 1 file? Express your answer in terms of m in its simplest form. (b) Joshua paid $10 for 1 book and 1 file. If the book costs $7, how much change would Joshua receive from the cashier? RY08C39 15. Pauline has y stamps and Ali had 106 more stamps than she. Julia has half as many stamps as Pauline and Ali. (a) How many stamps does Julia have? Give your answer in terms of y. (b) If y = 8, how many stamps does Julia have? MG08C41 𝟏
16. Isaac has 4y Pokemon cards. He has as many cards as Justin. Kenneth has 3 cards 𝟑
fewer than Isaac. How many cards do the boys have altogether? NH08S37 17. A calculator cost $n. A pen cost twice as much as the calculator. Jane bought 6 calculators and 9 pens. How much did she pay altogether? TN08S38
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18. Salim took part in a triathlon. He swam 3w m during the swimming event. He then cycled 500 m more than the distance he had swum. Finally, he ran three times as far as he had swum. (a) Express in terms of w, the total distance covered for all three events. (b) If w = 400, find the total distance he had covered for all three events. AC08S37 19. Jeff saved $5 each day and Mei saved $y less than Jeff each day. After two weeks, they were still short of $30 to buy a fan. How much did the fan cost? RG08S36 20. Rachel is x years old now. Her mother is 36 years older than Rachel. Her father’s age is the sum of Rachel’s age and her mother’s age. How old is Rachel’s father? SC08P37 21. The mass of a pen is 8n grams. The mass of a ruler is 2n grams. What is the total mass of 2 pens and 6 rulers? RG08P36 22. Amir was left with $4n after buying 2 identical pens at $2.15 each. (a) Find the total amount of money he had at first. Leave your answer in terms of n. (b) Given that n = 7, how much money did he have at first? SN08P37 2009 23. I spent exactly $6 on some pens. If 4 pens cost $n, (a) How much is 1 pen? (b) How many pens did I buy? NH09S09 24. (a) 4 belts cost $6b. How much do 10 belts cost? Express your answer in terms of b. (b) If b = 16, find the cost of 7 belts. SC09S07 25. Sharon bought m pens and 3 notebooks for $5. Each pen cost 40 cents. (a) Express the cost of 1 notebook in terms of m. (b) If m = 5, how much did each notebook cost? HP09P06 26. Lanoo exercised for a total of (4r + 9) min in a week. For the first three days, he exercised for r minutes per day. For the next two days, he exercised for 35 minutes per day. For how long did he exercise for the rest of the week? SN09P08 27. The usual admission fee to an amusement park was $w. Senior citizens were given a 50% discount. How much would a group of 8 people have to pay if 3 of them were senior citizens? HP09S09
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28. Last year the total age of Mr Tan and his wife is p years old. His wife is 1 year younger than him. What is his wife’s age 2 years from now? Express your answer in terms of p. RG09P07 2010 29. Simplify 15k + 7 ÷ k × 9k – 21. SN10S03 30. Find the value of 6w + (5 + 3w) + 2 when w = 50. RG10P01 31. Leroy had only $9 and he needed to buy 85 magnets. His father gave him another $r.
The magnets were sold in a pack of 5 for $r. How much more money did he need to pay for all the 85 magnets? SN10C09 32. A pen costs $y. A book costs 40₵ more than a pen. A ruler costs 20₵ less than a book. How much would I need to buy 3 pens and one ruler? RG10P08 33. The recipe for baked salmon is as follows: For each portion of 500g of salmon: First, steam for rmins. 𝟑
Then, bake in the oven for h. 𝟒
The baked salmon is now ready to be served.
How many minutes will it take to cook 2 kg of salmon? Give your answer in terms of r. SN10P10 34. Jeremy is k years old. In 10 years’ time, his brother will be 2 times his age. Express their total age in 10 years’ time in terms of k. RY10S05 35. 3y books cost $10. Find the cost of 9 books. Express your answer in terms of y. CH10S01 36. If k = 6, find the value of
4𝑘 3
– 3 + 8k + 10 – 7k. NY10S04
37. A train ticket for a child cost $2p. Mr Andrews paid $38 for 14 child tickets and 3 adult tickets. How much is the cost of an adult ticket in terms of p? PC10P02 38. There was half a box of biscuits left. Father ate twice as many pieces of biscuits as Sister. I ate the remaining 5 pieces. If Father ate 4p pieces, how many pieces of biscuits were there in a full box? MB10P04
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39. Timmy is n years old now. In 3 years’ time, his sister will be thrice his age. Express their total age in terms of n. CH10P02 40. The length of a piece of rope is 2 m. It is p cm longer than a piece of string. What is the total length of the rope and the string? SC10P01 2011 41. Ryan had $(50 + 8x). Sam had $9x more than Ryan. Ryan was given another $x and Sam was given twice as much the amount given to Ryan. How much did they have now altogether? Give your answer in terms of x. RS11C01 42. Eleven children were given funfair tickets to sell. Each child sold 12y tickets. Each ticket cost $5. If y = 4, what was the total amount of money collected from the sale of the funfair tickets? NY11S03 43. Tim is x years old. His sister is 8 years older than him. Find their total age in 3 years’ time. NH11P01 44. Simplify the expression 3 – 6w + 12 × 4w + 22. RG11S02 45. Wilson bought 3 kilograms of flour. He made a dough using w grams of the flour. The remaining flour is packed equally into 5 packets. How much flour was there in each packet? Leave your answer in terms of w. SN11S03 46. Each box of chocolates cost $p and each box of sweets cost half as much as each box of chocolates. Find the total cost of 3 boxes of chocolates and
4 boxes of sweets. Express your answer in terms of p. CH11S02 47. Two dozen exercise books cost $3k.
Find the cost of 96 exercise books In terms of k. RG11P01 48. Mr Tan's bookshelf has enough space for either 15x hardcover books or 20 paperbacks. If there are already 18 hardcover books and 4 paperbacks, how many more hardcover books can be placed on the bookshelf? Express your answer in terms of x. NY11P01 49. Ribbon A cost $m. Ribbon B cost thrice as much as Ribbon A. Jerry bought 5 pieces of Ribbon A and 8 pieces of Ribbon B. How much did he pay altogether? TN11S04
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PSLE Math Series
Unit 3.2 Algebra Model Method
2007 1. Leela, Siti, and Jane shared $264. Siti had $k less than Leela and Jane had twice as much as Siti. (a) How much did Siti have in terms of k? (b) If k = $8, how much did Leela and Jane have altogether? AC07P39 2008 2. Mark, Jason and David had 126 marbles. Jason had k more marbles than Mark and David had twice as many marbles as Jason. (a) How many marbles did Mark have in terms of k? (b) If k = 2, how many marbles did Jason and David have altogether? AC08P36 3. Andy has k stamps. Muthu has thrice as many stamps as Andy but 8 stamps fewer than James. (a) How many stamps do they have altogether? (Express your answer in terms of k). (b) If k = 9, how many stamps do the three children have altogether? HK08P40 2009 4. (a) Arif is 2x years old. His father is 4 times as old as he. His mother is 3 years younger than his father. What is their total age in terms of x? (b) If x = 4, find their total age. NY09C06 2010 5. Salleh weighs p kg. Vivek is three times as heavy as Salleh. Josiah is 8 kg lighter than Vivek. (a) What is the total mass of the three boys in terms of p? (b) If Salleh weighs 20 kg, what is the difference between Josiah’s mass and Salleh’s mass? AC10S13
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6. Shyan is h years old. Her mother is 3 times as old as she is. Her father is 5 years older than her mother. a) What is the total age of Shyan and her parents in 5 years’ time in terms of h? b) Given that Shyan is 7 years old, find the total age of Shyan and her parents in 5 years’ time. SN10S11 7. Siti is thrice as heavy as Ali. Ben is twice as heavy as Siti. Ben is (70 – u) kg heavier than Ali. What is Ali’s mass in terms of u? RG10S07 8. John has $m. Sally has 3 times as much money as John. Ravi has $8 less than the total of John and Sally. (a) Express the total amount of money the three children have in terms of m. (b) If m = 15, how much more does Ravi have than John? HP10P09 2011 9. Aisha and Mollie have a total of $c. Aisha has twice as much money as Mollie. Express the amount of money Aisha has in terms of c. RY11S01 2
10. A dining chair costs as much as a dining table. Mr Lim bought a dining table and 6 7
dining chairs. The dining table costs $q. (a)How much did Mr Lim pay altogether, in terms of q? (b) If q = $700, how much did Mr Lim pay? MG11S12 11. Ronda is 2k years old. She is 5 years younger than Hong Wai and twice as old as Colin. What is their total age in 4 years’ time? Leave your answer in terms of k. SN11S07 12. Jack had 8p marbles. Samuel had twice as many marbles as Jack. Dave had 7 marbles less than Samuel. a) How many marbles did Dave have? b) How many marbles did they have altogether? NH11S07 13. Mrs Kaur and Mrs Yap went shopping together. Mrs Kaur had $21h more than Mrs Yap. After Mrs Kaur spent $85h, Mrs Yap had 5 times as much money as Mrs Kaur. (a) Express the amount of money that Mrs Kaur had at first in terms of h. (b) If h = 8, find the amount of money that Mrs Kaur had left. NY11C06 14. Hannah is w years old, Vicky is twice as old as Hannah and Nur Sarah is 5 years older than Hannah. (a) What is the sum of the three girls’ age now? (b) What is the sum of the three girls’ age in 10 years’ time? RY11C06
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Unit 3.3 Algebra Average
PSLE Math Series
2007 1. A group of w boys planned a camping trip and they brought food to last them for 35 days. If 6w more boys joined the camp, how many days would the same amount of food last? NY07P36 2. The average mass of 5 boys is 5y kg. The total mass of another 2 boys is 67 kg. What is the average mass of the 7 children? (Express your answer in terms of y) RG07P36 3. The average weight of 5 boys is 8w kg. When 2 more children whose weights are 11w kg and 12w kg respectively join the group, what is the average weight of the boys now? RY07P36 2008 4. The total height of 3 women is 53e cm. 2 of them have an average height of 144 cm. (a) How tall is the 3rd woman in terms of e? (b) Given that e = 8 cm, find the height of the 3 rd woman. SN08S38 2009 5. The average marks received by Jane, Alice, Susan and Mabel in a recent Science test were 76 marks. Jane and Alice both got 8y marks each while Susan got half of Mabel’s marks. How many marks did Susan score for the test? Express your answer in terms of y. RG09S07 2010 6. An egg tray with w eggs weighs 500 g. The empty egg tray weighs 20 g. (a) What is the average mass of an egg in terms of w? (b) If w = 12, what is the average mass of an egg? RY10C06 7. The average height of 2 boys is k cm. The taller boy is 8 cm taller than the shorter boy. Find the height of the shorter boy in terms of k. SN10P05
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2011 8. The average mass of Bala, Craig and Eddie is (4d + 50) kg. Craig is one and a half times as heavy as Bala and twice as heavy as Eddie. (a) What is the total mass of the 3 boys? Give your answer in terms of d. (b) If d =13, what is Eddie's mass? Give your answer to 2decimal places. MG11P08 9. The average age of 3 girls is x years. The oldest girl is 16 years old and the youngest girl is half as old as the oldest girl. (a) What is the age of the third girl? (b) If x = 13, what is the age of the third girl? HP11P07 10. Five pupils, Ali, Brian, Charlie, Dan and Emil, sat for a test. Ali, Brian and Charlie's average score was y. Dan's score was y. The total score for Dan and Emil was 172 marks. (a) Express the average score for all the pupils in terms of y. (b) Given that Dan's score was 78, find the average score for all the pupils. RG11P06
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Unit 3.4 Algebra Miscellaneous
PSLE Math Series
2007 1
3
2
5
1. If of a number is d, what is of the number? PH07C38 𝟏
2. Helen spent of her money on a watch. Her mother gave her $h more. 𝟐
𝟐
She later spent of what she had on a skirt. 𝟑
After all her shopping, Helen had $2h left. (a) What was the cost of her skirt? (b) How much money did Helen have at first? PH07C40 3. The ratio of the number of women to the number of men in an engineering firm was 3 : 5. When 5y men left the firm due to retrenchment, the ratio of the number of women to the number of men in that company became 4 : 5. How many people were working in the firm at first? RG07S37 4. The distance between Town A and Town B was y km. Kim and Gillian travelled from Town A to Town B at a constant speed. They both started their journey at the same time. When Gillian covered half the journey, Kim covered 16 km from Town A. When Gillian completed the whole journey, how far from Town B was Kim? PH07P41 2008 5. The figure below shows a cuboid measuring 10 cm by 5 cm by 3y cm. 10 cm
3y cm 5 cm (a) Find the perimeter of the shaded face of the cuboid in terms of y. (b) If y = 6, what is the perimeter of the shaded face? RS08C36
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6. The length of rectangle B is twice the length of rectangle A. Find the total area of rectangles A and B. MG08S36
3 cm
t cm
A
B
5 cm
7. (a) The breadth of a rectangle is p cm and its length is 3 times its breadth. Express the perimeter of the rectangle in terms of p in the simplest form. (b) Find the area of the rectangle when p = 4. NY08S40 8. The breadth of a rectangle is 2h cm. Its length is 3 times its breadth. Express the length and perimeter of the rectangle in terms of h in its simplest form. SC08S40 9. Valerie wants to print x number of invitation cards. She has to pay a basic fee of $40 and an additional 50₵ for printing each card. (a) How much does she have to pay in terms of x? (b) If she wants to print 280 cards, how much does she have to pay? NY08P40 10. The figure is made up of two squares.
3g cm g cm
(a) Express the perimeter of the figure in terms of g cm in the simplest form. (b) If g = 3, find the area of the figure. MG08P36 2009 11. Given that p : (q + r) = 1 : 3, r : (q + s) = 1 : 2 and p : s = 2 : 5. (a) Find p : q : r : s (b) Find (r + q) : (p + s) NY09P12
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12. The length of a rectangle is thrice as long as its width. Its perimeter is 16p cm. (a) Find the length of the rectangle in terms of p. (b) Find the area of the rectangle if p = 4. AT09C13 2010 13. 5 sharpeners and 8 books cost $49. If 1 sharpener and 1 book cost $u, find the cost of 9 books. NH10C10 14. Super Laundry charges the following rates for its laundry service. First 5 shirts Every additional shirt
S x each $1
(a) How much will it cost Mrs Tan to wash 14 shirts? (b) How much change would Mrs Tan get if she gives the cashier 2 fifty-dollar notes? MG10S11 15. The figure is made up of a square and a rectangle. The breadth of the rectangle is equal to the length of the side of the square. The side of the square is r cm. The length of the rectangle is twice as long as the length of the side of the square. Find the perimeter of the figure. SN10S04
16. The figure below is made up of a triangle in a square. The area of the square is 144 cm 2. Find the area of the shaded triangle and express it in terms of x. RY10S04
17. The breadth of a rectangle is 2y cm. Its length is 6 times its breadth. Find the perimeter of the rectangle in terms of y. RG10S02
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18. The table below shows the parking charges at a shopping centre. Duration
Charges ($) 2a a
First hour Subsequent half hour or part thereof After 6 p.m. 5a (per entry) How much would a shopper have to pay for parking her car at the car park from 2.40 pm to 7.30 pm? MG10P10 19. The table below shows the parking charges at a car park. Duration Charges First hour $1.50 1 x cents Every subsequent hour or part thereof 2
1
If Mrs Tan parked her car at the car park for 3 hours, how much must she pay? Leave 4
your answer in terms of x. RS10P04 2011 20. Mr Lim takes 6z minutes to saw a piece of wooden plank into 3 equal pieces. How long would he take to saw the same wooden plank into 12 equal pieces? RY11S03 21. The length of a rectangle is y cm. The ratio of its length to its breadth is 2 : 1. (a) What is the perimeter of the rectangle? (Give your answer in terms of y) (b) Find the perimeter of the rectangle if y = 24 cm. AC11S06 22. The perimeter of a rectangle is 24y cm. If the ratio of the length of the rectangle to its breadth is 3 : 1, find the length of the rectangle in terms of y. RS11S03 23. Look at the number patterns in the squares. What is the missing number in the square? RS11P05 2x 6x 4a 12a 6h 18h x
3x
2a
6a
3h
24. The figure is made up of a big square and 3 identical smaller squares. Find the shaded area. TN11S07
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PSLE Math Series
4.1 4.2
Unit 4 Data Analysis
Graph Pie Charts
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PSLE Math Series
Unit 4.1 Data Analysis Graph
2007 1. The graph below shows Miss Lim’s monthly savings from April to October. Her average savings from March to September is $200.
(a) How much did Miss Lim save in March? (b) Express her savings in July as a fraction of her total savings from May to August. Give your answer in its simplest form. NY07C44 2. There are 40 pupils in each of the three Primary 6 classes in Super Primary School. The bar graph shows the number of girls in each class.
What percentage of the pupils in the Primary 6 classes are boys? SC07S36
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3. The graph below shows the number of visitors to the Singapore Zoological Gardens in a certain week.
(a) Find the total number of visitors on Tuesday and Saturday. (b) Express the number of visitors on Wednesday as a percentage of the total number of visitors for the week. AT07S36 4. A group of children was asked how many siblings he/she had. The bar chart below shows the result of the survey.
(a) Find the number of children involved in the survey. (b) Find the total number of siblings the children in the group have. NH07S38
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5. Four Objects A, B, C and D are placed inside a container, one after another. The graph shows the mass of the container when empty and when Objects A, B, C and D are placed in it.
(a) Name the objects which are heavier than the container. (b) Find the average mass of the objects. SC07S38 6. The graph below shows the number of patients who visited a clinic during a certain week.
(a) Find the total number of patients who visited the clinic on Wednesday and Thursday. (b) There were 40% fewer patients on Saturday than on __________. HK07P38
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7. The table below shows the number of pupils who were late for school from January to May this year. There were 80 latecomers during this period of time. Month Jan Feb Mar Apr May Number of latecomers 16 10 12 22 ? (a) How many pupils were late for school in May? (b) Plot the missing data in the bar graph drawn below.
(c) What percentage of the number of latecomers came late in the month of January? HP07P38 8. The graph below shows the number of story books read by the pupils in a class.
(a) What was the total number of pupils in the class? (b) What fraction of the pupils in the class read more than 3 story books? (c) What is the total number of story books read? NH07P44
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9. The graph shows the amount of money collected from the sales of files in 5 months.
(a) What was the decrease in the amount collected from April to May? (b) Each file was sold at $6. How many files were sold from January to May? PC07P(2)38 10. In a 10 km race, the line graph below shows the information of Cyclists A and B.
(a) Refer the graph above and fill in the following blanks using the words “slower” or “faster” to describe the two cyclists. Cyclist A moved ___________ in part I than in part II of the journey. Cyclist B moved ___________ in part I than in part II of the journey. (b) Find the speed difference between part I and part II of Cyclist B’s journey. (Leave your answer in m/min.) PH07P43
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11. The graph below shows the number of houses built during the period from January to July.
(a) What was the average number of houses built during March to June? (b) What percentage of the total number of houses built was the month of April? AC07P42 12. The graph below shows the electricity consumption of the Chan family for 5 months.
2
(a) In which month was the electricity consumption that of March? 3
(b) The electricity consumed is charged at the rate of 20 cents per kWh. How much did the Chan family pay for electricity from January to May? SC07P38
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2008 13. The graph below shows how John spent his pocket money for five days. Study it carefully and answer the questions.
(a) What is John’s daily expenditure? (b) What percentage of the total sum does he spend on food? SC08P36 14. The bar graph below shows the number of chicken pies sold on 5 days.
(a) What was the number of chicken pies sold on Wednesday? (b) How many percent more chicken pies was sold on Friday than on Tuesday? (c) If each chicken pie was sold for $2.50, what was the amount collected on Thursday? AC08P40
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15. The line graph shows the number of computers sold by 4 salesmen in a month. Study the graph and answer the following questions.
(a) How many computers did John sold more than Derek? (b) Express the number of computers sold by Andrew and Meng as a fraction to the total number of computers sold. SC08S36 16. The graph shows the number of pizzas sold at a canteen in five days.
(a) The numbers of pizzas sold on Wednesday was half the number sold on ________. (b) If each pizza was sold at $0.80, how much did the stall-holder collect for the five days? SC08S37
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17. The graph below shows the number of houses sold from January to July.
(a) What was the average number of houses sold from March to June? (b) What percentage of the houses sold was in April? Round off your answer to 2 decimal places. MB08S44 18. A survey to find out the number of children in each household was carried out in a HDB block. The bar chart below shows the result of the survey.
(a) Find the number of households with more than 2 children. (b) Find the total number of children in the HDB block. NH08S36
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19. The line graph shows the number of watches sold by ABC Watch Company in the first 6 months of a year.
(a) In which 2 months did ABC Watch Company sell the same number of watches? (b) Find the percentage increase in the number of watches sold from January to February. (c) Find the ratio of the number of watches sold in March to the number of watches sold in June. AC08S40
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2009 20. The line graph below shows the amount of organic fertilizer needed per square metre of land.
(a) How much fertilizer is needed for a piece of land of area 7 m 2? (b) School XYZ has an organic farm which measures 30 m by 40 m. If each grain of fertilizer costs 5₵, what is the cost of the fertilizer needed for the school? HK09P08 21. The line graph below shows the number of DVDs sold by a shop from 2005 to 2008.
(a) What was the average number of DVDs sold per year? (b) How many percent more DVDs were sold in 2008 than 2007? NH09S08
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2010 22. The graph below shows the number of SMS messages sent by student subscribers in the first 5 weeks of 2010 of a particular telco.
Based on the information provided in the graph, answer the following questions: (a) In which week was there a 25% decrease in the number of SMS messages sent from the week before? (b) Calculate the average number of SMS messages sent in the first 4 weeks of 2010. MB10P09
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23. The bar graph shows the sales of a company over a number of years. 3
(a) In which year was the value of sales that of Year 3? 4
(b) Find the average sales of the company over the 5 years. (c) The value of sales in Year 6 increases the average sales of the company over the 6 years to $1 070 000. What was the value of sales in Year 6? NY10P14
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24. The graph below shows the number of stamps collected by 4 boys.
(a) What is the average number of stamps collected by each boy? (b) How many stamps must Daryl give Albert so that both boys will get the same number of stamps? CH10P09
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25. The graph below shows the amount of money collected from 4 games stalls at a carnival.
(a) What is the average amount of money collected from each game stall? (b) If Games stall C wants its collection to be 20% more than games stall B, how much more money must it earn? CH10S09
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26. The graph below shows the distribution of children per household in a particular estate.
(a) How many households in the estate have more than 1 child? (b) Find the total number of children in the estate. AT10C07 27. The graph below shows the number of children who visited a library during a certain week.
(a) Find the total number of children who visited the library on Friday and Saturday. (b) There were 40% fewer children on Saturday than on ________________. NH10S08
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28. The bar graph shows the number of customers who dined in a fast food restaurant in the month of June. Study the graph carefully.
(a) What percentage of customers dined in Week 4? (b) Find the percentage decrease in Week 2. (c) If the number of customers increased by 30% in the first week of July when compared to the whole month of June, how many more customers dined at the restaurant in the first week of July? MG10P12 29. The floor of a rectangular shaped room was painted by a worker. The line graph below shows the painted area of the floor of the rectangular room at regular time interval till the room was completely painted.
If the breadth of the rectangular room was 2 m, find the perimeter of the room. NY10P05
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30. The graph below shows the number of members in a club from 2004 to 2009.
(a) During which one-year period was the decrease in membership the greatest? (b) What is the percentage increase in membership from year 2005 to 2006? RY10P03 2011 31. Water was drained from a tank from 2taps, Tap A and Tap B attached to it. Water was first drained from Tap A and after 6 minutes, water was also drained from Tap B. Both taps were then turned off at the same time after a period of time. The graph below shows the amount of water in the tank over 12 minutes.
In one minute, how many litres of water were drained out from Tap B? HP11P09
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32. The bar graph below shows the Science results of a group of pupils. Find the average marks obtain by pupils who scored 40 marks, 50 marks and 70 marks. NY11P04
33. The graph below shows the number of television sets sold by Shop A and Shop B from April to August.
(a) Use the information given in the graph to complete the table given below. Month
Shop A
April
200
May
600
Shop B
500
June July August
600 600
(b) What was the total number of television sets sold by Shop A from April to July? (c) Shop A sold each television set at a fixed price of $1200. In September, a sum of $418 800 was collected from the sales of television sets. How many more television sets were sold in July than September? NY11P12
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34. The graph below shows the number of SMS and calls made by Cindy through her mobile phone over a 5-day period. Study the graph carefully and answer the questions.
(a) On which two days were the number of calls made the same? (b) On which day was the ratio of the number of calls made to the number of SMS made 1 : 2? (c) Find the total number of calls and SMS Cindy made over the 5-day period. RY11P09 35. The line graph below shows the number of cars sold in showroom from January to June.
(a) In how many months were the sales less than 450 cars? (b) What percentage of the total number of cars sold was the number of cars sold in Jan and Feb? Round of the answer to 2 decimal places. AT11C09
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36. The line graph below shows the number of handbags sold over 6 months in a shop. Study it carefully and answer the following questions.
(a) What was the average number of handbags sold in the months of October and December? (b) In which month did the shop sell approximately 10% of the total number of handbags sold?AT11S01
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PSLE Math Series
Unit 4.2 Data Analysis Pie Charts
2007 1. The pie chart represents the number of four types of balls kept in a storeroom.
(a) What percentage of the balls were netballs? (b) There are 30 basketballs. Find the number of volleyballs. PC07P(2)36 2. The pie chart below shows the expenditure of Mrs Wong’s monthly salary.
𝟏
If Mrs Wong spent of her monthly salary on groceries, how much was her monthly 𝟑
salary? RG07P38
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3. The pie chart shows how Mr Tan used his monthly salary in June.
(a) How much did Mr Tan save? (b) In August, Mr Tan’s salary increased by 5%. If he spent the same amount of money in August as in June, what fraction of his August salary did he save? AC07S40 4. The pie chart below shows the number of members of four co-curricular activities in a school.
(a) Find the ratio of the number of the chess club members to the number of the tennis club members. Express your answer in the lowest term. (b) Express the number of badminton members as a fraction of the number of basketball members in the lowest term. HP07S38
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5. A group of pupils were asked to choose a co-curricular activity. The pie chart represents their choices. The same number of pupils chose Basketball and Volleyball.
(a) 60 pupils chose Table Tennis. How many pupils chose Basketball? (b) The ratio of the number of pupils who chose Basketball to the number of pupils who chose Soccer is 3 : 10. How many pupils chose Scouts? PC07P(1)39
2008 6. The pie chart below shows the sale of compact discs in a shop on a Friday.
(a) What fraction of the compact discs sold was pop songs? (b) If a total of 360 compact discs were sold on Friday, how many of these discs were pop songs? HK08P38
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7. The pie chart shows the number of people in a shopping centre on a weekend. There 𝟏
were 4 times as many women as girls. 𝟐
Express the number of boys as a fraction of the number of men. RG08P40
8. The pie chart shows how Mr Ken used his monthly salary in May. Mr Ken’s monthly expenditure for the month of May
(a) How much did Mr Ken save? (b) In July, Mr Ken’s salary increased by 5%. If he saved the same amount of money in July as in May, what fraction of his July salary did he save? MB08P40
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9. Use the information in the table below to answer the questions. The table below shows the results of a survey on 200 married couples. How often do you go to the movies? Name of group Size of group Answer given A A small number “Very often” B 13% “Often” C 25% “Sometimes” D More than half “Hardly ever” A pie chart is drawn to represent the results of the survey. (a) Write the letter B in the correct part of the pie chart shown.
(b) How many adults gave the answer as “Sometimes”? MG08P37 10. The pie chart shows the different kinds of toys sold by Uncle Tommy at a carnival. He sold a total of 1260 toys. Study the chart and answer the following questions.
(a) What percentage of the toys sold was balls? (b) How many tangrams did he sell at the carnival? RY08P38
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11. The pie chart below represents the number of men, women, boys and girls at the stadium watching a football match.
(a) What fraction of the spectators were adults? (b) The ratio of the number of women to the total number of children was 2 : 3. If there were a total of 1500 spectators at the football match, how many women were there? NY08P39 2009 12. The pie chart below shows the different types of muffins sold in a bakery. A total of 240 muffins were sold.
(a) How many banana muffins were sold? (b) If a chocolate muffin cost $1.60, how much did the bakery collect from the sale of chocolate muffins? AC09P09
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13. The pie chart below shows the results of a survey done on the preferences of 700 movie viewers. Half of the viewers prefer Japanese and Korean movies.
(a) How many viewers like to watch Japanese movies? (b) The ratio of the number of viewers who like American movies to the number of viewers who like Korean movies is 7 : 4. How many viewers like American movies? PL09P10 14. The pie chart below shows the different types of CCA a group of pupils participated in. 5 more pupils participated in Badminton than Athletics. How many pupils participated in Athletics? RY09P11
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15. A group of 260 consumers participated in a survey where they were asked to choose the most important factor of consideration when purchasing a vacuum cleaner. The pie chart below represents their choices. Use it to answer (a), (b) and (c).
(a) What percentage of all the consumers chose “Colour” as the most important factor of consideration? (b) How many consumers chose “Ability to remove dust effectively”? (c) Among all the consumers who chose “Ability to remove dust effectively”, the number of males to that of females was in the ratio 6 : 7. Among the females, 27 of them are home-makers. How many of the females are not home-makers? SN09P11 16. The pie chart below shows the type of food consumed by people in a food court. The ratio of the number of people who consume burgers to those who consume fried rice is 1 : 3. Given that 80 people like to eat burgers, how many people are there at the food court? CH09P10
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17. Some secondary one boys were asked to name their favourite sport. Their choices were represented on the pie chart below.
There was an equal number of boys who liked athletics and swimming. 80 boys chose football as their favourite sport. (a) What fraction of the boys liked swimming? (b) Find the total number of secondary one pupils who took part in the survey. RG09P10 2010 18. The pie chart shows the number of coloured buttons in a box. The number of red buttons is the same as the number of yellow buttons.
How many blue buttons are there in the box? RG10P06
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19. The number of cars, motorcycles and trucks in a car park are shown on the pie chart below. The ratio of the number of trucks to the number of motorcycles is 5 : 7. There are 48 cars in the car park. (a) How many trucks are there? (b) If the cars and trucks have 4 wheels each while the motorcycles have 2 wheels each, find the total number of wheels represented in the pie chart. RS10P14
20. There are 4 types of fish in a tank. The pie chart below represents the number of each type of fish in it. The ratio of the number of guppies to the number of swordtails is 2 : 3.
(a) What is the ratio of the number of guppies to the number of swordtails to the number of angelfish? Express your answer in its simplest form. (b) If 60 more guppies are added in the tank, there will be an equal number of guppies and angelfish. What fraction of the fish in the tank will be guppies? Express your answer in its simplest form. PC10P11
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21. The pie chart below shows Sarah’s expenses from her holiday overseas. (ABC is a straight line.) The amount of money she spent on air ticket was twice the amount she spent on entertainment.
(a) Find the percentage of her expenses spent on entertainment. (b) If she spent $9000 for the holiday, how much did she spend on shopping? HK10P08 22. The pie chart below shows how Marcus spent his allowance last month. He spent equal amount of money on movie and stationery. How much did Marcus spend on handphone bill? RY10P07
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23. The pie chart below shows how MrSoh spends his monthly salary. 1
He spends of his salary on sports. 8
(a) What is his monthly salary? (b) If he spends half of his salary on rent and bills, what fraction of his salary is spent on
bills? (c) If he spends the same amount on food and transport, how much more is spent on rent than on food? RV10P11
24. The pie chart below shows the number of pupils who played in the games on the annual Sports Day.
(a) The total number of participants on Sports Day was 3600. How many fewer participants were there in Basketball than Floorball? (b) How many participants played Frisbee? RY10S12
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25. The pie chart below shows the number of different types of food items sold in a bakery on a particular day. AB and XY are diameters.
(a) If a total of 100 tarts and 50 buns were sold, what was the total number of food items sold in the bakery on that particular day? (b) What percentage of the food sold were puffs? NH10S05 26. The pie chart below shows the number of different types of canned drinks sold in a day. PQ is the diameter of the circle. O is the centre of the circle. (a) If only 15 cans of Pepsi were sold, what was the total number of canned drinks sold that day? (b) How many more percent of 7-UP canned drinks than iced-lemon tea canned drinks were sold? NH10S18
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27. A group of pupils was asked to name their favourite fruit. The number of pupils who liked grapes is twice the number of pupils who like orange. The results were represented in the pie chart below. How many pupils chose orange as their favourite fruit? RY10P04
28. A mobile phone manufacturer conducted a survey on a group of consumers to find out the various factors affecting consumers’ choices when purchasing mobile phones. The pie chart below represents the data collected from the survey.
If 240 more consumers consider the design of the phone more important than the price of the phone, how many consumers chose ‘User-friendliness’ as the most important factor of consideration when purchasing a mobile phone? SC10P06
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2011 29. A survey on 720 pupils' preference for pets was conducted in a school and the findings are presented in the pie chart below. (a) What fraction of the pupils likes to keep hamsters as pets? (Give your answer in its simplest form) (b) How many more pupils like dogs than cats? AC11P10
30. The pie chart below shows the proportion of coloured beads in a box. Study the pie chart and answer questions (a) and (b) below.
(a) What fraction of the total number of beads are green and yellow in colour? (b) If there are 72 red beads, what is the ratio of the number of blue beads to the number of yellow beads? RY11S11
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31. The pie chart below shows the number of computers sold in a company from July to October. An equal number of computers were sold in July and in August. The ratio of the number of computers sold in August to the number of computers sold in October is 3 : 2. If 480 computers were sold in the 4 months, how many computers were sold in September? RY11P04
32. The pie chart shown below shows the number of children who own pets. AOB and COD are straight lines. (a) How many children keep hamsters as pet? (b) Express the number of children who keep rabbits as pets as a percentage of the number of children who keep cats as pets. Give your answer correct to 1 decimal place. MG11P17
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33. The pie chart below shows the number of people visiting a theme park over five days. (a) How many people visited the theme park on Friday? (b) How much did the theme park collect for the five days if the entry fee was $4.50 per person? HK11P08
34. The pie chart represents the number of red, yellow and blue marbles. There are 3 more red than yellow marbles. How many yellow marbles are there? NH11P08
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PSLE Math Series
5.1 5.2 5.3 5.4 5.5 5.6
Unit 5 Fraction
Four Operations Unit/Model Method Comparison 1 Comparison 2 Remainder Concept Equal Parts pslemathseries.com
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Unit 5.1 Fraction Four Operations
PSLE Math Series
2008 1. 1 kg of grapes cost $2.50 and 1 kg of longans cost $3.60. 𝟏
𝟏
𝟐
𝟑
Mrs Devan bought 2 kg of grapes and 1 kg of longans. How much did she pay altogether? MG08S38 2009 𝟐
2. A plumber had a pipe which was 9 m long. He cut it into 14 pieces of m each. Then he 𝟓
cut the remaining pipe into some pieces of
𝟕 𝟐𝟎
m each. How many metres of pipe was
he left with? SN09C07 3.
5 6
1
m of raffia is cut into shorter pieces. Each of the shorter pieces must measure m. 4
(a) How many
1 4
m pieces are there?
(b) What is the length of the remaining piece? NH09C06 4.
𝟏𝟑 𝟏𝟓
𝟏
m of ribbon is cut into shorter pieces. Each of the shorter pieces must measure m. 𝟑
𝟏
(a) How many m pieces are there? 𝟑
(b) What is the length of the remaining piece? (Give your answer in its simplest form) RY09C08 2010 3
3
7
8
5. What is the sum of and ? Round off the answer to the nearest tenth. NH10C01 7
6. A wooden rod measuring 43 m long is cut into smaller pieces each of m long. What is 9
the length of the remaining rod? SN10S02 7. Henry made
𝟏𝟓 𝟏𝟔
𝟐
ℓ of lemonade. In the morning, he sold of the lemonade. In the 𝟓
𝟏
afternoon, Henry sold ℓ of the lemonade. How many litres of lemonade had Henry 𝟓
left at the end? RG10P10
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8. A 40-gram serving of breakfast cereal contains sugar. Another 10 grams of sugar is 4
added to it. What fraction of the resulting mixture is sugar? NH10P07 7
3
8
28
9. Amy has m of cotton twine. She cuts it into pieces of length
m each for her artwork.
(a) What is the maximum number of the pieces she can cut from the cotton twine? (b) What is the length of the remaining cotton twine? RY10S06 𝟑
𝟐
𝟒
𝟗
10. of a number is 30. What is of the number? Express your answer as a mixed number. PC10P03 2011 𝟐
11. Yazid took h to wrap 4 parcels. He spent an equal amount of time wrapping each 𝟑
parcel. At this rate, how long would it take Yazid to wrap 7 such parcels? AC11S03 12. Mrs Ong had an 8-m long piece of string. She cut it into 2 pieces. The length of the 3
shorter piece was of the length of the longer piece. Mrs Ong kept the shorter piece and 4
6
used the longer piece to tie some parcels. She used m of string to tie each parcel. 7
a) Find the maximum number of parcels Mrs Ong was able to tie. b) What was the length of string left after tying all the parcels? SN11S14 13. A tailor has 3 metres of cloth. He uses
4 15
metres of cloth to make a headband. What is
the maximum number of headbands he can make with his cloth? NH11S02 4
1
5
4
14. Ruth mixed 3 ℓ of mango syrup with 8 ℓ of water. Then she poured the mixture into six 3 4
-ℓ bottles and gave the remainder to Tessa. How many litres of the mixture did Tessa
receive? SN11C02 15.
10 11
1
kg of sugar is packed into little bags. If each bag contains only kg of sugar, how much 7
sugar is left unpacked? (Give your answer as a fraction in the simplest form) AT11C05 7
16. 4 identical containers can hold kg of flour. How many kilograms of flour can 15 such 8
containers hold? Leave your answer as a fraction. SN11P01 𝟑
𝟒
17. The mass of a bag of sugar is kg. The mass of a bag of flour is of the mass of the bag 𝟖
𝟗
𝟑
of sugar. If the mass of a packet of peanuts is of the mass of the bag of flour, what is 𝟓
the mass of the packet of peanuts? Leave your answer in grams. NY11C09
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18. Mrs Ravi distributed some sweets equally among 9 boys and 11 girls. Each boy gave
𝟐 𝟑
of what he received to the girls. As a result, the girls received a total of 1020 sweets. (a) How many sweets did each boy have left? (b) What was the total number of sweets distributed by Mrs Ravi? SN11C07 19. A ball was dropped from a certain height. Each time it touched the ground, it bounced 𝟏
to a height which was of the height from which it was dropped. Given that it reached 𝟑
a height of 1.54 m on the third bounce, find the height at which it was dropped at first? RY11P02 𝟏
20. of a 400-gram pancake mixture is sugar. Another 100 g of sugar is added to the 𝟒
mixture. What fraction of the final mixture is sugar? (Leave your answer in its simplest form.) RS11P07 3
1
4
8
21. What is the difference between and ? Give your answer as a decimal. NH11C02
22. Find the perimeter of the rectangle shown below. NY11C01
23. Arrange the following numbers in ascending order. RG11P03 5 4
, 2, 1.22, 1
3 4
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PSLE Math Series
Unit 5.2 Fraction Unit/Model Method
2007 5
1. Leon had of what Jim had. 11 Andy had $250 less than Jim. 1 If Andy had more than Leon, how much did Jim have? NH07C38 5
2
2. Lisa and Melinda had $175 altogether. After they had given away of the total sum of 5
7
money, Lisa had as much money as Melinda. How much money must Melinda give to 8 Lisa so that they will now have an equal amount of money? AC07S37 3. A group of pupils sat for two tests, test A and test B. 1 The number of pupils who failed test A was of those who passed test A. 7 Given that there were 20 pupils who failed test A, (a) how many pupils passed test A? 1 (b) The number of pupils who failed test B was of those who failed test A. What 4 fraction of the pupils passed test B? RG07P44 4. Tom tied his pen to his pencil as shown in the diagram above to form a toy. The length 𝟑
of the pencil is the length of the pen. What is the length of the toy? MB07P41 𝟓
3
5. Using of his money, Derek could buy 8 similar pens. 5
If he was given an extra dollar, he could use it together with the rest of his money to buy another 6 such pens. How much money had Derek? MB07P43 6. Tina, Ken and Roger share 460 marbles. Tina gets 33 more marbles than Ken. Roger gets 1 as many as Ken. How many more marbles than Roger does Ken have? RY07C43 3
2008 5
7. In one day, Johann can make 450 kites and Darren can make as many kites. How many 9 days are required to make 3500 kites by both of them? NH08C40
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8. Nora bought a bottle of detergent. She used an equal amount of detergent each day. 2 She had of the detergent left after 5 days. She had 1.2 ℓ of detergent left after another 3 7 days. What was the volume of the detergent at first? NY08C42 9. Melvin had a bag of sugar. His family used an equal amount of sugar each day. After 3 4 days, he had of the sugar left. After another 5 days, he had 7 kg of sugar left. How 5 much sugar was in the bag at first? RY08C38 2
1
1
10. of the pupils in a school are boys and the rest are girls. of the boys and of the girls 5 2 2 wear glasses. What is the enrolment of the school if 430 pupils wear glasses? SN08C40 11. Troy’s monthly allowance is $42 more than Earl’s. Earl spends $54 more than Troy 𝟏 𝟑 every month. Earl’s savings is of Troy’s savings. If Troy spends of his allowance 𝟐 𝟕 every month, what is his allowance for the entire year? SN08P46 12. An equal number of male and female runners took part in the National Education Marathon last year. 980 male runners and 350 female runners quit running and did not 1 complete the marathon. The number of male runners left was the number of female 6 runners. What was the total number of runners at the start of the marathon? RY08C42 2
13. A shopkeeper had some apples. of them were red while the rest were green. Liling 1
1
5
bought of the red ones and of the green ones. There were 84 apples left. How many 4 3 apples did Liling buy altogether? MG08C42 2
14. Jill bought some blue and red markers. of the markers she bought were blue and the 3
3
1
rest were red. She gave away of the blue markers and of the red markers, she had 4 4 100 markers left. How many markers in all did she buy at first? RY08C43 15. A faulty weighing scale showed a reading of 0.2 kg when nothing was placed on it. A box 5 which contained 21 identical books was placed on the weighing scale. After of the 7 books were removed from the box, the weighing scale showed a reading of 32.68 kg. Given that the mass of each book was 0.8 times the mass of the box, find the mass of the box. NY08C45 1
16. At a Mathematics competition, there were 84 winners. of them won either gold or 2
5
silver medals. of them won either silver or bronze medals. How many of them won 6
silver medals? MB08C37 17. The number of pupils in Primary 6C is 2 more than the number of pupils in Primary 6D. There are 22 boys in Primary 6C and 16 boys in Primary 6D. The number of girls in 4 Primary 6C is of the number of girls in Primary 6D. What fraction of the pupils in 5
Primary 6C are girls? MB08P41
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18. Four friends, Alice, Billy, Carol and David shared a total number of 81 chocolates. Alice 𝟒
received of the total number of chocolates received by Billy, Carol and David. Billy 𝟓 𝟐
received of the total number of chocolates received by Carol and David. Carol 𝟑 received twice as many chocolates as David. (a) What fraction of all the chocolates does Billy have? (b) How many chocolates did Alice receive? RY08P45 2
19. Mrs Raj spent of her money on 3 blouses. She bought another 2 similar blouses and 13 5 handkerchiefs with the rest of her money. (a) What fraction of Mrs Raj’s money was spent on buying the 13 handkerchiefs? Give your answer in its simplest form. (b) If Mrs Raj was given 1 handkerchief free for every 6 handkerchiefs bought, how many handkerchiefs would she have got altogether if she had spent all her money on handkerchiefs? MG08P48 20. A factory was required to produce a certain number of toys in four days. 1 On the first day, it produced of the required number of toys. 5 On the second day, it produced another 20 toys. On the third day, it produced as many toys as those produced on the first two days. On the fourth day, it completed the remaining 8 toys. How many toys did the factory produce in the four days? NH08P42 2009 21. Wilson and Yi Lin had $71 altogether. Yi Lin and Patrick had $105 altogether. Wilson had 3 of the money that Patrick had. How much money did Yi Lin have? NY09C08 5
6
1
22. A jug with a capacity of 0.98 ℓ is full of juice. of the juice is poured into a glass. 7 3 (a) How much juice is left in the jug? 2 (b) The capacity of the glass is of the capacity of the jug. If the capacity of a bottle is 5 thrice as much as the capacity of the glass, what is the total capacity of the bottle, the jug and the glass? Leave your answer in ℓ. SN09C10 23. The original amount of money Samuel had to the original amount of money Nigel had 5 1 was 4 : 5. After Samuel spent of his money on clothing, of it on gifts and gave $1500 9 3 to his mother, he had $560 left. What was the total amount of money both men had originally? SN09C17 24. In January, Mrs Krishnan spent $360 on groceries. In February, she spent 3
9 10
of the
amount she spent in January. In March, she spent of the total amount she spent in the 4 previous 2 months. How much did she spend on groceries in the 3 months altogether? RY09CR10
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25. The table below shows the number of fruits in a shop. One of the numbers has been erased. Type of fruit Pear Mango Star fruit Water melon
Number of fruits 89 84 ? 52
1
If of the total number of fruits is star fruit, what is the total number of fruits in the 4 shop? AT09S07 26. In a math competition, participants can obtain 4 possible award: Gold, Silver, Bronze 𝟑
𝟏
𝟕 𝟏
𝟒
and Participation. of the participants obtained Gold awards, of them obtained Silver awards, and of them obtained Bronze awards. Given that there were less than 𝟔 100 participants taking the competition, (a) How many participants obtained the award for Participation? (b) How many more participants obtained Gold awards than Bronze awards? RG09S16 27. Mark had some stamps. He pasted 1
5 11
of the stamps on 5 postcards and 5 envelopes. On
each postcard, he pasted as many stamps as he pasted on each envelope. If he had 150 4 stamps left, how many stamps did he paste on each envelope? RY09C15 28. Aisha, Bala, Cindy and Danny went to buy a gift for Miss Emily. They shared the cost equally among themselves. However, Danny forgot to bring the money. So, his friends 𝟑 paid for the gift first. Cindy paid of the amount Aisha and Bala paid. Bala paid $10 𝟓 more than Aisha. The next day, Danny returned $24 to Cindy and some money to Aisha and Bala. How much did Danny return to (a) Aisha? (b) Bala? NH09S18 2
29. Mrs Ker had a bag of brown sugar. After she used some of the brown sugar, she had of 1
3
the brown sugar left. Then she distributed of what she had left equally between her 4 neighbours, Mrs Dee and Mrs Bheem. Finally, Mrs Ker had 437.5 g of brown sugar more than MrsBheem. How much brown sugar did Mrs Ker use? Leave your answer in g. SN09P12 2010 30. Farmer Ted collected 386 eggs on Monday. He collected 164 more eggs on Tuesday than 1 on Monday. After selling some of the eggs, he found that he had of the total number of 4 eggs left. How many eggs did he sell? SN10P06
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1
31. There were some children at a party. of the children were boys. After of the girls had 4 2 left the party, there were 30 more boys than girls remaining at the party. How many children were at the party at first? HP10P08 4
2
32. Mrs Tan had of her pencils left after selling 567 of them at $0.70 each. She sold of the 7 3 remainder at $0.30 each. How much did she receive from the sales of the pencils? RG10S12 2
33. Tommy and Peter have a total of 2982 stamps. Tommy has of the number of stamps 5 Peter has. How many more stamps does Peter have than Tommy? RY10S02 3
34. of a school population are girls. There are 120 more girls than boys. What is the total 5
school population? NH10C04 1
1
35. A flask is filled with chocolate powder. A teapot, twice as large as the flask, is filled 3 4 with chocolate powder. Then the flask and the teapot are each filled with water completely and all the contents are mixed together into a chocolate drink. What fraction of the chocolate drink is the chocolate powder? SN10C08 2
5
36. 520g of flour can fill of a container. Find the amount of flour needed to fill of the 7 12 container. SN10S01 37. Jug X and Jug Y are filled to the brim with water. If all the water in Jug X is poured into Container Z, another 28 ℓ of water is needed to completely fill it. If all the water in Jug Y is poured into Container Z, another 35 ℓ of water is needed to completely fill it. If the water in Jug X and Jug Y is poured into Container Z, it will completely fill Container Z. 3 How much water does Jug X contain when it is filled? SN10S08 7
1
38. Sue spent of her allowance on Monday. She spent $15 more on Tuesday than on 4 Monday. She finished all her allowance on Wednesday on 2 books that cost $12 each. What was her allowance? RV10P05 1
39. There are 152 pupils in the Math Club. of the boys and 5 girls took part in a Math 11 Olympiad Competition. An equal number of boys and girls did not take part in the competition. How many girls are there in the club? RV10P03 2011 40. Lu Lu Garments imported T-shirts from overseas and sorted them into 3 different 3 2 colours. of the T-shirts were red and of the T-shirtswere green. The rest of the T-shirts 7
5
were yellow. There were 912 more green T-shirts than yellow T-shirts. How many green T-shirts were imported? AC11P07
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41. Mdm Tan spends of her money on 3 dresses and 8 pairs of spectacles.With the rest of 5 her money, she can buy another 6 dresses. If she spends all her money on spectacles only, how many pairs of spectacles can she buy? RY11S04 𝟏
𝟐
42. There were an equal number of boys and girls at a funfair. After of the boys and of 𝟑 𝟗 the girls left the funfair, there were 25 more girls than boys remaining behind. (a) How many boys were there at the funfair at first? 𝟑
(b) Later 165 more children turned up at the funfair. Then there were as many boys 𝟒 as girls. What was the total number of girls present at the funfair at the end? AC11S16 43. Sarah cut a piece of cardboard into 2 equal parts. One part was shared between her 3 friends, Leila and Abdul, such that Leila's share was of Abdul's. If Abdul received 48.8 5 cm2 more than Leila, what was the area of cardboard that Sarah had originally? SN11S01 44. Polly, Queenie and Remmy were given an equal number of charity tickets to sell. However, none of them completed selling their share of tickets. Polly sold 6 times as 1 many tickets as Queenie and was left with 12 unsold tickets. of the tickets sold by 3 Remmy was 3 more than those sold by Queenie. The three of them sold a total of 239 tickets. How many charity tickets did each of them receive? SN11S11 45. A contractor needed to cover an entire hall with tiles. On the first day, he laid 319 tiles. He completed tiling the rest of the hall in 7 days using an equal number of tiles each day. 8 At the end of the 4th day, he was able to tile of the hall. How many tiles did the 15 contractor use to cover the entire hall? SN11S15 𝟓
𝟓
46. At a camp, of the campers were Primary Four pupils. of the remaining campers 𝟏𝟏 𝟖 were Primary Five pupils and the rest were Primary Six pupils. There were 154 more Primary Four pupils than Primary Six pupils. Halfway through the camp, some Primary 𝟕
Six pupils left the camp. As a result, of the remaining campers were Primary Four and 𝟖 Five pupils. How many Primary Six pupils left the camp site? SN11S16 5
1
8
4
47. Mary had as many sweets as Lucy. After Lucy gave of hersweets to Mary, Mary had 10 more sweets than Lucy. How many sweets did Mary have at first? NH11S06 𝟑
𝟏
48. In a confectionery, of the cupcakes baked were strawberry cupcakes. of them were 𝟓
𝟐
𝟐
chocolate cupcakes and the rest were grape cupcakes. of the strawberry cupcakes 𝟕
𝟏
were sold. This was of the number of chocolate cupcakes sold. The number of grape 𝟏
𝟐
cupcakes sold was the total number sold in the other two flavours. Given that there 𝟒 were 190 cupcakes left, how many cupcakes were there at first? NY11P16
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49. Buckets A, B and C contain 16 litres, 12 litres and 14 litres of water respectively. of the 8
1
water from Bucket A was poured into Bucket C. Then ofthe water from Bucket B was 3
4
poured equally into Buckets A and C. In the end, of the water from Bucket C was 11 poured back into Bucket A. How many litres of water were in Bucket C in the end? RG11P13
2
50. Shawn saved of his pocket money every month. When Shawn's pocket money was reduced by
1
5
10
, his savings become $18. What was his pocket money at first? RS11P06 3
51. Mrs Lee and Mrs Tan went shopping. Mrs Lee spent of her money and had $120 left. 8
1
Mrs Tan had of her money left after spending twice as much as Mrs Lee. What was the 3 total amount of money the women had before they went shopping? RS11C10 1
52. Vincent spent of his allowance on a basketball, $145. 50 on a pair of shoes and had 3 $24.50 left. How much was Vincent’s allowance RY11C02 1
1
3
5
53. A box weighs 10 kg when filled with oranges. A similar box weighs 7 kg when filled with carrots. If the mass of the oranges is twice as heavy as the carrots, what is the mass of the empty box? RY11C03 2
1
54. A box contained some buttons. of them were blue, of them were yellow and the rest 3 5 were red. There were 36 more yellow buttons than red buttons. How many buttons were there altogether? RY11C04 55. Mrs Tan baked some cheese muffins and some chocolate muffins. After she sold 3
1 3
cheese muffins and of the chocolate muffins, she had twice as many cheese muffins 5
than chocolate muffins left. If Mrs Tan baked 50 more cheese muffins than chocolate muffins, find the total number of muffins Mrs Tan baked. RY11P07 2
1
56. Sharif and Raj had some picture cards. After Sharif gave of his cards to Raj, he had of 5 3 the total number of picture cards. If Raj had 144 picture cards in the end, (a) how many pictures did he receive from Sharif? (b) How many more picture cards did Raj have than Sharif in the end? MG11P15
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57. Wendy has 80 more stamps than Mary but 50 more stamps than Jean. Wendy gives
𝟏 𝟐
𝟏
of her stamps to Mary. Then Mary gives of her stampsto Jean. If Jean has 62 more 𝟓
stamps than Wendy, how many stamps does Mary have in the end? CH11P17 4
58. In the middle of the month, Gary withdrew of his money from the bank. He spent $136 5
on a computer game and the remaining $224 to buy a tennis racket. When he received 5
his salary at the end of the month, he deposited of it in the bank. As a result, the 8
amount in the bank was increased to $817.50. What is Gary’s salary? AT11C10 1
59. Three boxes, A, B and C contained a certain number of counters. Box C contained as 4
many counters as A and B. There were 98 more counters in Box A than in Box C. Box B contained 174 more counters than Box C. (a) How many counters did the three boxes contain altogether? (b) How many counters were in Box B? HP11P13 𝟕
60. Varsha had some 20-cent and 50-cent coins. of the coins were 20-cent coins and the 𝟖
𝟓
rest were 50-cent coins. After Varsha had spent $72.50 worth of 50-cent coins and of 𝟕
𝟐
the 20-cent coins, she had of the coins left. Find the total amount of money Varsha 𝟕
had left. RG11S17
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Unit 5.3 Fraction Comparison Problems 1
PSLE Math Series
2007 𝟐
1. A container weighs 0.466 kg when it is filled with coffee powder. It weighs 0.406 kg 𝟑
𝟏
when of the coffee powder is removed. What is the weight of the container when it 𝟒
is empty? RG07S44 7
1
8
2
2. A tank, when filled with water, had a mass of 17 kg. When filled, it had a mass of 11 kg. What was the mass of the empty tank? NH07S40 2008 𝟏
3. The mass of a wooden crate which contained bricks was 80 kg when it was filled. 𝟐
𝟏
When 26 kg of bricks were removed, the crate became filled. What was the mass of 𝟑
𝟑
the wooden crate with bricks when it was filled? TN08S45 𝟒
2009 4. A container, when
7 8
1
filled with water, had a mass of 19 kg. When filled, it had a mass 2
of 13 kg. What was the mass of the empty container? NH09S10 5. A jar weighs 3.207 kg when it is 𝟕 𝟖
𝟓 𝟏𝟐
filled with candies, and weighs 4 kg 120 g when it is
filled with candies. What is the total mass of the jar when it is completely filled with
candies? SN09C08 1
6. The total mass of a metal tin and its biscuits when completely full is 8 kg. When 3 kg of 4
the biscuits is taken out, it is only half full. What is the mass of the biscuits and the metal 1
tin when it is full? (Give your answer in its simplest form.) RY09C06 3
𝟏
7. A tank was full of water. Hazlin poured 3.8 ℓ of water into the tank and the tank 𝟒
𝟕
became full. How much water was in the tank at first? RS09P07 𝟗
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2010 𝟓
𝟏
𝟔
𝟓
8. A box has a mass of 29 kg when it is filled with sand. When it is filled with sand, it has a mass of 10 kg. Find the mass of the empty box. CH10S07 2011 1
1
9. When a bottle was full, it had a mass of 300 g. When it was full, it had a mass of 400 g. 8
4
3
What was its mass when it was full? RS11C04 4
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PSLE Math Series
Unit 5.4 Fraction Comparison Problems 2
2008 1
1. Mr Tan bought a laptop for $1200 and spent of his remaining sum of money on a 4
3
printer. At the end, he had of the original sum of money left. 7
(a) What fraction of his money was used to buy the printer? (b) How much money did Mr Tan have at first? RG08P42 𝟐
2. Mrs Lee needed to tie two parcels. She used 78 cm of string for the first parcel and of 𝟕
the remaining string to tie the second parcel. If the length of the remaining string is equal to the total length of the string used, what was the length of the string she used to tie the two parcels? SN08C41 𝟏
3. Peter read 810 pages of a storybook on Friday. On Saturday, he read of the remaining 𝟔
pages. If he still had 50% of the book to complete, find the number of pages in the book. NH08C45 1
4. Tom spent $30 of his money on a book. He spent of the remainder on a pen and still 4
1
had of his original amount of money left. Find the amount of money he had at first. 3
AC08S38 1
5. A fruit seller sold 80 apples and threw away of the remaining apples which had turned 7
2
bad. of his apples were left. How many apples had he left? NH08S38 5
2009 𝟏
6. Kumar spent $1729 on a set of encyclopedia. He spent of the remainder on a camera 𝟒
𝟐
and still had of his money left. Find the total amount of money he had at first. 𝟓
SN09S08 2010 7. At a party, there were some balloons. 25 balloons burst and 10% of the remaining balloons flew away. If only 60% of the balloons were left, how many balloons were there at first? NH10S13 pslemathseries.com
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1
3
4
8. Daniel spent $25.50 on a book and of the remainder on a water bottle. He still had of his money left. Find the total amount of money he had at first. RS10P07 9. Corine won a sum of money in a contest. She spent $240 of the money on Monday. She 1
spent 30% of the remaining money on Tuesday and of the rest of the money on 2
Wednesday. Then she found that she had 20% of her original sum of money left. How much was the original sum of money? RV10P06 2011 10. Auntie Rosnah made some curry puffs for sale. She sold 448 of them in the morning and 4 7
of the remainder in the afternoon. She was left with 20% of all her curry puffs. How
many curry puffs were sold in the afternoon? CH11S07 1
11. Mitchell spent some money on a frying pan and of the remainder on a cooking pot. She 3
4
then had $128 left. The cost of the cooking pot was of the cost of the frying pan. 7
(a) How much did the cooking pot cost? (b) How much did she spend altogether? SN11C10 12. A shopkeeper sold 837 candies on the first day. The next day, he sold 60% of the 𝟏
remaining candies. As a result, the number of candies left became of the number 𝟕
candies he had at first. How many candies did the shopkeeper have at first? TN11S13
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Unit 5.5 Fraction Remainder Concept
PSLE Math Series
2007 1
1. A box contains red, yellow and green marbles. Half of the marbles are red and of the 8
remaining marbles are yellow, while the rest of the marbles are green. If there are 210 more green marbles than yellow marbles, how many marbles are there altogether in the box? RG07S36 4
2. Tom worked 20 days in August. He gave 0.15 of his salary to his mother, used of the 5
remainder and saved the rest. He saved a total of $340 in August. How much did he receive for a day’s work? NY07P38 𝟑
𝟒
𝟖
𝟓
3. Melissa spent of her money on 3 pencils and 8 pens, and of the remainder on 15 markers. 𝟐
Each pencil cost as much as a pen. 𝟑
Each marker cost $0.20 more than a pencil. What is the cost of a pen? RG07P47 3
4. 1 durian cost 3 times as much as a mango. Mrs Lee spent of her money on some 7
1
mangoes and of her remaining money on 3 durians. How many mangoes did she buy? 4
RY07S39 𝟑
𝟏
5. Benjamin spent of his money on 6 toys and 6 erasers, and of the remainder on 10 𝟕
𝟒
𝟏
cards. Each eraser cost as much as a toy. Each card cost $0.30 more than an eraser. 𝟕
How much money did Benjamin spend on each toy? NH07P42 2008 𝟏
𝟒
6. A packet of candies cost as much as a box of chocolate. Miss Tan spent of her 𝟐
𝟗
money on 16 boxes of chocolate. She then spent
𝟑 𝟏𝟎
of the remainder on some packets
of candies. She had $140 left. (a) How much money did Miss Tan have at first? (b) How many packets of candies did Miss Tan buy? RS08S44
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7. Kenny and Joan had some stickers. Kenny had thrice as many stickers as Joan. Kenny 2
2
3
5
used of his stickers and gave of the remainder to Joan. Kenny then had 30 stickers left. How many stickers did Joan have at the end? NH08C39 8.
𝟐 𝟕
𝟏
of the marbles in a box are red. of the remaining marbles are blue and the rest are 𝟔
yellow. There are 280 more yellow marbles than blue marbles. How many red marbles are there? HK08P42 2009 1
4
5
7
9. Mrs Liu spent of her monthly salary on a handbag, of the remainder on a vacuum cleaner and saved the rest of her monthly salary. If she saved $1890, what was her monthly salary? PL09P12 1
10. Tricia has some pink, red and yellow ribbons. of them are pink ribbons. Four fewer 3
1
than of the remainder are red ribbons. The remaining 24 are yellow ribbons. How 3
many pink ribbons does Tricia have? RG09P09 𝟏
𝟐
𝟓
𝟓
11. of the audience in a hall are women. of the remaining audience are men. The rest are children. If there are 266 boys in the hall and the number of girls is twice as many as the number of boys, find the number of men in the hall. SN09C15 𝟑
𝟏
𝟖
𝟑
12. Nadine spent of her salary on food and of the remainder on transport. Then she shared the rest of the salary equally with her siblings such that each of them received 𝟏 𝟏𝟐
of her total salary.
(a) How many siblings does Nadine have? (b) Given that Nadine and her siblings received $208 each, how much money did Nadine spend on transport? SN09C14 2010 1
1
4
3
13. There are some roses in a box. of them are yellow and of the remaining roses are pink. The rest are red. If there are 18 more red roses than yellow ones, how many roses are there in the box? SN10P01 14. Alexa received a number of text messages on her mobile phone. 𝟑
𝟏
𝟓
𝟔
𝟐 𝟏𝟏
of them were from
her superiors, were from her parents and of the remaining text messages were from her cousins. There were a total of 559 text messages from her superiors and parents. How many text messages did Alexa receive from her cousins? SN10C15
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1
3
3
15. James had some money. He spent of his money on food and of the remainder on transport. What fraction of his money was left? RY10C02 𝟏
16. Mr Li earns $36600 a year. Every month, he spends of his salary on his family 𝟒
𝟐
expenses and gives of his remaining salary to his mother. How much of his salary is 𝟓
he left with every month? RY10S08 2011 1
2
17. Fred was given some pocket money. He spent of his money to buy games and saved 3 3 of the remainder. He used the rest of the money onfood. If he spent $120 altogether, how much did he save? CH11P07 𝟐
𝟑
𝟓
𝟒
18. In a garden, of the flowers are lilies. of the remainder are roses and the rest are 𝟑
sunflowers. There are 568 more roses than lilies. After of the lilies are sold, how 𝟒 many flowers are left in the garden? RY11C14 1
19. In a countdown concert, half of the audience was adults, and of the remaining 3
audience were boys and the rest were girls.
Given that there were 2338 girls in the concert, how many people attended the concert? RG11S06 20. A toy purchaser bought some toy trains and toy cars. A toy train cost 6 times as much 𝟑
𝟏
𝟖
𝟓
as a toy car. He spent of his money on buying toy cars and of his remaining money on 7 toy trains. How many toy cars did he buy? RG11P09 1
5
5
8
21. Cathy spent of her money on pens and of her remaining money on 2 books. Each book cost 15 times as much as a pen. How many pens did she buy? NH11P07
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Unit 5.6 Fraction Equal Parts
PSLE Math Series
2007 1.
3 4
1
of Alice’s salary is the same as of Betty’s salary. If Alice earns $200 less than Betty, 2
how much does Betty earn? NH07S37 2008 2.
5 8
1
of Diva’s money is the same amount as of Rashid’s money. Diva has $14 less than 2
Rashid. How much money do Diva and Rashid have altogether? RY08S37 𝟑
𝟐
𝟓
𝟑
3. There are 1425 cows and sheep in a farm. of the cows is equal to of the sheep. (a) How many cows are there in the farm? (b) How many more cows than sheep are there in the farm? MB08S37 4.
𝟏
𝟏
of Mark’s coins is of Siti’s coins. All of Mark’s coins are 50-cent coins, while Siti has 𝟒 a combination of 50-cent and 20-cent coins. Mark has 16 more coins than Siti. If Siti gives half of her 20-cent coins to Mark, Mark will have $42.40. How much money did Siti have at first? MG08P44 𝟓
5. Among the commuters on board a train, the number of children to the number of 𝟐
𝟏
adults was in the ratio 3 : 4. of the number of women was equal to of the number 𝟑 𝟒 of men. (a) What is the ratio of the number of men to the number of women to the number of children? 𝟏 (b) When 108 commuters alighted from the train, the number of men decreased by 𝟐
𝟏
and the number of children decreased by . How many commuters were left on 𝟑 board the train? SN08P47 2009 𝟏
𝟐
𝟐 𝟐
𝟓
6. A bag contains some green, red and blue marbles. of the red marbles is equal to of the green marbles. The number of blue marbles is of the total number of green and 𝟑
red marbles. If there are 12 more blue marbles than green marbles, how many marbles are there in the bag altogether? CH09P07
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7.
𝟑 𝟓
𝟐
of the pupils in School A are girls. of the pupils in School B are girls. 𝟑
There is an equal number of boys in School A and School B. There are 400 more pupils in School B than School A. Find the total number of pupils in the two schools. RY09P10 𝟑
𝟏
𝟒
𝟐
8. Annie earns $640 less than her sister, Bernice. of Annie’s salary is the same as of Bernice’s salary. How much do the sisters earn altogether? NH09S07 2010 9.
1 3
2
of the price of a pair of soccer boots is the same amount as of the price of a soccer 5
ball. What is the ratio of the price of the soccer ball to the price of the pair of soccer boots? AT10C04 1
1
10. of the length of Stick A is the length of Stick B. If Stick A is 20 cm longer than Stick B, 4 2 find the total length of the 2 sticks. NH10S01 𝟏
𝟑
𝟒
𝟓
11. of the length of a blue ribbon is equal to of the length of a green ribbon. If the
length of the green ribbon is 24.75 m, find the length of the blue ribbon. PC10P08 𝟑
𝟏
𝟓
𝟒
12. Kiran and Amirun had $12 650 together. Kiran spent of his money and Amirun gave
of his money to his wife. They found that they had the same amount of money left. (a) How much did Kiran have at first? (b) What is the ratio of Kiran’s money to Amirun’s money at first? Express your answer in its simplest form. RY10C12 𝟏
𝟑
𝟓
𝟕
13. After saving for a month, of Heidi’s savings was equal to of Joseph’s savings. After Heidi spent $356 and Joseph saved an additional $428, they had an equal amount of money in their savings. How much did Heidi and Joseph save altogether in the end? RG10S13 2011 𝟐
𝟑
14. of Ali's story books was the same as of Raju's story books. 𝟑 𝟓 (a) Who had more story books? (b) If Ali had 100 fewer books, how many books would Ali have? MG11S06
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PSLE Math Series
6.1 6.2 6.3 6.4 6.5 6.6
Unit 6 Percentage
Logical Problems Unit/Model Method More Than Change Concept Remainder Concept Equal Parts pslemathseries.com
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PSLE Math Series
Unit 6.1 Percentage Four Operations
2007 1. The table below shows the statistics of a town’s population. However, some data has been accidentally deleted. Population 40000 Below 15 years old 15 – 64 years 65 years and over (Elderly) 5500 Support Ratio 6 (Number of Residents Aged 15 – 64 Years Per Elderly Resident) What percentage of the citizens in the town are below 15 years old? NY07P37 2. Jerry filled a 10-litre jar with syrup. He then poured out 1 litre of the syrup from the jar and filled the jar with water. After that, he poured out 1 litre of the mixture from the jar and refilled the jar with water. Lastly, he poured out another 1 litre of the new mixture from the jar and refilled the jar with water. What is the percentage of the syrup in the jar now? PH07S46 2008 3. The usual selling price of a TV set is $3000. At a sale, it is sold at a 20% discount. Ben pays for it in 12 monthly instalments which include an interest rate of 5% per year. (a) How much does Ben have to pay for each monthly instalment? (b) For cash payment, a further 5% discount is given based on the discounted price. If the delivery charge is $40, how much would the total payment in cash be? NH08S47 4. At a practice, a netball player threw the ball at the net 100 times. For the first 70 throws, the ball went into the net 2 times out of every 5 throws. For the remaining throws, she managed to score 80% of the throws. How many times did the ball miss the net? MG08P42 5. Mr Tan sold golf balls in packs of five. The original selling price of each pack of golf balls was $20. He sold 60% of his golf balls at $20 per pack and the rest at a discount of 30%. He collected $1056 from the sale of all the golf balls. How many golf balls did he sell altogether? HK08P44
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6. Of a group of 100 pupils, 60 pupils like to play badminton and 80 pupils like to play table-tennis. If 50 pupils like to play both badminton and table-tennis, what percentage of pupils like neither badminton nor table-tennis? NH08S40 7. Mr Ong wants to buy a computer priced at $1445. If Mr Ong makes a full payment, he will enjoy a discount of 8%. If he pays by instalments, no discount is given. He will then have to pay 10% of the selling price of the computer and 12 monthly instalments of $120 each. How much does Mr Ong save if he were to pay in full instead of paying by instalments? SN08C44 2009 8. Mrs Lim wanted to top up her car to full tank with $80 worth of petrol. The table shows the discounts given by 3 different petrol kiosks. Petrol Kiosk Discount X 12% discount Y $9 cash discount Z 15% discount Among all the petrol kiosks, only Petrol Kiosk X and Petrol Kiosk Y charge a 7% GST on its discounted price. (a) Which petrol kiosk offered the best discount? (b) If Mrs Lim were to go to the petrol kiosk which offered the best discount, how much would she save? SN09C13 9. The petrol tank of Su Min’s car was 70% empty. He went to a petrol station and topped up 25 litres of petrol. When he reached home, the petrol tank was 70% full. Given that he used 5 litres of fuel to get home from the petrol station, find the capacity of the petrol tank. AT09S09 2010 10. Harem scored 11.8 seconds for his shuttle run test. His teacher allowed him to re-take the test another two times. Harem’s second timing was 90% of his first timing. His third timing was 0.9 seconds less than his second timing. Find the total time that he scored for the three tests. Round off your answer to 1 decimal place. SN10C12 11. A Media Club consisted of 75 members. 32% of the members were boys. After some boys joined the club and some girls left the club, the club enrolment became 68, and the final number of boys was the same as the final number of girls. How many boys joined the club and how many girls left the club? SN10C14
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12. Mrs Lee paid $1337.50 for a washing machine and a coffee table, including 7% GST. If the washing machine cost $725 before GST, what was the cost of the coffee table before GST? AC10S01 13. Minah used 40% of the flour she had to bake a few cakes and 30% of it to bake some cookies. After that, she still had 360 g of flour left. How much flour did she have at first? RY10S03 14. Ashley paid $1200 for two LCD television sets during a clearance sale as shown in the diagram below. If he had not bought them during the sale, how much more money would he have had to pay for the two television sets? AC10S11
15. At a clearance sale, Ken purchased a model plane at $192.60, inclusive of 7% GST. How much GST did Ken pay? MG10P05 16. The original price of a blouse was $45. After getting a discount, Mrs Lee paid $36. Find the percentage discount. RG10S01 3
17. Express 1 as a percentage. NH10C02 8
2
18. of 80 km is the same as _____% of 320 km. RG10S05 5
19. At the Great Singapore Sale, Jennifer bought a handbag which was on a 30% discount off its original price. She paid $874.10 which was inclusive of a 7% GST on the discount price. What was the original price of the handbag? NY10P01 20. Susan went to buy some Christmas cards. She was given a 20% discount for the cards. With the discount she could buy 6 more cards. How many cards could she buy if there was no discount? RV10P01
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21. Find the capacity of the Moo Moo Milk in its new packaging. Express your answer in litres. MB10P02
2011 22. Mr Lee bought some T-shirts for $425. If he was given a discount of 15%, he would be able to buy 5 more identical T-shirts for the same amount of money. What was the original price of each T-shirt? AC11P09 23. What percentage of 3.2 m is 6 m? RY11S02 𝟑
24. In an examination, 92% of the candidates passed. 72 of the failures were boys and of 𝟓
the failures were girls. 1380 girls passed the examination. (a) What was the total number of pupils who sat the examination? (b) What percentage of the candidates who passed the examination were boys? MG11S17 25. Mega Electronic Store sold 200 MP3 players during a sale. 45% of them were sold at a discount of 40%. The remaining MP3 players were sold at a further 15% discount on the discounted price. (a) How much would a customer save if he bought the MP3 player at the discount of 40%? (b) Find the total amount received from the sale of the MP3 players. SN11S12
26. A departmental store was having a storewide discount of 20%. Samy bought a pair of jeans at $56. What was the original price of the pair of jeans? NH11S05
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27. Mdm Fatimah gave 8% of her monthly salary to charity. When her salary was decreased by $100, she continued to give the same percentage of her salary to the charity. If the charity received $248 monthly from Mdm Fatimah after the decrease in her salary, what was Mdm Fatimah's salary before the decrease? RS11S10 28. At a sale, the price of a computer was reduced by 40% to $1200. Find the original price of the computer. CH11S01 29. The usual price of a sari was $298. After a discount, the price of the sari became $253.30. What was the percentage discount for the sari? NY11C03 30. If 5% of a sum of money is $80, find the value of 80% of the money. NH11C05 31. The usual price of a skirt was $24. Before Christmas, it was sold at a discount of 40%. During the post-Christmas sale, the price of the skirt was further reduced by 15% on the discounted price. How much was the skirt during the post-Christmas sale? SN11C04 32. A bag is sold at $120 after a discount of 20%. What is the original cost of the bag? CH11P01 33. Ashley paid $102.72 for a dress inclusive of 7% G.S.T. How much was the G.S.T.? RG11S05 34. In a survey, some pupils were asked if they preferred volleyball or table tennis.
𝟏𝟑
of
𝟐𝟎
the pupils chose volleyball, 75% of the pupils chose table tennis and 5% of the pupils did not choose any of the two sports. Given that 90 pupils chose volleyball and table tennis, how many pupils took part in the survey? AT11C11 35. A shopkeeper bought a handbag for $360. What is the selling price of the handbag so that he can allow a discount of 10% of the selling price and yet earn 10% on the cost price? NH11P09 36. Shop A sold a laptop for $1200. This was 125% of the price of a similar laptop sold in shop B. (a) Find the price of the laptop in Shop B. (b) During a sale, both shops offered the same percentage discount. Aishah bought the laptop from shop B and found that she paid $175.20 less than the discounted price in Shop A. What is the percentage discount given during the sale? RG11S15
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PSLE Math Series
Unit 6.2 Percentage Unit/Model Method
2007 1. A tank is 36% filled with water. If 75% of the water in the tank is poured out and 364 cm3 of water is poured in, the tank is filled to the brim. What is the volume of the tank? NY07S37 2. 60% of the pupils in a training camp wore spectacles. 80 of these pupils were boys and 𝟏
the remaining were girls. 12 girls in the training camp did not wear spectacles. What 𝟑
percentage of the total number of pupils in the camp were boys who did not wear spectators? RY07S42 3. Gerald used 60% of his money to buy 12 buns and 3 curry puffs. Each curry puff cost twice as much as a bun. How many curry puffs could he buy with the rest of his money? NY07C38 4. Ann, Ian and Kelvin went shopping together. They brought a total of $580 with them. Ann spent 20% of her money. Ian spent $30 and Kelvin spent twice as much as Ann. At the end, they had $370 left. How much money did Ian and Kelvin have together at first? AT07S48 2008 5. At a furniture store, the price of a computer set is 20% that of a sofa set. Miss Lim bought a computer set and a sofa set and was given a 30% discount on both items. She paid a total of $2730 for them. (a) What was the price of the sofa set before discount? (b) What was the price of the computer set after discount? RS08P46 6. Teddy saves 80% as much as Meifen and Roy saves 30% as much as Teddy. Meifen uses 16% of her savings to buy 8 similar pens. Each pen costs $4. How much does Roy save? MB08P47 7. Celine, Devi and Fatimah shared some ribbons. Celine received 20% of the ribbons. The rest of the ribbons were shared between Devi and Fatimah in the ratio 13 : 7. If Devi received 48 ribbons more than Fatimah, how many ribbons did Celine receive? TN08S42
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8. Mr Tan gave some marbles to Andy, Benny, Calvin and Dave. Andy received 180 marbles. Benny received 80 fewer marbles than Calvin. Calvin received 30% of the total number of marbles given by Mr Tan. Dave received 20% of the total number of marbles given by Mr Tan. How many marbles did Benny receive? AC08S47 9. Harry, Rebecca and Mark receive a sum of money each month as pocket money. Harry has $120 more pocket money than what Rebecca has. Mark has 80% as much as what Harry has. Mark has $40 more than Rebecca. (a) How much does Rebecca have as pocket money each month? (b) If Rebecca saves 15% of her pocket money each month, at least after how many months would she be able to save enough to buy an MP4 player which costs $484? RS08S45 2009 10. A, B, C and D are four numbers. A is 25% of B, C and D. B is 60% of C. D is 50% of B and C. (a) Find the ratio of A : B : C. (b) Express A as a percentage of C. NH09C16 11. A Spaceship Lego set costs $80 more than a Tommy train set at a toyshop. During its anniversary, a storewide 20% discount was given to all customers. In addition, members of the toyshop enjoy an additional 10% discount. Mr Tan, a member of the toyshop, paid a total of $345.60 for the Spaceship Lego set and the Tommy train set. Calculate the original price of the Spaceship Lego set. CH09P16 12. Bryan had 50% as many stickers as Alvin. After Bryan gave away 30% of his stickers and Alvin gave away 75% of his stickers, they had 90 stickers left altogether. How many stickers did Alvin have at first? CH09P08 13. Amelia has a stamp collection. 60% of them are Japanese stamps and the rest are Korean stamps. She gave away 63 Korean stamps and 25% of the Japanese stamps. 𝟓
She then had of her stamp collection left. How many stamps did Amelia give away? 𝟖
RS09P15 14. There were ducks, goats and hens at a farm. 15% of the animals were ducks. There were 180 fewer ducks than hens. The remaining 121 animals were goats. What percentage of the animals at the farm were goats? Leave your answer correct to 2 decimal places. SN09S14
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15. At an enrichment camp, the number of boys was 45% of the number of girls. When 20% of the boys left the camp, there were 192 more girls than boys. How many children were at the camp at first? PL09P13 16. At a fashion school, 70% of the models were Singaporeans and the rest were Malaysians. 2
75% of the Singaporean models and of the Malaysian models were female. If there 3
1200 models at the fashion school, how many male models were there at the school? HK09P16 2010 17. Cecilia had 100 less stamps than Usha. Rahim had 350 stamps. Usha had 30% of the total number of stamps the four friends had. George had 20% of the total number of stamps of the four friends. How many stamps did Cecilia have? RY10P10 18. Mr. Yeo gave 25% of his monthly salary to charity. When his salary was increased by $300, he continued to give the same percentage of his increased salary to charity. (a) How much more money did Mr. Yeo give to charity after the salary increment? (b) If the charity received $575 from Mr. Yeo after the increase in his salary, what was Mr. Yeo’s salary before the increment? NH10P14 2011 19. Donavan, Ethan, Freddy and Gilbert shared some trading cards. Donavan received 20% of all trading cards. Ethan received 48 fewer trading cards than Donavan. Freddy received twice as many trading cards as Ethan and Gilbert received the remaining 432 trading cards. (a) Find the total number of trading cards shared by the 4 boys. (b) If Donavan was given additional trading cards, he would have a total 487 trading cards. Find the percentage increase in the number of trading cards Donavan has. SN11P15 20. Raju has solved 260 Math problems to prepare for his mid-year examinations. He planned to finish the rest of the Math problems in the next 6 days by solving the same number of Math problems each day. If he completed 32% of the Math problems in the next 4 days, how many Math problems would he have solved altogether? RY11S07 21. May received 55% of the votes of her class to become Class Captain. If May received 4 more votes than the other candidate, what was the total number of votes? AC11S04
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22. I have some red and blue ribbons in a bottle. If I add in 20 red ribbons, 60% of my ribbons are blue. If I add in another 60 blue ribbons. 75% of my ribbons are blue. How many ribbons have I in the bottle? NH11C07 23. Darren and Yenni both had a mango stall. On a particular day, Darren sold 85% of the number of mangoes Yenni sold. If both of them sold 555 mangoes altogether, how many more mangoes did Yenni sell than Darren? SN11C15 24. Vanessa used some colored beads to make a bag. 44% of the beads were red and the rest were either blue or yellow. The ratio of the number of blue to yellow beads used was 3 : 5. If she used 46 more red beads than blue bead, how many beads did she use in all? AT11C16 25. There were some pens and pencils in a box. When Ali took out 24 pencils, there were five times as many pens as pencils left. If he had taken out 60% of the pens from the box instead, he would have twice as many pencils as pens left. How many pens were in the box at first? TN11S11
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PSLE Math Series
Unit 6.3 Percentage More Than
2007 1. Mrs Yeo had 60% more books than Mdm Lim. Miss Tang had 25% fewer books than Mrs Yeo. Mrs Yeo and Mdm Lim gave Miss Tang some books in the radio 3 : 1. As a result, Miss Tang had 1.5 times as many books as before. Given that Mrs Yeo had 240 more books than Mdm Lim in the end, how many books did Mrs Yeo give to Miss Tang? NY07S45 2. Baker Tan baked some cookies to sell. She baked 10% of the cookies on the first day. On the second day, she baked 25% more than on the first day. She baked 9 more cookies on the third day than on the second day. By then, she had baked 50% of the cookies. How many cookies did she bake in all? PH07S44 3. Mr Tan earned a fixed monthly salary in the year 2005. In November, he spent 25% of his monthly salary. In December, he spent 40% more than what he spent in November. (a) If his total expenditure for the 2 months was $960, what was his salary in November 2005? (b) If Mr Tan received a 5% increase in pay in the year 2006, what would be his new monthly salary? NH07S47 4. Mrs Heng sold some comic books from Monday to Sunday. On Saturday, she sold 20% more than the average number of comic books sold in a week. On Sunday, she sold 30% more than the average number of comic books sold in a week. She sold 18 more comic books on Sunday than on Saturday. (a) How many comic books were sold from Monday to Friday? (b) Each comic book was sold at $3.60. How much money was collected from Monday to Friday? PH07P48 5. When a train departed from Somerset Station, 24% of the passengers were children while 75% of the adults were men. There were 25% more girls than boys, and 114 more men than women. At Orchard Station, 9 women and 3 girls left the train. How many female passengers were on board the train when it departed from Orchard Station? RG07S46 pslemathseries.com
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6. John had 80% more money than Lily. Kevin had half of what John had. When Lily gave $320 to Kevin, both of them had the same amount of money. (a) How much did Kevin have at first? (b) If John gave 40% of his money to his parents, how much money had he left? NH07C44 7. Stephanie and Tanya shared $64 between themselves. When their mother gave them another $10 each, Tanya had 32% less money than Stephanie. (a) How much money had Tanya in the end? (b) What was the ratio of Tanya’s money to Stephanie’s money at first? Give your answer in the simplest form. PH07S45 8. Azman had 25% more marbles than Chongfu. Chongfu had 60% more marbles than Bala. During a game, Azman and Bala lost some marbles to Chongfu in the ratio 3 : 1. In the end, Azman and Bala had 780 and 480 marbles left respectively. How many marbles did Azman have at first? NY07P46 2008 9. Derek, Javier and Alex shared a cash prize of $1800. Derek received 25% of the prize while Javier received 20% less than what Derek got. (a) How much money did Alex receive? (b) If Alex spent 30% of his share on an iPod, how much money had he left? MB08C45 10. Marcus had 50% more stamps than Gina. Marcus gave away half of his stamps and had 750 left. How many stamps did Gina have? NH08C36 11. Kelly bought a dress which cost 10% more than a scarf. She bought 4 scarves for $180. A blouse cost 30% less than a dress. How much did she pay for the blouse? TN08S44 12. At a concert, 30% of the audience were children. The number of men was 10% more than the number of children. There were 222 women at the concert. How many people attended the concert? AC08S44 13. Sweetie Shop sold fruit candies, milk candies and mint candies. 43% of them were fruit candies and 228 were milk candies. There were 50% fewer milk candies than mint candies. How many per cent more fruit candies than milk candies were there? Leave the answer correct to the nearest percent. SN08S43 14. Patty earns 12.5% more than Tanny. If they earn $1156 altogether, how much does Patty earn? NH08P40
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pslemathseries.com 15. Oliver earns a fixed monthly salary. In November, he saved 40% of it. In December, he
saved 75% more than what he saved in November. His total savings for the two months in $979. (a) What is his monthly salary? (b) How much more money did he spend in November than in December? MB08S47 16. The line graph below shows the number of visitors at the zoo from Monday to Saturday. (a) If each visitor paid $12 for a ticket, how much money was collected on weekdays? (b) The number of visitors who visited the zoo on Sunday was 30% more than the number of visitors on Friday. What was the difference in the number of visitors between Saturday and Sunday? NY08C43
17. Alvin, Beth and Caleb had some marbles in the ratio 3 : 1 : 4 respectively. Caleb gave 40% of his marbles to Alvin and Beth. As a result, Alvin had 90 more marbles than Caleb and Beth had 70% more marbles than before. (a) What was the percentage increase of Alvin’s marbles after receiving marbles from Caleb? (b) How many marbles did Caleb have at first? AT08C48 2009 18. The mass of Mr Smith is 40% more than that of Mrs Smith’s. Their son, Kaeden’s mass is 40% less than that of Mrs Smith. If Mrs Smith is 24 kg heavier than Kaeden, what is Mr Smith’s mass? RS09S11
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19. The graph below shows the sales of bags in a shop from January to June.
If the shop owner wants the sales in the second half of the year (Jul to Dec) to be 25% more than the sales in the first half of the year (Jan to Jun), how many bags must he sell in the second half of the year? SC09S06 2010 2
20. In 2008, Rochelle received a monthly salary of $7767 for years. For the rest of the year, 3
her salary was $6850 per month. In 2009, the total salary that she received for the whole year was 30% less than the total salary that she received in 2008. How much was her total salary in 2009? SN10C10 21. Georgette and her friends were assigned to fold paper stars in three weeks’ time. In the first 11 days, they folded 70 paper stars on each day. In the next 6 days, they folded 20% less than the total that they had folded in the last 11 days. If they still had 108 paper stars to fold per day for the remaining number of days, how many paper stars were they assigned to fold altogether in three weeks’ time? SN10C17 22. Amos’ salary is 20% more than Steve’s but 20% less than Joe’s. If their total salary is $2220, find Amos’ salary. NH10C07 23. Alfie and Ken went to a book shop. Alfie bought 3 story books at $4.80 each and a dictionary at $25.60. He spent 25% more than Ken. Ken bought only comics at $6.40 each. How many comic books did Ken buy? AT10C09 24. John had $180 more than Raymond at first. Both bought a different printer with some of their money. In the end, Raymond was left with $20 more than John. If John’s printer cost 50% more than Raymond’s printer, how much does John’s printer cost? CH10P11
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25. Daniel had 40% more stickers than Brandon. Daniel and Brandon each gave 20% of their stickers to Calvin. As a result, Calvin’s stickers increased by 80%. If Daniel has 20 more stickers than Calvin in the end, how many stickers did Brandon have at first? CH10P17 26. Gerry had some green, red and blue beads. She had 25% more green beads than red beads, and 20% less blue beads than green and red beads. (a) What was the ratio of red beads to green beads to blue beads? (b) If there were 11 more blue beads than green beads, how many red and green beads were there? MG10P15 27. Yanling had 60% more stamps than Lena. Tricia had 75% fewer stamps than Yanling. Yanling and Lena gave Tricia some stamps in the ratio 4 : 1. As a result, Tricia had 2
𝟏 𝟐
times as many stamps as before and Yanling had 300 stamps more than Lena in the end. How many stamps did Lena give to Tricia? HK10P16 2011 28. Judy earned a fixed salary every month. In January, she spent 30% of it. In February, she spent 40% more than what she spent in January. If she spent a total of $1350 for the two months, what was her monthly salary? RY11S09 29. In a fruit basket, there are 2 more oranges than apples. The number of oranges is 25% more than the number of apples. How many fruits are there in the basket? RS11S04 30. 3750 people visited the carnival on Tuesday.
The number of tourists who visited the carnival on Tuesday was 25% more than the number of tourists on Monday.
How many people visited the carnival over the two days? RG11S02 31. Katelyn had some green, red and blue ribbons. She had 25% more green ribbons than red ribbons and 20% less blue ribbons than red ones. (a) What is the ratio of red ribbons to green ribbons to blue ribbons? (b) Katelyn exchanges all her blue ribbons for some red and green ribbons. She now has an equal number of red and green ribbons. How many more green than red ribbons did she have at first if she has 244 red ribbons now? RS11P10 32. Mr Yeo always gives 80% of his money to his wife. However, his income for this month was 35% less than last month. As a result, the amount of money he gave to his wife decreased by $175. What was his income last month? NH11C12
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33. In a boutique, the number of dresses sold was 70. This was 40% more than the number of blouses sold. How many blouses were sold? AT11C02 34. Owen has 20% more marbles than Danny. Danny has 40% less marbles than Connie. Owen has 21 marbles less than Connie. How many marbles does Danny have? CH11P03 35. Daphne had 20% fewer books than Jocelyn. Yan Ming had 8 more books than Jocelyn. If Jocelyn were to give 4 books to Daphne, they would both have an equal number of books. (a) How many books did the 3 girls have altogether? (b) Yan Ming went to buy some new books. The new ratio of books that Yan Ming had to the ratio that Jocelyn had then became 3 : 2. How many new books did Yan Ming buy? AC11S17 36. Bemie and Ahmad shared the cost of a meal. Bemie paid $15. If Bemie paid $2 less, Ahmad would have had to pay 20% more. What was the cost of the meal? MG11S03 37. Michelle had 60% more cards than Adila. Usha had 35% fewer cards than Michelle. Michelle and Adila gave Usha some cards in the ratio of 3 : 1. As a result, Usha had 1
𝟏 𝟐
times as many cards as before. Given that Michelle had 238 more cards than Adila in the end, how many cards did Michelle give to Usha? RY11P16 38. Kumar had 50% more bookmarks than Leon. Max has 75% as many bookmarks as Kumar. Kumar and Leon gave Max a number of bookmarks in the ratio 3 : 1. As a result Max had twice as many bookmarks as before. And Leon had 16 bookmarks more than Kumar. How many bookmarks did Kumar give to Max? AT11S17
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PSLE Math Series
Unit 6.4 Percentage Change Concept
2007 1. In a club, the number of men increased by 20% to 600 and the number of women decreased by 20% to 600. (a) Find the number of men in the club at first. (b) What was the overall increase or decrease in the total membership of the club? PH07S38 2. Valley Department Store sold a dress for $585. This was 17% more than the price of a similar dress in Wiki Department Store. During a sale, both stores offered the same percentage discount on the dress. Christine bought the dress in Wiki Department Store and found that she paid $68 less than the discounted price in Valley Department Store. (a) Find the price of the dress in Wiki Department Store before the sale. (b) What is the percentage discount given during the sale? RG07P48 3. Mr Yeo earned a monthly salary of $3000 which was 20% more than the monthly salary of Mr Poon. (a) What was Mr Poon’s monthly salary? (b) When both Mr Yeo and Mr Poon’s monthly salaries were increased by the same percentage, Mr Yeo would earn $590 more than Mr Poon. What was the percentage increase in their salaries? NY07P39 4. In a shop, different customers were given different discounts. Mr Tan paid $280 for a hand-phone at a discount of 20%. However, Mr Chen paid $301 for a similar hand-phone. Want was the percentage discount given to Mr Chen? PH07P36 5. During a sale, a departmental store offered a storewide discount of a certain fixed percentage. MrsGoh paid $16 for a dress during the sale and saved $4. (a) What is the percentage discount? (b) How much did MrGoh save if he paid $20 for his purchases during the sale? MB07P42
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6. Marvin bought a box of fruits. 30% of the fruits are apples and the rest oranges. He realized that half of the apples were rotten and threw them away. He then bought some oranges and the number of oranges increased by 40%. After that, he found out that there were 52 more fruits in the box. How many fruits were there in the box at first? AC07P44 7. In July, Pauline spent 20% of a sum of money on tuition, 60% on food and saved the rest. In August, the sum of money was increased by 15%. She spent the same amount of money on tuition but increased her savings by 30%. She saved $390 in August. (a) How much money did she spend on tuition in July? (b) How much did she spend on food in August? PC07P(2)47 2008 8. From January to February, a salesman’s monthly income increased by 20%. However, from February to March, it decreased by 25%. If his income in March was $450 less than his income in January, what was his income in February? MG08C47 9. In an office, the number of male workers increased by 20% to 96, and the number of female workers decreased by 30% to 84. (a) Is there an overall increase or decrease of workers? (b) Find the overall increase or decrease in the total number of workers. NY08P44 10. During a sale, a departmental store offered a storewide discount of a certain fixed percentage. Mr Ishak paid $36 for a shirt during the sale and saved $9. (a) What was the percentage discount? (b) How much did Mr Ishak save in all if he paid a total of $96 for all his purchases during the sale? MB08C46 11. The ratio of Father’s mass to Mother’s mass is 5 : 2. If Father’s mass decreased by 20%, by what percentage should Mother’s mass be increased so that their total mass is the same as before? SC08S39 12. Mr Muthu gives 30% of his salary to his father every month. This month, there is a 6% increase in his salary. Hence, the sum of money he gives to his father increases by $81. (a) How much did he give to his father last month? (b) What is his salary for this month? RY08P46 13. The amount of sales in Sports Store had increased by 30% in April 2008 as compared to March 2008. However, the amount of sales decreased by 10% in May 2008 as compared to the amount of sales in April 2008. The difference in the amount of sales between March 2008 and May 2008 was $7650. What was the difference in sales between April and May 2008? AC08P46
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14. Mr Koh spent $560 in March which was 35% of the salary he earned for that month. He saved the rest of his salary. In April, his salary increased by 40%. If he spent the same amount in both March and April, what percentage of his salary did he save in April? RS08S38 15. The ratio of men to women in an auditorium is 7 : 8. There was a 15% increase in the number of women after 60 women entered the auditorium. What was the total number of men and women in the auditorium at first? RY08S41 2009 16. Zen always saves 20% of his salary. When his salary is increased by 5%, his savings increases by $22. How much is his new salary? NH09C13 17. Chris had a sum of money. He spent 70% of it on a house and the rest on a car. One year 1
later, the value of the house increased by of the original value, while the value of the 7
car decreased by 25%. Chris then sold both his house and his car at these values and found that he had $10 000 more than the original sum of money he had at first. How much did he spend on the car? AT09S16 18. In September, Rafael received a monthly salary of $2698 and she saved 20% of it. In December, her salary was reduced by 5% and she continued to save 20% of her salary. How much less was her savings in December compared to that in September? Leave your answer correct to the nearest dollar. SN09S10 19. Dan and Ella shared a sum of money. When Dan’s share increased from $500 to $605, the amount Ella received decreased by 15%. How much did Ella receive at first? RG09S06 20. 65% of the animals on a farm were cows and the rest were goats. When 240 more cows and goats were added to the farm, the percentage of cows increased by 20% and the number of goats doubled. How many goats were there on the farm at first? AC09P17 21. There were 1260 pupils in a school at the beginning of the year. The ratio of the number of Chinese pupils to Malay pupils to the other races was 5 : 4 : 3. In the middle of the year, 273 pupils joined the school and the percentage of Chinese pupils increased by 28%. The number of Malay pupils and the number of pupils of other races increased by an equal number. (a) How many Chinese pupils joined the school at mid-year? (b) By what percentage was the number of Malay pupils increased? HP09S14
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2010 22. A man saves 20% of his income. If his income is increased by 15%, his savings is increased by $24. Find his income. NH10C06 23. The price of a blouse is decreased by 20% to $60. What was the original price of the blouse? NH10S02 24. Sanjay has a box of 55 blue, yellow and red marbles in the ratio of 4 : 2 : 5 respectively. He puts 20 more marbles into the box. As a result, the number of blue marbles increased by 25% and the number of the yellow marbles is increased by 50%. (a) How many red marbles has he in the end? (b) How many percent more red marbles than blue marbles has he in the end? AT10S16 25. Robert always spends 60% of his monthly income. His income in August was less than that in July. As a result, his expenditure in August decreased by $1134. (a) If his expenditure in July was $2520, what was the percentage decrease in income in August? (b) If Robert’s expenditure in September was $756 more than his expenditure in August, what was the ratio of his income in September to his income in July? NY10S18 26. At Bedok MRT station, there were 420 commuters on a MRT train. There were 16% more children than men and 36% fewer women than men on the train. At the next station, 46 commuters alighted the train and 135 commuters boarded the train. The number of men in the train increased by 50% and the number of children decreased by 𝟏 . What was the percentage increase in the number of women? RS10P18 𝟑
27. Miss Flora had tulips, roses and carnations in her shop. In July, she sold a total of 1350 tulips, roses and carnations, of which 30% were tulips. There were as many roses as tulips sold. In August, the sale of carnations increased by 45%. This made up 27% of the total sales of tulips, roses and carnations. What is the percentage increase in the total sales of tulips and roses from July to August? (Leave your answer correct to 2 decimal places.) SN10P16 28. Old MacDonald had a total of 840 chickens and ducks in his farm. 65% of them were chickens and the rest were ducks. After selling 300 chickens and ducks altogether, the percentage of chickens was reduced to 55%. How many ducks did he sell? RY10S10 29. A fan club had 150 members last year. This year, the number of male members reduces by 20% and the number of female members increases by 20%. As a result, there are now as many male members as female members. How many members does the club have this year? NH10S16
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30. The number of balls in Box A is of the number of balls in Box B. 2 10% of the balls in Box A and 10% of the balls in Box B was moved to Box C. As a result, the number of balls in Box C increased by 20%. There are 72 balls in Box C now. How many balls were there in Box B at first? RG10S16 2011 31. The length of a rectangle is increased by 25% and its breadth is increased by 30%. What is the percentage increase in its area? NY11S09 32. The number of members in a stamp-collectors club increased by 40% from March to April. However, the number of members dropped by 25% from April to May. If the difference in the number of members between March and May were 9, how many members were there in May? AC11S10 33. The ratio of the number of ducks to the number of geese on Farmer Zhou’s farm was 5 : 6. When Farmer Zhou acquired 242 more ducks, there was an overall increase of 40% of the total number of ducks and geese he had at first. (a) How many ducks and geese were there on Farmer Zhou’s farm at the end? (b) What was the percentage increase in the number of ducks on Farmer Zhou’s farm? AC11S18 34. Cindy had four times as many postcards as Annie. After Cindy gave 20% of her postcards to Jane and Annie gave 10% of her postcards to Jane, the number of Jane’s postcards increased by 75%. Jane had 252 postcards in the end. How many postcards did Cindy have at first? NH11S16 35. Peter’s Mathematics score for the mid-year examination was 76. His Mathematics score for the year-end examination was 95. Find the percentage increase in his Mathematics score. NY11P03 36. Wendy’s first test score was 80. Her second test score was 95. Find the percentage increase in her score. NH11C01 37. The ratio of Jamal’s mass to Kathy’s mass is 4 : 5. Jamal’s mass is increased by 40% and Kathy’s mass is decreased. What percentage of Kathy’s mass must be decreased so that their total mass remains the same? TN11S12 38. Ken and Sam share some marbles. The ratio of the number of marbles Ken has to the number of marbles Sam has is 5 : 3. If Ken’s marbles increases by 15%, what percentage of Sam's marbles must be
decreased so that the total number of marbles they have remained unchanged? CH11P08
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PSLE Math Series
Unit 6.5 Percentage Remainder Concept
2008 1. Freddy took out 0.3 of his money from his savings box. He spent 0.75 of it and had $48 left. He put the money back into the savings box. His grandmother then gave him $31 to put into his savings box. How much money was there in his savings box finally? MB08C41 2. Jaffa gave 60% of his marbles to his brother and 25% of the remainder to two friends. Each of his friends received 30 marbles. How many marbles did his brother receive? NY08C39 3. Mrs Ang bought some cookies. She gave 30% of the cookies to her niece and ate 40% of the remaining cookies. If she had 42 cookies left, how many cookies did she buy? MB08P37 4. Mrs Sharpe had some doughnuts. She gave 20% of the doughnuts and another 8 more to Mrs Ekis. After she gave 25% of what was left behind to Mrs Ufron, Mrs Sharpe had 9 doughnuts left for herself. How many doughnuts did Mrs Sharpe give away in all? SN08S39 5. Mr Yong bought 1 500 pens. He sold 30% of them at $2.50 each and 80% of the remainder at a discount of 12%. (a) What was the selling price of a pen after the discount? (b) Mr Yong sold the rest of the pens at cost price and earned $1038. What was the cost price of each pen? RG08S46 6. Joyce gave $480 of her monthly salary to her mother. She gave 30% of the remainder to her father. Altogether, she gave 58% of her monthly salary to her father and mother. She saved 20% of her monthly salary. (a) What percentage of her monthly salary did she give to her father? (b) How much did she save? RY08S44 2009 7. Michael spends 25% of his monthly allowance on transport. He spends 60% of the remainder on food and saves the rest. What percentage of his monthly allowance does he save? RS09P08
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8. A school library had only English, Chinese and Malay books. 55% of the books were English books. 20% of the remainder was Malay books and the rest were Chinese books. The number of Malay books was 432 less than the number of Chinese books. Find the total number of books in the library. NY09S08 9. June, Mei and Andrea made tarts to sell at a fun fair. June made 20% of the tarts. Mei made 30% of the remaining tarts. Andrea made the rest of the tarts. June and Mei made an average of 264 tarts each. The tarts were sold in a box of 30 and each box was sold at $12. How much would they collect from the sale of all the tarts? SC09S12 10. James spends 20% of his monthly income on transport, 30% of it on food and 10% of the remainder on clothes. He saves the rest of his income. If his monthly savings is $900, find his monthly income. AT09C11 2010 11. Mrs Kumar spent 25% of the class funds on photo-copying notes for the pupils. She spent 40% of the remaining amount on art materials. How many percent of the class fund was left? PC10P06 12. George had some trading cards. He gave 75% of them to Mary and 20% of the remainder to Charlie. He then had 140 trading cards left. (a) How many trading cards had George at first? (b) How many percent more trading cards did Mary receive than Charlie? RY10S14 13. John had a sum of money. On Monday, he spent 25% of his money. On Tuesday he 𝟏
spent of his money. On Wednesday, he spent 25% of what he spent on Monday and 𝟑 Tuesday. If he had $39 left, how much did he have at first? RG10S11 2011 14. Henry spends 35% of his salary on transport. Of the remainder, he spends $500 on food, 40% on rent, 16% on miscellaneous items and he saves the rest. If he earns $4 500 every month, how long will he take to save enough to buy a computer which costs $1650? MG11P07 15. 20% of the people who attended a party were children. 45% of the adults were men. There were 240 more men than children. How many women were at the party? MG11S13
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PSLE Math Series
Unit 6.6 Percentage Equal Parts
2007 1. There are some oranges in 3 boxes, A, B and C. 40% of the number of oranges in Box A is equal to 25% of the number of oranges in Box B. The number of oranges in Box C i s
𝟏 𝟑
of the number of oranges in Box B. (a) Express the number of oranges in Box C as a fraction of the number of oranges in Box A. 𝟏
(b) If of the oranges in Box B are taken out and placed in Box C, there will be 36 𝟐
oranges left in Box B. How many oranges are there in Box C? (c) What is the total number of oranges? NH07P48 2008 2. There are some pears in three baskets, A, B and C. 40% of the number of pears in Basket A is equal to 25% of the number of pears in Basket B. The number of pears in 𝟏
Basket C is of the number of pears in Basket B. 𝟑
(a) Express the number of pears in Basket C as a fraction of the number of pears in Basket A. 𝟏
(b) If of the pears in Basket B are taken out and placed in Basket C, there will be 36 𝟐
pears left in Basket C. How many pears are there in Basket A? SC08S48 3. Fatimah and Choo Seng have some stickers. 40% of Fatimah’s stickers is equal to 25% of Choo Seng’s. Choo Seng has 120 stickers more than Fatimah. How many stickers does Fatimah have? RG08P39 2010 4. 30% of Joe’s sum of money is 50% of Kim’s sum of money. If Kim has $72, how much money has Joe? NH10C05 5. Adam and Eve each have some magazines. 40% of the number of magazines Adam has is equal to 20% of the number of magazines Eve has. If Eve has 20 more magazines than Adam, how many magazines does Eve have? MG10S02
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6. There are some boys and girls in the indoor sports hall. of the number of boys in the 2
indoor sports hall is the same as 60% of the number of girls. If there are 25 more boys than girls in the indoor sports hall, how many children are there altogether? RG10P02 7. Joanne and Tomomi bought the same bag from the same shop when they went 𝟐
shopping together. Joanne spent 75% of her money on the bag and Tomomi spent of 𝟑
hers. What percentage of their total sum of money was the cost of a bag if the girls had $100 left altogether? (Round off your answer to the nearest tenth.) MB10P10 2011 8. Muthu, Ali and Bill shared a sum of money. 30% of Muthu's share was equal to 80% of Ali's share. Bill's share was 25% of Muthu's share. Ali had $185 more than Bill. (a) Find the total sum of money. (b) If Muthu gave Bill 55% of his share, what percent of Bill's share was Ali's share? Round off your answer to 1 decimal place. CH11P16
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Unit 7 Ratio
PSLE Math Series
7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8
Unit/Model Method Repeat Identity Constant Difference Unchanged Quantity Constant Total Total Value Changing Quantities Overlapping Shapes
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Unit 7.1 Ratio Unit/Model Method
PSLE Math Series
2007 1. A school bus can carry a total of 30 adults or 45 children. There were 84 adults and 50 children already seated in 5 school buses. How many more children can be seated in these 5 school buses? PH07C44 2. In a frog-leaping competition, for every two leaps made by a big frog, a small frog would have to leap thrice. In a 100-m race, the big frog leapt 50 times. (a) How many times did the small frog leap? (b) How many metres did the small frog move with each leap? MB07P45 3. A box contained some twenty-cent coins, some ten-cent coins and some five-cent 𝟑
coins in the ratio of 3 : 2 : 1 respectively. of the twenty-cent coins were taken out and 𝟓
replaced by the same number of five-cent coins. Then 120 ten-cent coins were taken out and replaced by the same number of five-cent coins. In the end, the ratio of the number of twenty-cent coins, ten-cent coins and five-cent coins became 6 : 5 : 19 respectively. (a) What is the total number of coins taken out of the box? (b) What is the total value of the coins taken out of the box? RY07S48 4. There were 81 passengers on a train. The ratio of the number of adults to the number of children was 7 : 2. Some boys alighted from the train and the ratio of the number of men to boys became 9 : 1. (a) If there were 27 women and 5 girls on the train, how many boys alighted from the train? (b) What was the new ratio of the number of adults to the number of children after the boys had alighted? NH07C47 5. In an auditorium, the ratio of the number of competitors to the number of noncompetitors is 8 : 5. The ratio of the number of male competitors to the number of 3
female competitors is 7 : 4. Given that of the non-competitors are males and there are 5
32 female competitors, how many males and females are there in the auditorium? AC07P47 pslemathseries.com
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6. Bryan, Henry and Daniel had some marbles. of the marbles belonged to Bryan. The 9
remaining marbles belonged to Henry and Daniel in the ratio 3 : 5. Given that Bryan had 161 more marbles than Henry, find the number of marbles belonging to Daniel. AC07S43 7. Packets of assorted candies were sold in 2 different sizes – standard and large. The large packet contained twice as many candies as the standard packet. In the standard packet, the ratio of the number of coconut candies to the number of strawberry candies was 4 : 5. In the large packet, the ratio of the number of coconut candies to the number of strawberry candies to the number of toffee candies was 1 : 2 : 3. A family bought 1 standard and 1 large packet. (a) What was the ratio of the number of coconut candies to the number of strawberry candies to the number of toffee candies? (b) The family ate 21 candies. As a result, the ratio of the number of coconut candies to the number of strawberry candies to the number of toffee candies became 2 : 3 : 3. How many candies were left?AT07S43 8. Bernard and Emily wanted to buy a birthday present for their mother with their savings. The ratio of Bernard’s savings to Emily’s savings was 3 : 4. Bernard and Emily shared the cost of the birthday present in the ratio of 2 : 3. 𝟏
Bernard used of his savings to pay for his share. Emily, after paying for her share, had 𝟐
$21 left. How much did the present cost? NH07S48 9. Alex, Benjamin and Charlie were given some funfair tickets to sell. Each ticket was sold 2
for $7. Alex sold of the tickets. Benjamin and Charlie sold the remaining tickets in the 3
ratio 1 : 2. Alex sold 40 more tickets than Charlie. How much money did the 3 boys collect altogether? NH07S44 10. The ratio of the number of guppies to the number of goldfish in Mr Chua’s pond was 2 : 3. When he added a total of 70 guppies and goldfish into the pond, the ratio became 4 : 3 and the number of guppies became 100. How many goldfish did Mr Chua add into the pond? PC07P(2)44 11. Ali, Bala and Krisnan went to a shopping centre and bought a present for their friend. They agreed to share the cost of the present equally but Ali did not have any money with him that day and Bala did not bring enough to pay for his share. As a result, the amount of money Bala paid to that paid by Krisnan was 1 : 4. The next day, Bala returned $12 to Krisnan. Find (a) How much money Bala brought along with him to the shopping centre and (b) the cost of the present. MB07P47
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2008 3
12. Mrs Lee had 140 stalks of flowers in her shop at first. of the flowers were roses while 7
the rest were orchids. She sold 15 roses and some orchids. As a result, the ratio of the number of roses left to the number of orchids in her shop became 9 : 14. How many orchids did she sell? AT08S41 13. At a fruit stall, the number of oranges is the same as the number of apples at first. 6 oranges and 14 apples were sold. As a result, the ratio of the number of oranges to the number of apples became 7 : 5. (a) How many apples were left? (b) How many fruits were there at first? AC08P48 14. The number of Carrie’s beads to the number of Sally’s beads was 2 : 8. Carrie then gave
1 3
of her beads to Sally. Finally, Sally gave 143 beads back to Carrie and they both had the same number of beads. How many beads did Sally have at first? RS08P39 15. Tom, Jerry and Daniel had some stickers. The total number of stickers Jerry and Daniel had was two times as many as Tom. The ratio of the number of stickers Jerry had to the number of stickers Daniel had was 3 : 5. Tom and Daniel had 180 stickers altogether. How many stickers did Tom have? RS08C39 16. In a pet shop,
3 10
of the animals are hamsters. The rest of the animals are birds and fishes.
The ratio of the number of birds to the number of fishes in 9 : 5. There are 360 more birds than fishes. (a) How many animals are there altogether? (b) How many more hamsters than fishes are there? RS08C46 17. There were 500 cubes and marbles in a container. The ratio of the number of cubes to the number of marbles was 7 : 18. After Candia took out 45 cubes from the container 4
and put in some marbles, of the objects in the container were marbles. 5
(a) How many cubes were left in the container? (b) How many marbles did Candia put in? RY08C48 18. Miss Ng had a total of 72 pens and pencils. There were 16 more pens than pencils. She gave away 12 pens and bought some more pencils. She then found that the ratio of the number of pencils to the number of pens became 9 : 8. How many pencils did she buy? SN08C45
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19. In a school, there are 1280 pupils. There are 120 more girls than boys. On a certain day, 20 boys and some girls went on an excursion. The ratio of the number of boys to the number of girls in school that day was 7 : 8. How many girls went on the excursion that day? MG08S47 20. The ratio of the amount of money in John’s savings account to the amount of money in Mohan’s savings account was 12 : 7. John and Mohan shared the cost of a computer set in the ratio 3 : 2. John used up 50% of his savings to pay his share for the computer set. Mohan had $1650 left in his savings account after paying for his share. What was the cost of the computer set? RS08S42 21. Xiaoling, Yoka and Zana each had some money. The ratio of the amount of money Xiaoling had to the amount of money Yoka had was 7 : 3 at first. Xiaoling lent $43 to Zana and Yoka borrowed $185 from Zana. In the end, Xiaoling had the same amount of money as Yoka. (a) How much money did Yoka have at first? (b) How much did Xiaoling and Yoka each have in the end? MG08P46 2009 22. Felicia and Hazel had badminton practice every day. The ratio of the number of hours Felicia practiced per week to the number of hours Hazel practiced per week was 9 : 4. Felicia practiced for 45 hours more than Hazel every week. Find the total number of hours they had badminton practice in 3 weeks. SN09C09 23. In a group of 1088 children, 256 are girls. The ratio of the number of boys who play the piano to the number of girls who do not play the piano is 11 : 3. If there are 192 girls who do not play the piano, express the number of boys who do not play the piano as a fraction of the total number of children who play the piano. SN09C12 24. The ratio of Jonathan’s weekly saving to Galton’s weekly saving is 8 : 5. If Jonathan saves a total of $288 more than Galton in two weeks, what is Galton’s weekly saving? (Assuming that Jonathan saves the same amount each week) NH09C07 25. Abbie, Ellen and Faheem sold umbrellas to raise funds for charity. Each umbrella was 1
priced at $22.50. Abbie sold of the umbrellas while Ellen and Faheem sold the 6
remaining umbrellas in the ratio 2 : 7 respectively. If Faheem sold 364 umbrellas more than Abbie, what was the total amount of money collected by them? SN09S13
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26. Mrs Wong has 2000 plants in her farm. 65% of the plants were orchids and the rest were roses. After some orchids were sold, and some roses were added, the percentage of orchids became 45% of the all the plants in the farm. Given that 125 roses were added, how many orchids did she sell? RY09P17 27. At Carpark P, the number of lorries to that of vans was in the ratio 3 : 7. At Carpark Q, the number of lorries to that of vans was in the ratio 8 : 9. When 40% more lorries from an industrial park entered Carpark P, and 20% of the vans at Carpark Q moved to Carpark P, there were 76 fewer lorries at Carpark P than at Carpark Q. How many vehicles were there altogether at the two carparks finally? SN09P17 3
28. Kathy sold of her school’s fund-raising tickets to her brother. She sold the rest of her 8
tickets to Michael and Raju in the ratio of 3 : 7. Find the ratio of the number of fundraising tickets Kathy sold to her brother to the number of tickets she sold to Raju. RY09C09 29. In 2008, the ratio of the number of boys to the number of girls in XYZ School was 5 : 3. In 2009, 455 students joined the school and there are now 3 times as many boys and 2 times as many girls as in 2008. How many children were in the school in 2008? RY09C11 2010 30. A sum of money was divided among Charles, Devi and Enoi in the ratio 2 : 3 : 4 respectively. Enoi received $60 more than Charles. What was the sum of money? HK10P01 31. A sum of money was shared between Jack and Jill in the ration 3 : 8. Jill gave half of her share to Jack. What is the new ratio of Jack’s share to Jill’s share? NH10C03 32. The ratio of the number of apples to the number of mangoes to the number of oranges is 7 : 6 : 4. If there are 828 more apples than oranges, how many mangoes are there altogether? SN10S05 33. Farmer Wong had a total of 6600 geese and turkeys. There were 780 more geese than turkeys. After selling 950 turkeys and buying some geese, the ratio of the final number of turkeys to that of geese was 1 : 3. How many geese did he buy? SN10S14 34.
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of the guests at a party are adults. The ratio of the number of boys to the number of
girls is 7 : 13. There are 330 more adults than girls. What is the total number of people at the party? NY10S07
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35. Mrs Tan had some red and blue balloons in a bag. The number of red balloons was twice the number of blue balloons. She started removing balloons from the bag, each time taking out 4 red balloons and 6 blue balloons. After a while, only 120 red balloons were left in the bag. What was the total number of red and blue balloons in the bag at first? HP10P17 36. The number of pens in Box X and Box Y are in the ratio 3 : 2. All the pens in Box Y are green. The ratio of green pens to blue pens in Box X is 4 : 5. There are 12 more green pens in Box Y than in Box X. How many blue pens are there? HK10P09 37. Three boxes A, B and C contain 50 marbles each. Some marbles are moved from Box A and Box B to Box C so that the number of marbles in Box A, Box B and Box C are in the ratio 2 : 3 : 5. How many marbles are moved to Box C? AT10C14 1
38. The ratio of the number of apples to the number of pears at a fruit stall is 4 : 5. After of 2
the apples is sold, there are 45 more pears than apples. How many pears are there? RY10C08 39. Janice had three boxes, A, B and C, containing a total of 1512 pearls. The number of pearls in Box A to the total number of pearls was 2 : 7. Janice sold 190 pearls from Box B 1
and sold of the pearls in Box C. The number of pearls left in Box B to the number of 4
pearls left in Box C was 2 : 1. How many pearls were there in Box C at first? RG10P14 40. Aimei, Bala and Carl won some money in a lucky draw. The amount of money won by Aimei, Bala and Carl was in the ratio 8 : 5 : 4. They saved some of the money and spent the rest. Aimei saved $480, Bala saved $540 and Carl saved $120. The amount of money spent by Aimei, Bala and Carl was in the ratio 8 : 3 : 5. (a) Find the ratio of the amount of money saved by Aimei to Bala to Carl. Give your answer in its simplest form. (b) How much money did Aimei win? PC10P12 3
41. There were some fruits in a warehouse. of them were apples and the rest were 7
1
oranges. After throwing away 27 apples and of the oranges that were rotten, there 3
4
were of the fruits left. 5
(a) How many fruits were thrown away? (b) How many apples were there at first? HP10P16
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42. A carton contained pears and apples in the ratio 9 : 4. The shopkeeper threw away 60 pears that were rotten. He then added 60 apples to the carton. As a result, there were an equal number of pears and apples in the carton. How many pears were left in the carton? AC10P06 1
43. Jack, Betty and Lynn shared the cost of a present. Jack paid of the total cost of the 3
present. The amount paid by Betty and Lynn is in the ratio 1 : 3. If the cost of the present is $30, how much did Betty pay? CH10P06 44. Jan and Kay had equal number of sweets and equal number of chocolates. Jan ate 12 sweets and Kay ate 18 chocolates and then the ratio of Jan’s sweets to chocolates became 1 : 7 and the ratio of Kay’s sweets to chocolate became 1 : 4. How many sweets did Jan have at first? NH10C12 45. Anna, Belinda and Clare bought a vase and shared the cost equally amongst themselves. Clare did not bring her money, so Anna and Belinda paid for the vase first. Anna paid 0.25 more than what Belinda had paid. The following day, Clare paid her share to both Anna and Belinda. (a) Clare paid Belinda $6.55. How much did Clare pay Anna? (b) Clare’s brother bought a similar vase at the same shop during a sale and was given a discount of 20% of the price that Clare and her friends paid for. How much did Clare’s brother pay for the vase? NH10P15 46. JiaHui went shopping with twice as many $10-notes as $50-notes. She then bought a blouse with half of her $10-notes. What is the ratio of the amount of money she had left to that she had originally? MB10P05 2011 47. John, Jack and Judy shared 132 marbles in the ratio of 2 : 3 : 1. Judy gave all her marbles equally to the 2 boys. What is the ratio of the number of marbles John has to the number of marbles Jack has now? RG11S01 48. The ratio of John’s pencils to Peter’s pencils was 4 : 5. If Peter gave half of his pencils to john, what would be the new ratio of John’s pencils to Peter’s pencils? NH11C03 49. Emma bought some walnut and blueberry muffins in the ratio 5 : 3. She packed all of them into 24 boxes. There were 6 blueberry muffins in each box. How many more walnut muffins than blueberry muffins did Emma buy? SN11S04
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50. There are 36 pupils in a class. The ratio of the number of boys to the number of girls is 5 : 4. If 2 more boys join the class, what fraction of the class are girls? Express your answer in its simplest form. NH11S11 51. Ray's collection of Malaysia stamps to Singapore stamps was in the ratio 5 : 1. After he had given his cousin 30 Malaysia stamps, he had 2 fewer Malaysia stamps than Singapore stamps. How many stamps did he have at first? RS11S07 1
52. Jack, Kristine and Lina painted some chairs for their school classrooms. Jack painted of 2
the number of the chairs.Kristine and Lina painted the remaining number of chairs in the ratio of 3 : 5. Jack painted 65 more chairs than Kristine. (a) How many chairs did Jack and Lina paint altogether? (b) The school would save $4 for every chair painted. What was the total savings for the school? RG11P11 53. The ratio of the number of apples in Box A to the number of apples in Box B is 3 : 2. All the apples in Box B are green. The ratio of the number of green to the number of red apples in Box A is 4 : 5. There are 20 more green apples in Box B than in Box A. How many red apples are there? RS11P08 54. A shopkeeper had some blue and red pens in his bookshop. There were twice as many red pens as blue pens. The shopkeeper sold the pens in bundles of 2 red pens and 3 blue pens. After selling all the blue pens, he still had 120 red pens left. How many pens did he have in his bookshop at first? RS11P17 55. Mr Tan had some apples and oranges in the ratio 4 : 5. After selling 170 apples and 25% of the oranges, the ratio of the apples to oranges left became 1:2. What was the number of fruits Mr Tan had in the end? RY11P12 1
56. The ratio of the number of males to the number of females at a performance is 5 : 7. of 4
3
the males and of the females are children. What is the ratio of the number of adults to 4
children? Express your answer in simplest form. CH11P02 57. There were some raspberries and strawberries at Ms Umi's fruit stall. There were 1.5 times as many strawberries as raspberries at the stall. What was the ratio of the number of raspberries to the number of strawberries to the total number of berries? NY11S04 58. A boat can take either 6 adults or 9 children. Given that there are 8 boats with 4 adults in each boat, what is the maximum number of children the boats can still take? HP11P02
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59. In an aquarium, there were 121 swordtails. The ratio of the number of male swordtails 2
to the number of female swordtails was 4 : 7. A few days later, 33 swordtails died, of 3
which were males. Express the ratio of the number of male swordtails to the number of female swordtails left in the aquarium. Give your answer in the simplest form. AC11S05 60. Cindy has 650 hair bands, clips and ribbons altogether. The ratio of the number of hair bands to the number of clips is 7 : 5. If Cindy has 30 fewer ribbons than clips, how many hair bands does Cindy have? AC11S11 61. A carton can either hold 180 cuboids or 220 cubes. When 108 cuboids are already in the carton, what is the maximum number of cubes that can be put in the carton? RS11P02 62. Alex, Brad and Clara shared some erasers in the ratio 4 : 5 : 6 at first. 1
During a game, Brad won of Alex’s erasers while Clara lost 10 erasers to Brad. As a 4
3
result, Alex now has as many erasers as Clara. How many erasers did each of them 4
have at first? NH11C17 63. The ratio of the number of golf balls in Box A to the number of golf balls in Box B was 5 : 4. 10 golf balls were taken out from Box A and placed into Box B. The two boxes then had the same number of golf balls. How many golf balls were there in Box A at first? RS11C03 2
64. of Rani’s balloons were red and the rest were green. She gave away 15 green balloons 9
and bought another 25 red balloons. She then had the same number of red and green balloons. How many green balloons did she have at first? RS11C08 65. During a survey, 342 women responded that they preferred romantic comedies to other types of movies. The ratio of the number of women to the number of men who liked romantic comedies was 3 : 1. (a) How many people liked romantic comedies? (b) The ratio of the number of people who liked romantic comedies to those who did not was 2 : 3. If 25% of the people who did not like romantic comedies were women, how many men took the survey altogether? RY11C18 66. In a seminar of 504 people, there were 288 more women than men. What was the ratio of the number of men to the number of women'? (Give your answer in the simplest form. RS11S01
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67. A box contains hotdog buns, custard buns and curry buns. The ratio of the number of 5
hotdog buns to the number of custard buns is 7 : 2. The number of curry buns is of the 6
total number of hotdog and custard buns. After some hotdog buns were sold, there were an equal number of hotdog buns and custard buns. If there were 276 buns in the end, how many hotdog buns were sold?SN11C08
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Unit 7.2 Ratio Repeat Identity
PSLE Math Series 2007
1. The number of tutors to the number of pupils at a tuition centre is 3 : 22 respectively. 4
The number of girls is the number of boys. If there are 18 fewer girls than boys, how 7
many tutors are there at the tuition centre? RY07C48 2. Alex, Ben and Darren planted 520 seeds. For every 7 seeds Alex planted, Ben planted 4 seeds. And for every 3 seeds Ben planted, Darren planted 8 seeds. How many seeds did Darren plant? HP07S40 𝟑
3. The number of Chinese at a concert is the number of Malays. The number of Indians 𝟒
𝟏
is the number of Chinese. If there are 126 Chinese, how many people are there at the 𝟑
concert? RY07C36 4. At first, the ratio of the number of marbles received by John and Peter was 4 : 7. The ratio of the number of marbles received by Peter and Sam was 9 : 5. Then, John gave 𝟏 𝟏𝟐
𝟏
of his marbles to Sam, and Peter gave of his marbles to Sam. 𝟗
As a result, Sam had 135 marbles in the end. (a) Find the ratio of the number of John’s marbles to the number of Sam’s marbles at first. (b) Find the total number of marbles received by the 3 boys. RG07P46 5. The ratio of Ali’s money to Jay’s money is 5 : 3. The ratio of Jay’s money to Dave’s money is 4 : 2. The three boys had a total of $988. How much more money does Ali have more than Dave? RY07S37 2008 6. Ali, Baba and Carapa inherited a sum of money from their father. The amount of money Ali received to the amount of money Carapa received was in the ratio 3 : 5. 𝟑
Carapa’s amount was that of Baba’s. Ali’s amount was $770 less than Baba’s. 𝟒
(a) What is the ratio of Ali’s money to Baba’s money to Carapa’s money? (b) How much money did they get altogether? NH08C44
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7. The ratio of the cost of an air ticket to Thailand to the cost of an air ticket to London is 1 : 5. The ratio of the cost of an air ticket to Japan to the cost of an air ticket to London is 1 : 2. Find the cost of an air ticket to Japan if it cost $300 to fly to Thailand. AT08C39 8.
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of Alethea’s bangles was twice as many as Millicent’s bangles. Millicent and Amber had
bangles in the ratio 6 : 7. All of them paid a combined total of $528 on the bangles. Given that each bangle cost the same, how much did Alethea pay for her bangles? SN08S40 3
9. Three friends, Billy, Chitra and Denny shared a sum of money. Billy had of what Chitra 4
had. Chitra had twice as much as Denny. Denny had $50 less than Billy. How much was the sum of money? MG08C36 2009 10. The ratio of the number of toy cars Jackson has to the number of toy cars Kris has is 3 : 5. The ratio of the number of toy cars Kris has to the number of toy cars Adam has is 3 : 4. If Jackson has 22 toy cars less than Adam, how many toy cars does Kris have? RS09P09 11. In a fish tank, the ratio of the number of angelfish to the number of goldfish is 3 : 2. The ratio of the number of guppies to the number of angelfish is 5 : 2. How many fish are there altogether if there are 8 goldfish? NH09P07 𝟖
12. Jai, Maira and Lynn have 760 stickers altogether. Jai has as many stickers as Maira 𝟗
and
𝟔 𝟏𝟏
as many stickers as Lynn. If Jai and Lynn want to have an equal number of
stickers, how many stickers must Lynn give to Jai? SN09S11 2
3
3
5
13. School A has as many pupils as School B. School B has as many pupils as School C. If School A has 2234 pupils, how many pupils does School C have? PL09P06 3
8
4
11
14. Rope A is as long as Rope B. Rope B is
as long as Rope C. Rope A is 25 cm shorter
than Rope C. What is the total length of the three ropes? HK09P09 2010 15. The ratio of Amy’s height to Betty’s height is 1 : 2. The ratio of Betty’s height to Carmen’s height is 3 : 5. Betty is 144 cm taller than Amy. What is the average height of the 3 girls? RY10C11
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16. There are red, blue and green balls in a box. The ratio of the number of red balls to the number of blue balls is 3 : 5. The ratio of the number of blue balls to the green balls is 3 : 5. What is the ratio of the number of red balls to the number of green balls? NH10S03 2011 17. There are thrice as many students in tuition centre A as there are in tuition centre B. Tuition centre C has - as many students as tuition centre B. What is the ratio of students in tuition centre A to the students in tuition centre C? RG11S04 𝟕
18. of Maria’s savings was twice of Adele’s savings. The ratio of Adele’s savings to Safia’s 𝟗 is 14 : 5. How much was Maria’s savings if the 3 girls have a total of $3080? SN11S13 𝟐
𝟑
19. A pen costs as much as a magazine and as much as a book. If the book costs $14 𝟓 𝟏𝟏 more than the magazine, (a) how much does the pen cost? (b) what is the total cost of the 3 items? NH11S12 20. Three girls, Eileen, Lisa and Pamela, had some savings. Pamela had thrice Lisa's savings. 𝟓 Eileen's savings was $374 less than Pamela's savings. Eileen's savings was as much as 𝟗 Lisa's savings. How much savings did Lisa have? CH11S15 𝟏
21. My salary is more than my sister but 20% less than my brother. 𝟓 If our total salary is $11 100, what is my sister’s salary? NH11C14 22. Ali, Ben and Carl weighed themselves using a defective bathroom scale as shown in the 2 diagram. The average mass of the 3 boys was 72.6 kg. Given that Ben is of Ali’s mass 3
4
and Carl is of Ben’s mass, what is Carl’s actual mass? MG11P10 5
23. Jeff has 45% as many sweets as Melvin and 40% fewer sweets than Alfred. If they have a total of 132 sweets, how many sweets does Jeff have? AT11C07 24. Lucy had a box of buttons. The number of square buttons was 40% of the number of 𝟐 round buttons. The number of oval buttons was of the number of square buttons. 𝟑 (a) Given that there were 60 oval buttons, how many buttons were there in the box? (b) What fraction of the buttons was round? (Express your answer in its simplest form) HK11P12
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Unit 7.3 Ratio Constant Difference
PSLE Math Series
2007 1. Mrs Lim bought a total of 120 apples and oranges in the ratio of 3 : 5. After she gave away an equal number of each type of fruits, the ratio of the number of apples to the number of oranges left is 3 : 8. How many apples does she have now? HK07P42 2. Two candles of equal length are lit at the same time. Candle A takes 10 hours to burn down while Candle B takes 5 hours. Candle A will be exactly three times as long as Candle B after how many hours? AT07S40 3. Taufik arranged a rectangle and a square and painted them in three colours as shown in the figure below. The ratio of the area of the rectangle to that of the square is 3 : 1. The ratio of the area of the red part to that of the blue part is 4 : 1. The length of the square is 9 cm. (a) What is the area of the purple part? (b) What is the ratio of the area of the purple part to that of the figure? PC07P(1)43
Red Purple Blue
2008 4. At first, a shopkeeper had 156 apples and 72 oranges. After he sold the same number of apples and oranges, the number of apples left was 4 times the number of oranges left. How many apples did the shopkeeper sell? RS08P36 5. A shopkeeper had some red and blue pens. The number of red pens was 25% of the total number of pens. After selling away 30 red pens and 30 blue pens, the number of red pens became 25% of the number of blue pens left. How many pens did he have at first? NY08S46
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6. Sarah is 38 years younger than her father. In 6 years’ time, Sarah’s age will be that of 3
her father’s age. How old is Sarah’s father now? TN08S37 7. John had some local and foreign stamps. The ratio of the number of his local stamps to the number of foreign stamps was 2 : 3. After he had given away 30 local stamps and 30 foreign stamps, the ratio of the number of local stamps to the number of foreign stamps became 5 : 9. (a) How many local stamps did he have at first? (b) Find the total number of foreign stamps he had left? AC08S43 8. The number of girls who registered for art class was 20% of the number of boys. On the actual day, 3 more girls and 3 more boys turned up for the class. As a result, there were 1 3
as many girls as boys at the art class. What was the total number of children who came
to art class? SC08P40 9. Juyi had a total of 208 cheese and tuna buns in the ratio 7 : 6. After she gave away an equal number of each type of bun, the number of cheese and tuna buns left was in the ratio 7 : 3. (a) Did the fraction of tuna buns that Juyi had increase, decrease or remain the same? (b) How many buns did she give away? MB08P45 1
10. Jason’s age is of Tiffany’s age. Tiffany will be 27 years old in 2 years’ time. In how many 5
1
years’ time will Tiffany’s age be 1 times of Jason’s age? AT08C40 2
11. At first, Shop X has 156 kg of rice flour and Shop Y has 72 kg of rice flour. After each shop sold the same quantity of rice flour, the amount of rice flour that Shop X has was 4 times that of Shop Y. How many kilograms of rice flour did Shop X sell? RY08C45 12. Box A contained 134 marbles and Box B contained 18 marbles at first. An equal number of marbles was then added to each box. As a result of this, Box A had 5 times as many marbles as Box B. (a) How many marbles were added to each box? (b) Next, some marbles were transferred from Box A to Box B so that there was an equal number of marbles in each box. How many marbles were there in each box in the end? RY08S48
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2009 2
13. Rahim’s age is of his grandfather’s. His grandfather will be 100 years old in 19 years’ 9
1
time. In how many years’ time will Rahim’s age be that of his grandfather’s? NY09C12 4
14. Korey’s allowance to Skyler’s allowance was in the ratio 10 : 11. Both of them spent an 𝟕
equal amount. Then Korey’s remaining allowance was of Skyler’s remaining 𝟗
allowance. What percentage of Skyler’s allowance did she spend? Leave your answer correct to 2 decimal places. SN09P13 15. The ratio of the amount of money Colin has to the amount of money Daniel has is 4 : 7. After each of them spends $28, their ratio becomes 3 : 7. Find the amount of money Colin has now. SC09P06 2010 16. Ahmad is 46 years old. He is 24 years older than his son. How many years ago was the ratio of Ahmad’s age to his son’s age 5 : 2? NH10S09 17. At present, James is 24 years old and he is twice as old as his cousin. How old was James when he was 3 times as old as his cousin? HP10P03 1
18. John’s age is of his father’s age now. His father will be 36 years old in 4 years’ time. 8
3
How old will John be when he is of his father’s age? MG10S12 5
19. The ratio of the number of stickers Alex had to the number of stickers Beng Han had was 1 : 3. After each of them received 25 stickers, the ratio became 3 : 4. How many stickers did they have altogether at first? AT10C15 20. At first, Matthew has twice as many soccer cards as Ivan. Each of them then bought the same number of cards. As a result, both of them now have 160 cards in total. If Matthew now has 30 more cards than Ivan, find the number of cards each of them bought. AC10S06 21. Candle A and candle B are of the same length. Candle A, which is broader, can burn for 5 h while Candle B, the thinner candle, can burn for 4 h. If both candles are lighted at the same time, how long does it take for Candle A to be twice as long left as Candle B? RV10P17
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22. Tom is as old as David now. In 6 years’ time, the ratio of Tom’s age to David’s age will 3
be 3 : 5. How old is David now? AT10C05 23. Basket A and B have an equal number of marbles. 3
The number of blue marbles in basket A is of the number of blue marbles in basket B. 5
3
The number of red marbles in basket B is of the number of red marbles in basket A. 7
What is the ratio of the number of blue marbles to the number of red marbles in basket B? RG10S04 24. Joan puts some black buttons and white buttons equally into two boxes. The ratio of the number of black buttons to the number of white buttons in the first box is 3 : 2. The ratio of the number of black buttons to the number of white buttons in the second box is 7 : 3. What is the ratio of the total number of black buttons to the total number of white buttons in both boxes? SC10P05 2011 25. A florist had 84 stalks of orchids and 4 times as many stalks of roses in her shop. After buying an equal number of orchids and roses, the ratio of the number of orchids to the number of roses became 5 : 9. How many stalks of orchids and roses did she buy altogether? SN11S09 26. In three years’ time, Jimmy's age will be twice that of Mary's age. Three years ago, Jimmy's age was 4 times that of Mary's age. How old is Mary now? RG11P07 27. Tammy is 8 years old. Her father is 38 years old. 1
In how many years’ time will Tammy’s age be of her father’s? NH11C10 3
28. Class A and Class B have the same number of pupils. The ratio of the number of boys in Class A to the number of boys in Class B is 3 : 2. The ratio of the number of girls in Class A to the number of girls in Class B is 3 : 5. Find the ratio of the number of boys in Class A to the number of girls in Class B. RY11C05 29. Two years ago, John was 20 years older than his niece. How old will John be when he is 5 times as old as his niece? TN11S01 30. Box A and Box B contain the same number of apples. The number of red apples in Box 𝟐
𝟏
𝟑
𝟒
A is of that in Box B. The number of green apples in Box B is of that in Box A. What fraction of the apples in Box B are red? AT11S07
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31. In a box, the number of gold coins is 20% of the number of silver coins. Faizal added 8 𝟏
more gold coins and 8 more silver coins into the box. As a result, there were as many 𝟒
gold coins as silver coins in the box. Find the total number of coins Faizal has in the end. AT11S16
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PSLE Math Series
Unit 7.4 Ratio Unchanged Quantity
2007 1. There were 240 pupils in a hall. The ratio of the number of girls to the number of boys was 2 : 3. After some girls left the hall, the ratio of the number of girls to the number of boys became 2 : 4. How many girls left the hall? PH07C42 2. In 2005, the ratio of the number of boys to the number of girls in a school was 4 : 3. In 2006, 1620 more pupils joined the school and there were thrice as many girls and twice as many boys in 2005. How many pupils were there in the school in 2006? RY07C41 3. A library had 1560 books and magazines. 25% of them were magazines. After buying more new magazines, the number of magazines became 35% of the total number of books and magazines. How many new magazines were bought? RY07S40 4. There were some red and green beads in a container. If 75 more green beads are put into the container, the percentage of red beads will decrease from 30% to 20%. How many red beads are in the container? RG07P43 5. In a stadium, 20% of the people are performers for the National Day Parade and the rest are spectators. 65% of the spectators are males and there are 1200 more male spectators than female spectators. How many male spectators must leave the stadium so that 40% of the people in the stadium are male spectators? NY07S47 6. Ann and Ben were given some money each. If Ann spent $25 each week and Ben spent $75 each week, Ann would still have $1350 left when Ben had spent all his money. If Ann spent $75 each week and Ben spent $25 each week, Ann would still have $150 left when Ben had spent all his money. (a) How much money did Ann receive? (b) How much money did Ben receive? RG07S43
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2008 𝟏
7. In a concert hall, of the audience were children. 75% of the adults were women. 𝟕
There were 280 more women than children. (a) How many women were there in the hall? (b) During the interval, some men left the hall. As a result, 12% of the remaining audiences were men. How many men left the hall? NH08P48 8. At a farm, 40% of the animals are cows, 90% of the remainder are sheep and the rest are ducks. There are 56 more sheep than cows. After some cows died, 20% of the remaining animals at the farm are cows. How many cows are there left at the farm? SC08P48 9. There were 2200 children at a carnival. 56% of them were boys. How many more boys had to join the carnival so that the percentage of boys would increase to 60%? SN08S41 10. The number of blue paper clips to the number of white paper clips in a box was 5 : 3. Ryan removed 24 blue paper clips and the ratio of the number of blue paper clips to the number of white paper clips became 7 : 9. Find the total number of paper clips left in the box. SN08C38 11. Mark had some red and blue marbles in the ratio 5 : 3. After losing 96 red marbles, the ratio became 3 : 5. How many red marbles did Mark have at first? RY08P36 12. 20% of the people at the auditorium are adults. 25% of the children are boys. There are 80 fewer boys than girls. Assuming that the number of adults remain the same, how many girls must leave so that the number of adults is 50% that of the number of girls in the auditorium? NH08C47 13. A florist had some roses, tulips and carnations at first. For every 2 roses that were sold, 3 tulips were sold. For every 5 carnations that were sold, 7 tulips were sold. (a) Find the ratio of the number of roses to the number of tulips to the number of carnations the florist had at first. 𝟏
(b) After 24 roses were thrown away as they had wilted, of the remaining flowers 𝟕
were roses. How many tulips were there? NY08S47
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14. There were twice as many flowers in Box A than in Box B. The ratio of the number of lilies to the number of roses in Box A is 3 : 2. The ratio of the number of lilies to the number of roses in Box B is 2 : 3. When 6 roses were transferred from Box B to Box A, the ratio of the number of lilies to the number of roses in Box B became 3 : 4. (a) How many flowers were there in Box A after the transfer? (b) What was the ratio of the number of lilies to roses in Box A after the transfer? MB08C44 15. Mary and Jason each have some money. If Mary spent $80 per day and Jason spent $40 per day, Mary will have $500 left when Jason has spent all his money. If Mary spent $40 per day and Jason spent $80 per day, Mary will have $1100 left when Jason has spent all his money. What is the amount of money Jason has? AC08P41 2009 16. 60% of the people at a water theme park were adults. 75% of the remainder were boys. There were 140 more adults than girls. More children came to the park, after which 60% of the people in the park were children. How many more children came to the park? NH09P17 17. The ratio of the number of girls to the number of boys in the RosythAniManga Club last year was 3 : 2. When 24 girls joined the club this year, the ratio became 11 : 6. Find the number of girls in the club this year. RY09P13 18. At a shop, the ratio of the number of stalks of roses to the number of stalks of carnation was 4 : 5. Mrs Tan sold 176 stalks of carnations and was left with thrice as many stalks of roses as carnations. How many stalks of carnations did she have at first? SN09S09 19. The ratio of the number of apples to the number of oranges in a basket is 4 : 5. When Mother took 15 apples out to make apple pies, the ratio of the number of apples to the number of oranges became 3 : 10. How many fruits were there in the basket at first? RS09S07 4
20. At a party, only of the invited guests came. The ratio of the number of women to the 9
number of men present was 3 : 4. If 80 more men turned up for the party, the number of men would be twice the number of women. How many guests were invited? AT09C15 21. Mrs Lim had 50 stamps. 60% of them were local stamps and the rest were foreign stamps. After she used some local stamps, the percentage of stamps that were local stamps decreased to 20%. How many local stamps had she left? SC09P09
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3
4
22. Tom’s savings was of Jane’s savings. After Jane had spent $180, her savings became of Tom’s savings. How much did Tom save? RG09S09
23. Mrs Chan had some beads. 38% of the beads were red and the rest were yellow. After she had bought some more red beads, the percentage of red beads increased to 84% of the total number of beads. How many red beads did she buy if she had 496 yellow beads? NY09S09 24. At the start of a soccer match, the number of female spectators was twice the number of male spectators. After 230 female spectators left the match, the number of male spectators was thrice the number of female spectators. What was the total number of spectators at the start of the match? RY09C07 25. The ratio of the number of boys to the number of girls in School A is 4 : 1. The ratio of the number of boys to the number of girls in School B is 2 : 3. School A had twice as many pupils as School B. (a) What is the ratio of the number of boys in School A to the number of girls in School B? (b) After 30 girls left School A to join School B, the ratio of the number of boys to the number of girls in School B is now 5 : 8. How many girls are there in School B now? NY09C16 26. There were some prizes to be won at a Shop and Win contest. 35% were cash prizes and the rest were household items. Some cash prizes were given out and the percentage of cash prizes decreased to 22%. If there were 54 more household items than cash prizes at first, find the number of cash prizes being removed. SN09S15 27. The number of boys to the number of girls in Happy Kindergarten was 3 : 5. The number of boys to the number of girls in Merry Kindergarten was 4 : 5. Both kindergartens had the same number of boys. When 10 girls from Happy Kindergarten joined Merry Kindergarten, the ratio of the number of boys to the number of girls in Happy Kindergarten became 2 : 3. Find the total enrolment of the 2 kindergartens. SN09S17 3
28. Sparkles Jewellery Shop sold diamonds, rubies and emeralds. of the gemstones were 5
diamonds. There were 168 fewer rubies than diamonds. The ratio of the number of rubies to the number of emeralds was 7 : 3. After some rubies were sold, 30% of the remaining gemstones in the shop were rubies and emeralds. (a) How many rubies were sold? (b) Find the percentage decrease in the number of gemstones. Leave your answer as a fraction. SN09S18
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29. Country A and Country B took part in a Youth Game. From Country A, the ratio of the number of male supporters to the number of female supporters is 5 : 6. From Country B, the ratio of the number of male supporters to the number of female supporters was 1 : 1
3. The total number of supporters from Country A is of the total number of supporters 4
from Country B. (a) What is the ratio of the number of female supporters from Country A to the number of female supporters from Country B? Express your answer in the simplest form. (b) After 4985 male supporters from both countries left, the percentage of all the female supporters became 78%. How many more male supporters from Country B than Country A were there at first? PL09P16 30. Audrey and Belle have some money each. If Audrey spends $18 and Belle spends $24 each day, Audrey will still have $25 left when Belle has spent all her money. If Audrey spends $13 and Belle spends $30 each day, Audrey will still have $139 left when Belle has spent all her money. How much money do they have altogether? NY09S14 2010 2
1
5
4
31. Kenji had of the total amount Jace and he had. After Jace spent $45, she had of the amount Kenji had. How much did Kenji have? RS10P01 32. JiaHui had 350 jelly beans. 52% of them were orange flavoured. She ate some of the orange flavoured jelly beans and the percentage of orange flavoured jelly beans decreased to 44%. How many orange flavoured jelly beans did JiaHui eat? SC10P08 33. Kelly had 5100 beads. 20% of them were red. After Carol gave her some more red beads, the percentage of red beads increased to 40%. (a) How many red beads did Kelly have at first? (b) How many red beads did Carol give Kelly? RY10S15 34. There were an equal number of red and white roses in a flower shop. After 46 red roses had been sold, three times as many white roses as red roses were left. How many roses were there in the shop at first? AT10C06 35. Ali had some green and blue pens. 20% of his pens are blue. He then bought 45 blue pens and the percentage of his blue pens increased to 50%. How many pens did he have altogether at first? RS10P09 36. Mr Gopal had 210 red and blue pens of which 20% were red. He bought some more red pens and the percentage of red pens was increased to 30%. How many red pens did he buy? RY10P06
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37. In the morning, there were 750 people at a funfair. 30% of them were girls and the rest are boys. In the afternoon, some more girls joined the funfair and the percentage of girls increased to 40% of the total number of people. How many girls joined the funfair in the afternoon? NY10P09 38. There were some yellow and green beads in Container A and Container B. In Container A, the ratio of the number of yellow beads to the number of green beads was 7 : 2. In Container B, the ratio of the number of yellow beads to the number of green beads was 5 : 1. There were six times as many beads in Container A as in Container B. (a) What was the ratio of the number of yellow beads in Container A to the number of green beads in Container B? Give your answer in its simplest form. (b) After 84 green beads were put into Container B, the ratio of the number of yellow beads to the number of green beads in Container B became 4 : 5. How many green beads were there in Container B at the end? AC10P17 39. Ronnie and Rachel were each given some money. If Ronnie spent thrice as much as Rachel, he would still have $450 when Rachel had spent all her money. If Ronnie spent
1 3
of what Rachel had spent, he would have $690 when Rachel had spent all her money. (a) How much money was Ronnie given? (b) How much money was Rachel given? MG10S16 2011 40. Mr Ho bought a total of 1260 curry puffs and sardine puffs. The number of curry puffs was 75% of the number of sardine puffs. When some sardine puffs were sold, the number of sardine puffs formed 28% of the total number of puffs left. (a) How many curry puffs did Mr Ho buy? (b) How many sardine puffs were sold? SN11P16 41. A shopkeeper had some markers in red and blue. If 50 red markers and 25 blue markers were sold each week, there would be 500 red markers left when all the blue markers were sold. If 25 red markers and 50 blue markers were sold each week, there would be 800 red markers left when all the blue markers were sold. How many markers did the shopkeeper have at first? SN11P17 42. In a school hall, 40% of the pupils were girls. When 27 more girls entered the hall, the number of girls in the hall became 75% of the boys. How many pupils were there in the hall at the end? NY11S08 43. There was an equal number of guppies and goldfish in a tank at first. When 60 more gold fish were put into the tank, the percentage of guppies decreased to 20%. How many fish are in the tank now? RG11S09 pslemathseries.com
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44. The ratio of the number of pencils Kathy has to the number of pencils Joseph has is 3 : 2. After Kathy gives away 30 pencils, this ratio becomes 2 : 3. How many pencils does Kathy have at first? NH11S08 45. Neil and Paul had different sums of money. If Neil spent $40 each week and Paul spent $80 each week, Neil would still have $1 040 left when Paul spent all his money. If Neil spent $80 each week and Paul spent $40 each week, Neil would still have $320 left when Paul had spent all his money. How much money did Paul have at first? CH11S14 46. Joseph has some local and foreign stamps in 2 boxes. In Box A, the number of local and foreign stamps are in the ratio 3 : 4. In Box B, the number of local stamps is twice the number of foreign stamps. Joseph transfers half of the foreign stamps from Box A to Box B. The number of stamps in Box A becomes 105 and the ratio of the number of local stamps to the number of foreign stamps in Box B becomes 6 : 5. (a) How many foreign stamps have been transferred from Box A to Box B? (b) What is the number of stamps in Box B at first? RS11C16 47. The ratio of the number of Justin’s stamps to the number of Sean’s stamps is 3 : 5. When Justin gives 65 stamps to Sean, the ratio of the number of Justin’s stamps to the number of Sean’s stamps becomes 1 : 3. How many stamps did Sean have at first? RY11C08 3
48. There were 60 pupils in the canteen. of them were girls. When some girls left the 5
1
canteen, the number of girls who remained in the canteen was of the total number of 4
pupils who remained in the canteen. How many girls left the canteen? RY11C10 49. Mrs. Han baked 384 muffins in December. The ratio of the number of chocolate muffins to the number of butter muffins baked was 3 : 5. In January, the ratio of the number of chocolate muffins to the number of butter muffins baked was 7 : 4. If Mrs. Han baked the same number of butter muffins in both months, how many chocolate muffins did she bake in January than in December? AT11C15 1
50. The number of motorcycles in a carpark was the number of cars. There were 220 more 2
cars than motorcycles. After some motorcycles left the carpark, the number of cars in the carpark was ten times the number of remaining motorcycles. How many motorcycles left the carpark? HK11P06 51. 80% of the people in hall were adults. 75% of the children in the hall were boys. There were 36 more boys than girls. Some boys left the hall, after which 10% of the remaining people in the hall were boys. How many boys left the hall? NH11P13
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52. At a carnival, there were 40% more males than females. There was an equal number of males without caps to the number of females without caps. The number of males with caps to the number of females with caps was 6 : 2. (a) What was the ratio of the number of females with caps to the number of females without caps? 𝟑
(b) Midway, 800 females left the carnival. In the end, there were as many females as 𝟕
males remaining behind. How many people were at the carnival at first? RY11S15
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PSLE Math Series
Unit 7.5 Ratio Constant Total
2007 1. The owners of three bakeries compared their sales at the end of one day. Bakery A 2
3
3
5
made as much money as bakeries B and C combined. Bakery made as much money as bakeries A and C combined. If bakery B made $720 more than bakery C, how much did bakery A make? HP07S43 2. Fern and Wilbur shared 189 sweets in the ratio 4 : 5. Fern gave some of her sweets to Wilbur and the new ratio of Fern’s sweets to Wilbur’s sweets became 2 : 5. How many sweets did Fern give to Wilbur? PH07S37 𝟑
3. Anna, Ben, Cindy and Dan received a sum of money. Anna received of the total 𝟖
𝟏
amount of money received by Ben, Cindy and Dan. Ben received of the total amount 𝟑
received by Cindy and Dan. Cindy received 3 times as much as Dan. If Anna and Ben received $400, (a) Find the sum of money received by Anna, Ben, Cindy and Dan. (b) How many per cent more did Cindy receive than Ben? RG07S47 1
4. Four children, Angela, Belinda, Cristobel and Dorothy shared $240. Angela received of 2
the total amount of money received by Belinda, Cristobel and Dorothy. Belinda received 2 3
of the total amount of money received by Cristobel and Dorothy. Cristobel received 3
times as much money as Dorothy. (a) How much money did Dorothy receive? (b) What fraction of Angela’s money is Dorothy’s money if Angela gave $20 to Dorothy? HP07P43 5. At first, Bob had only $5-notes and Chris had only $2-notes. The number of notes Bob had is 80% of Chris’ notes. When Bob gives Chris $100, the number of notes Chris has now is 70% more than Bob. (a) How many notes did Bob have at first? (b) How much money does Chris have at the end? HP07P47
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6. There are 224 golf balls in Box and Box Q. When 48 golf balls were transferred from Box P to Box Q, the ratio of the number of golf balls in Box P to Box Q becomes 5 : 9. (a) How many golf balls should be transferred from Box Q to Box P so that the number of golf balls in both boxes is the same? (b) What is the ratio of the number of golf balls in Box Q to Box P at first? (Leave your answer in the simplest form.) RY07C44 7. Kavita had 50% fewer erasers than Mark. After Mark gave 15 of his erasers to Kavita, Kavita had 40% fewer erasers than Mark. How many erasers did Kavita have at first? PC07P(1)40 2008 8. Three sisters Ann, Belle and Cathy shared the cost of a present for their father. Ann paid 1 3
1
the total share of Belle and Cathy. Belle paid the total share of Ann and Cathy. If 5
Cathy paid $75 more than Belle, how much did the present cost? AT08S48 9. Sumin, Tania and Uma shared some beads among themselves. Sumin received
𝟑 𝟏𝟎
of
𝟒
the beads while Tania and Uma received the rest. Tania received of what she and 𝟓
Uma received altogether. If Sumin received 160 more beads than Uma, how many beads did Tania receive? MG08C45 10. Belle, Cathy and Denise had a collection of stickers. Cathy and Denise collected
7 10
of the
6
stickers. Belle and Denise collected of the stickers. Belle and Cathy collected 620 7
stickers altogether. How many more stickers did Denise collect than Belle? NY08P42 11. There were some marbles in Boxes A, B and C. Box A contained 60% of the total number of marbles in Boxes B and C. The ratio of the number of marbles in Box B to the total number of marbles in Boxes A and C is 1 : 4. There were 4 more marbles in Box C than in Box A. Find the total number of marbles in all the boxes. NH08S44 12. In a fruit shop, the ratio of the number of apples in Box A to the number of apples in B was 7 : 3. When 100 apples from Box A was transferred to Box B, the new ratio of the number of apples in Box A to the number of apples in Box B was 1 : 4. Later, 75% of the apples in Box B were sold. (a) What was the total number of apples in the shop at first? (b) What percentage of the number of apples that was not sold was in Box A? AT08S45
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13. The ratio of the number of marbles Jimmy has to the number of marbles Tim has was 3 : 4 at first. After Jimmy gave Tim 36 marbles, the ratio of Jimmy’s marbles to Tim’s marbles became 1 : 2. What was the total number of marbles they had altogether? RS08C47 14. Tina and Siti shared some stickers in the ratio 7 : 5 respectively. After Tina had given 30 stickers to Siti, both of them had an equal number of stickers. How many stickers did they have altogether? MG08C37 15. In Box A, the ratio of the number of blue balls to the number of green balls was 4 : 1. In Box B, the ratio of the number of blue balls to the number of green balls was 2 : 3. The total number of balls in Box A was twice the total number of balls in Box B. (a) What was the ratio of the number of blue balls in Box A to the number of green balls in Box B? (b) When 40 green balls were moved from Box A to Box B, the ratio of the number of blue balls to the number of green balls in Box B became 5 : 8. How many green balls were there in Box B at the end? RG08P46 16. The ratio of the number of strawberry sweets to mint sweets in box A is 4 : 5. The ratio of the number of strawberry sweets to the number of mint sweets in box B is 5 : 7. Box 𝟏
A has 1 times as many sweets as Box B. 𝟒
(a) Find the ratio of the number of strawberry sweets in Box A to the number of strawberry sweets in Box B. (b) When 14 mint sweets are transferred from Box A to Box B, the ratio of the number of strawberry sweets to the number of mint sweets in Box B became 9 : 13. What is the number of mint sweets in Box B after the transfer? SN08C47 2009 17. Allyson, Betty and Charlene shared to buy a watch for their father on his birthday. 𝟏
𝟏
𝟒
𝟓
Allyson paid of the total share of Betty and Charlene. Betty paid the total share of Allyson and Charlene. If Charlene paid $56 more than Betty, how much did the watch cost? AT09S17 18. There were some sweets in Boxes X, Y and Z. Box X contained 20% of the total number of sweets in Boxes X, Y and Z. The ratio of the number of sweets in Box Y to the total number of sweets in Boxes X and Z is 2 : 1. If there are 24 more sweets in Box Y than Box Z, find the total number of sweets in Boxes X, Y and Z. RG09P16
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19. Jeff, Tom and George shared a sum of money together. Jeff’s and Tom’s share made up of the sum of money while George’s and Jeff’s share made up
13 20
3 5
of the sum of money.
Tom and George had $285 together. How much more money did Tom receive than Jeff? HP09S16 20. The square below is divided into 4 parts, P, Q, R and S. 1
1
P and Q form of the square, while R and S form the other of the square. 2
1
2
2
5
2
The area of P is the area of Q, while the area of R is the area of S. What fraction of the square is the area of R? Leave your answer in the simplest form. HP09S07
21. Brendan has 40% more paperclips than Melvin. If Brendan gives Melvin 32 paperclips, Melvin will have 40% more paperclips than Brendan. How many paperclips has Brendan? NH09C10 22. Doran had
8 11
of the number of game cards Thomas had. After Thomas lost 18 cards to
Doran, they both had the same number of cards. (a) How many more game cards did Thomas have than Doran at first? (b) As the game continued, Doran won more cards from Thomas. How many more cards did Thomas lose to Doran such that Doran has 3 times as many cards as him? NY09S12 23. Adrian and Bill shared some stamps in the ratio 1 : 2. When Bill gave some stamps to Adrian, the ratio of Adrian’s stamps to Bill’s stamps became 5 : 4. (a) If Bill had 48 stamps left, how many stamps did they have altogether? (b) How many stamps did Bill give Adrian? NH09C14 24. The number of pupils in Team A to the number of pupils in Team B is in the ratio 7 : 6. If 45 pupils are transferred from Team A to Team B, the ratio will become 2 : 3. How many pupils are there altogether? AT09C16
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25. Lily, Mina and Oscar each donated some money to charity. The donation made by Lily 2
1
3
5
was as much as the total amount donated by Mina and Oscar. Mina donated as much as the total amount donated by Lily and Oscar. If Oscar donated $360 more than Mina, how much did Lily donate? RY09C13 2010 26. Three boys, Aaron, Ben and Charlie shared the cost of a birthday present for their father on his birthday. The ratio of Aaron’s share to the total of Ben’s and Charlie’s share was 1 : 3. The ratio of Ben’s share to the total of Aaron’s and Charlie’s shares was 1 : 5. Charlie paid $50 more than Ben. Find the cost of the present. RY10P11 27. Allison, Beth, Carl and David donated some money to the School Pocket Money Fund. The ratio of the amount donated by Allison to the total amount donated by Beth, Carl and David was 1 : 6. Beth donated
𝟑 𝟏𝟏
as much as the total donated by Allison, Carl and
David. Carl donated 10% of the amount donated by Allison, Beth and David. If David donated $20 more than Allison, what was the total amount donated by the 4 pupils? RV10P14 28. Fazillah, Linda and Winnie each owned a collection of comics. The total collection owned 3
4
2
5
by Linda and Winnie was as many comics as Fazillah owned. Linda owned as many comics as the total collection owned by Fazillah and Winnie. If Winnie owned 169 fewer comics than Linda, how many comics must Fazillah and Linda each give to Winnie in order for the three girls to have the same number of comics? RY10C16 2
29. Weiming had as many stickers as Shiyang. After Weiming gave 52 stickers to Shiyang, 3 2
Weiming had as many stickers as Shiyang. How many stickers did Weiming have at first? 5
AC10S12 30. The ratio of the amount of Paul’s savings to Benny’s savings was 3 : 5. After Paul received a part of Benny’s savings, the ratio of Paul’s savings to Benny’s savings became 9 : 7. The amount of savings Paul received from Benny was $24, what is the total amount of savings the boys had? RY10S09 31. The ratio of male members to female members in a swimming club is 8 : 5. There are 234 members who are foreigners and the rest are Singaporeans. The ratio of the number of foreigners to the number of Singaporeans is 6 : 5. If there are 80 female foreigners, what is the ratio of the number of female Singaporeans to the number of the male Singaporeans? RY10C18
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32. Wendy, Jenny and Marcus share a bag of marbles. The number of marbles owned by 1
Wendy is of the total of Jenny’s and Marcus’ marbles. The total number of marbles 3
owned by Jenny and Wendy is half of what Marcus has. If Wendy has 90 marbles more than Jenny, how many marbles does Marcus have? CH10S12 33. Four boxes, A, B, C and D, contain some marbles. 1
Box A contains of the total number of marbles in Boxes B, C and D. 7 1
Box B contains of the total number of marbles in Boxes C and D. 2
1
Box C contains 1 the number of marbles in Box D. 3
(a) If Boxes A and B contain 34 more marbles than Box C, how many marbles are there in Box A? (b) How many marbles must be removed from Box C to Boxes A, B and D so that it 1
contains of the total number of marbles? NY10S11 6
34. The circle below is divided into 4 parts, A, B, C and D. Part A and part C form one semicircle. Part B and part D form the other semi-circle. The area of part A to the area of part C is in the ratio of 1 : 3. The area of part B to the area of part D is in the ratio 1 : 2.
(a) What percentage of the whole circle is part D? (b) The area of Part C is bigger than part B by 20cm2. Find the area of the whole circle. NH10S16 35. Ellen and Lenny have some sweets. If Ellen gives away 12 sweets, the number of sweets Ellen has is
13 24
of the total number of sweets that both of them have. If Lenny gives away 3
12 sweets, the number of sweets Lenny has is of the total number of sweets that both 8
of them have. How many sweets do they have altogether? MG10P11 36. John and Sarah collected some cans for their class project. John collected 25% more than Sarah. Then he gave 20 of his cans to Sarah and she had 20% more cans than him. (a) How many cans did they have in all? (b) How many more cans must John give to Sarah in order for Sarah to have 25% more than him? MG10P18
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2011 37. The ratio of the number of beads John had to the number of beads Sally had was 3 : 7 at first. After Sally had given some beads to John, Sally had 76 beads less than John. The ratio of John's number of beads to Sally's number of beads became 3 : 2. (a) How many beads did Sally give to John? (b) What percentage of her beads did Sally give to John? RG11S10 38. Four children Min, Nathan, Tom and Caleb each have some savings. The amount of 1
money Nathan has is of the total amount of money Tom, Min and Caleb have. The 3
1
amount of money Tom has is of the total amount of money Nathan, Min and Caleb 4
1
have. The amount of money Min has is of the total amount of money Nathan, Tom and 5
Caleb have. If Caleb saves $1 035, how much do the four children have altogether? RY11S12 39. Jaycee has some $2, $5 and $10 notes. The number of $2 notes is 25% of the total number of notes. The ratio of the $5 notes to the total number of $2 and $10 notes is 2 : 5. Given that there are 18 more $10 notes than $2 notes, how much money does Jaycee have in all? SN11S17 40. Roy, Sam and Ted had a sum of money. Roy had 80% of Sam's money. Sam had 60% of 5
Ted's. After Roy gave $12 to Sam, he had of what Sam had. How much more money did 7
Ted have than Sam in the end? CH11S12 41. Andy, Ben and Carl went for dinner and paid a total of $935 for the meal. Andy paid 25% of what Ben and Carl had paid. Ben paid 20%more than what Andy and Carl had paid. How much did Carl pay for his share of the dinner?NY11P07 42. Sushila went shopping. She spent $588 on 2 dresses, 3 skirts and 2 pairs of sunglasses. The total amount spent on the dresses was 0.4 of the total amount spent of the skirts and sunglasses. 1
The total amount spent on the sunglasses was of the total amount spent on dresses 3
and skirts. (a) How much did she spend on the 2 pairs of sunglasses? (b) What was the cost of the third skirt if the average cost of the other 2 skirts was $88? NY11C16 43. The ratio of pupils in class A to those in class B was 4 : 5. After 2 pupils were transferred from class A to class B, the ratio became 2 : 3. How many pupils were in class A at first? NH11C04
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44. Charlene had some sweets and chocolates in a bag. If she ate one sweet, the ratio of the number of sweets to the number of chocolates left in the bag would be 2 : 3. If she ate one chocolate, the ratio of the number of sweets to the number of chocolates left in the bag would be 7 : 10. What was the ratio of the number of sweets to the number of chocolates Charlene had in the bag? RY11P11 45. Xavier, Yew Ming and Zason bought a watch for their mother on her birthday. Xavier 1
1
4
5
paid of what Yew Ming and Zason paid. Yew Ming paid of what Xavier and Zason paid. If Zason paid $56 more than Yew Ming, how much did the watch cost? AT11C13 46. A coin box contained only twenty-cent and fifty-cent coins in the ratio of 4 : 5. When 16 fifty-coins were taken out and replaced by some twenty-cent coins, the number of 𝟕
fifty-cent coins left in the box was of the twenty-cent coins. The total value of all the 𝟖
coins remained the same. Find the sum of money in the coin box. AT11C17 47. Xiaoming, Yanli and Zen went to a restaurant to have their lunch together. Each of them 3
paid a different amount for their meals. Xiaoming paid of what Yanli and Zen paid. 5
Yanli paid 40% of what Xiaoming and Zen paid. If Zen paid $3 more than Yanli, how much did Xiaoming pay for his meal? AT11S10
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PSLE Math Series
Unit 7.6 Ratio Total Value
2007 1. The tickets for a show are priced at $10 and $5. The number of ten-dollar tickets 1
available is 1 times the number of five-dollar tickets. 5 out of 6 ten-dollar tickets and all 2
the five-dollar tickets were sold. The ticket sales amounted to $5600. How much more would have been collected if all the tickets were sold? NY07P44/AT10C10 2. Durians were sold at $12 each. A mango cost 50% less than a durian. Walter paid $408 for some durians and mangoes. 70% of the fruits he bought were durians. How much more money did he spend on durians than on mangoes? AC07S44 1
1
3
9
3. Mrs Lee bought some fruits. of the fruits were oranges, of them were apples and the rest were pears. The prices of the fruits were as shown below: Oranges 40₵ each Apples 30₵ each Pears 60₵ each Mrs Lee spent $13.50 on the oranges and apples. How much did she spend on the pears? AT07S41 4. Sunshine coffee is a mixture of two grades of coffee powder A and B in the ratio of 5 : 7. If 1 kg of the coffee powder A cost $6 and 1 kg of the coffee powder B cost $12, what is the cost of 20 kg of Sunshine coffee? NY07S38 5. The total sale of different types of printers at Unique Store during its special 2-hour sale was $12 150. The number of Printer A and B sold was in the ratio 5 : 2. The number of Printer B and C sold was in the ratio 3 : 4. The price of Printer A was $50. The ratio of the price of Printer A to the price of Printer B to the price of Printer C was 1 : 3 : 6. How many printers did the store sell? SC07S48 3
6. The total cost of 28 textbooks and workbooks is $784. of the books are textbooks and 4
the remaining books are workbooks. A workbook costs half as much as a textbook. Find the difference in the price of a textbook and a workbook. RY07P46
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7. Mr Lim spent $1496 on some comics and dictionaries altogether. The number of comics bought to the number of dictionaries bought was in the ratio 3 : 2. A dictionary cost $4 more than a comic. The total cost of the comics was 20% more than the total cost of the dictionaries. Find the cost of a dictionary. PC07P(1)48 2008 8. Mr Singh had $315 worth of concert tickets. He sold 4 adult tickets and 3 child tickets. 1
Each adult ticket is 1 times as much as a child ticket. If the value of the tickets Mr Singh 2
3
had left is of the original amount, what is the cost of a child ticket? RY08C46 7
9. In a farm, there are three times as many ducks as goats. There is an equal number of cows and goats. The total number of legs of all these animals is 1400. (a) How many ducks are there in the farm? (b) How many cows are there in the farm? NH08C42 10. A promoter sold a total of $1140 worth of pots and pans in a week. The ratio of the cost of a pan to that of a pot is 1 : 3. The pot cost $45 and the promoter sold 12 more pans than pots. How many pans did he sell in the week? MB08C47 11. There were some $5, $10 and $50 notes in Jane’s wallet. The value of the $5, $10 and $50 was in the ratio 3 : 4 : 2. After spending 50% of her $50 notes, 10 of her $10 notes 2
and of her $5 notes, Jane had $200 left. Find the total amount of money Jane had in 3
her wallet at first. NH08C46 12. Mrs Tan spent $5190 on some blouses and shirts. The amount spent on the blouses was 4
$2310 more than the amount spent on the shirts. He bought times as many shirts as 5
blouses. Each shirt cost $13 less than each blouse. What was the total number of blouses and shirts bought by Mrs Tan? NH08S48 13. The admission cost to a concert was $10 per adult and $5 per child. On a particular day, a total of $2340 was collected. The ratio of the number of adults to the number of children present at the concert was 7 : 4. Find the number of children who attended the concert that day. AC08S45 1
1
4
6
14. Carrie has some dollar notes. are $2 notes and of the remainder are $5 notes. The remaining are $10 notes. If Carrie has $236 altogether, how many notes does she have in total? RY08S47
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15. Alvin, Bernard and Christopher were given some carnival tickets to sell. Each ticket was 2
sold for $10. Alvin sold of the tickets. Bernard and Christopher sold the remaining 3
tickets in the ratio of 1 : 2. Alvin sold 40 more tickets than Christopher. How much money did the 3 boys collect? MB08S45 16. Mr Tan bought three times as many badges as toy cars and spent $144 in total. He spent $84 more on toy cars than on badges. Given that a toy car cost $10.40 more than a badge, what is the cost of a badge? AC08P45 17. Siew Leng paid $8.56 for some 26-cent, 30-cent and 50-cent stamps. She bought 4 more 30-cent stamps than 50-cent stamps. There were twice as many 26-cent stamps as 30cent stamps. How many 26-cent stamps did she buy? RY08P47 18. The entrance fee to an exhibition was $4 for each adult and $3 for each student. If the total amount collected was $73 260, and the number of students was 11 times the number of adults, how many students were at the exhibition? MB08P42 19. Joanne had some twenty-cent coins and fifty-cent coins in a box. The percentage of the number of twenty-cent coins was 40% of the total number of coins Joanne had. Joanne took out 10 fifty-cent coins and put in twenty-cent coins of the same value. The percentage of the number of twenty-cent coins then became 50% of the total number of coins Joanne had. What was the amount of money in the box? RG08P48 20. Mrs Winder had some $50 notes and $10 notes. The number of $50 notes was 45% that of $10 notes. She spent 20% of the $50 notes. As a result, she had 192 mor e $10 notes than $50 notes. (a) How much money did Mrs Winder spend? (b) Express the total value of the $10 notes as a fraction of the total value of the $50 notes left. SN08P45 21. Mary had $72 in her piggy bank. The coins were in a mixture of 10-cent, 20-cent and 50-cent coins. There were twice as many 20-cent coins as 50-cent coins and three times as many 10-cent coins as 50-cent coins. (a) How many 20-cent coins were there in the piggy bank? (b) Mary decided to exchange all 10-cent and 20-cent coins for 50-cent coins. How many 50-cent coins would she have after the exchange? NY08P45
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2009 22. Three types of nuts, A, B and C come in packets of 200 g, 250 g and 500 g respectively. Packets of Nut A, Nut B and Nut C are mixed together in the ratio 3 : 4 : 5 to obtain 41 kg of an assortment of nuts. How many packets are used altogether? NH09S14 3
23. 800 people attended a concert. The cost of a child ticket is the cost of an adult ticket. 4
The total amount collected from the ticket sales was $9472. If 240 children attended the concert, how much was the cost of an adult ticket? RY09P15 24. There were some $2, $5 and $100 notes in Jane’s wallet. The value of the $2, $5 and $100 was in the ratio 4 : 5 : 3. After spending 50% of her $100 notes, 100 of her $2 notes 4
and of her $5 notes, Jane had $450 left. Find the total amount of money Jane had in 5
her wallet at first. NH09C15 25. The ratio of $2 notes to $5 notes in Joan’s piggy bank was 13 : 8. She exchanged 20 pieces of $2 notes for some $5 notes, after which, the ratio of $2 notes to $5 notes became 4 : 5. What was the total value of $2 notes and $5 notes in the piggy bank at first? NH09P13 26. Mrs Lim bought some forks and spoons in the ratio of 4 : 3. Each spoon cost 50 cents more than each fork. If she spent $156 altogether and the amount she spent on the forks was $12 more than the amount she spent on the spoons, how many forks and spoons did she buy? SC09P14 27. Ace Drama Company sold some tickets for a children’s performance. It sold the same number of $8 and $5 tickets in week 1 and collected a total of $1664. In week 2, it sold 96 more $8 and $5 tickets. If the company collected $632 more from the sale of $8 tickets than the $5 tickets in the two weeks, how many $8 tickets were sold altogether? NY09C18 𝟏
28. Mdm Ang bought some highlighters, pens and mechanical pencils. of them were 𝟒
𝟏
highlighters. The number of pens she bought was 6 more than the total number of all 𝟐
the items and the remaining were mechanical pencils. Each of the highlighters, pens and mechanical pencils cost $2.10, $4.05 and $1.60 respectively. She spent a total of $227.10 on all the items. How many pens did she buy altogether? NY09P18
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29. A set of dictionaries which fitted exactly 4 shelves, each 2.05 m long, was replaced by a new set. Every 7 old dictionaries was replaced by 4 new ones, each 5 cm thick. If the new set of dictionaries also fitted the 4 shelves exactly, what was the difference in the number of dictionaries between the two sets? SC09S17 30. Mrs Kee baked some cookies and packed all the cookies in 12 small boxes and 5 big boxes. There were equal number of cookies in each small box and equal number of cookies in each big box. Each big box contained 14 more cookies than each small box.
18 29
of the cookies baked were packed in small boxes. How many cookies were there in each small box? RG09P11 31. Madam Fatimah spent $140 on pens and erasers for her pupils on Children’s Day gifts. A pen cost $0.80 each and an eraser cost $0.50 each. The ratio of the number of pens bought to the number of erasers bought was 5 : 6. (a) How many pens did she buy? (b) How many erasers did she buy? RY09C16 5
32. Kai Ling bought some stationery. of her money was spent on pens and the rest was 8
spent on rulers and erasers. The number of rulers was twice as many as the number of erasers. The prices of the stationery were as follows: Ruler $0.40 each Eraser $0.70 each Pens $1.25 each She spent $20 on the rulers. How much money did she spend on the pens? AT09S11 2010 33. Siti made a row of 7 identical small cubes and a row of 5 identical big cubes as shown. The two rows are of the same length.
The length of one big cube is 6 cm longer than the length of one small cube. What is the length of each row of cubes? HP10P01 34. For every gram of sugar Mrs Pow used for baking, she needed 4 times as much flour as sugar. The sugar costs $2 per kg and the flour costs $3 per kg. Mrs Pow spent a total of $84 on the sugar and flour. How much flour did she use in all? SN10C07
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35. A bookshop owner had some books to sell. He sold each book for $18 at first. After selling some books, he reduced the price of the remaining books by $10 and finished selling all the books. The ratio of the number of books he sold at the reduced price to the number of books he sold at $18 was 2 : 3. If he collected a total of $2870 for all the books, how many books did he sell altogether? RV10P09 36. Mrs Reuben bought some pizzas for a group of children. The girls received thrice as many pizzas as the boys. There were an equal number of girls and boys. Each boy ate
𝟐 𝟗
𝟏
of a pizza and the boys finished all the pizzas given to them. Each girl ate of a pizza 𝟔
𝟏
and the girls had 4 pizzas left. How many pizzas did Mrs Reuben buy? NY10P16 𝟐
37. The table below shows the admission charges at a tourist attraction. Admission Charges Children $2 Adults $5 Senior Citizens $3 Promotion: 1 Child enters free for every 4 Adults (excluding Senior Citizens)
A group of people visited the attraction. The ratio of the number of children to the number of adults to the number of senior citizens was 3 : 6 : 4. The number of adults in the group could be divided into groups of 4 exactly. If the group paid a total of $270 on admission charges, how many children were there in the group? HP10P15 38. Talik was given some pocket money for recess. He realized that if he had spent$0.80 on each meal, he would have 8 meals fewer than if he had spent $0.60 per meal. Talik spent $0.60 on 8 meals and spent $0.80 on the remaining meals. How many meals did the money last him? MB10P12 1
39. The cost of a packet of dried prunes was that of a packet of dried mangoes. A 7
4
shopkeeper spent of his money on 24 packets of dried mangoes and 24 packets of 9
dried prunes. Then he used the rest of his money to buy another 9 packets of dried mangoes and some packets of dried prunes. 4
(a) If he had spent all of his money on dried prunes, how many packets of dried prunes 9
could he buy? (b) How many packets of dried prunes did he actually buy altogether? SN10S16
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3
4
5
40. At a rugby match of the spectators bought 1 packet of tidbits each. of the remaining spectators bought 2 packs of tidbits each. The rest of the spectators bought 4 packs of tidbits each. Given that all the spectators bought 3854 packs of tidbits, how many spectators were there at the match? SN10S17 41. Coin boxes A, B, C and D contained some one-dollar, fifty-cent, twenty-cent and ten-cent coins respectively. Coin box A had 6 times as many coins as Coin box C. Coin box B 1
contained 108 fewer than Coin box A. Coin box C contained the number of coins in 3
Coin box B and 4 times as many coins as Coin box D. What is the total amount of money in the four coin boxes? RY10C14 42. There were some kittens, puppies and lambs in an animal farm. The ratio of the number of kittens to the number of puppies is 3 : 2. If the kittens, puppies and lambs had a total of 1976 legs, how many more lambs than puppies were there? RY10C15 43. The ratio of the number of $100-notes to $5-notes that Angel had was 7 : 4. She exchanged 12 pieces of $100-notes for some $5-notes. After which, the ratio of the number of $100-notes to $5-notes became 1 : 16. What was the amount of money Angel had? AT10S15 44. Mrs Gopal and Mrs Ari went to the supermarket. Both women decided to spend all their money on either apples or pears and they would not buy the same fruit. Each apple cost 40 cents and each pear cost 60 cents. If Mrs Gopal bought only pears, she would have 9 more fruit than Mrs Ari. If she bought only apples, she would have 41 more fruit than Mrs Ari. How much more money has Mrs Gopal than Mrs Ari? MB10P06 45. Mdm Zhang packed some beads into 14 small boxes and 15 big boxes. There were equal number of beads in each small box and equal number of beads in each big box. Each big 3
box contained 5 more beads than each small box. of the beads were packed in small 8
boxes. How many beads were there in each small box? AC10P13 46. At a game stall, every child needed 4 tokens to exchange for a prize, while an adult 2
needed 5 tokens. Given that of the people who exchanged their tokens for prizes were 3
children and total of 1092 tokens were collected by the game stall, how many tokens were collected from the adults? SC10P07 47. Mr Yeo awards 15 points for every piece of work handed in on time and deducts 8 points for work handed in late. In the month of August, his class pupils collected 1073 points. For every piece 5 pieces of work given, Mr Yeo found that 2 pieces of work were handed in late. How many pieces of work were handed in on time? RY10C13
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2011 48. Miss Li sold watches and bracelets. Each watch was sold at $42. Each bracelet was sold 2
1
2
3
3
5
at of the price of each watch. Miss Li sold of the items and collected $3360. of the items sold were 35 watches. (a) How many bracelets were sold? (b) What was the total number of items left unsold? NY11S11 49. Mr Lee packed some oranges into big boxes and apples into small boxes. Each big box contained 50 oranges and each small box contained 30 apples. After packing, there were 12 more big boxes than small boxes. Given that there were 1240 fewer apples than oranges, how many oranges were there? HP11P15 50. Mdm Goh spent some money on 45 buns.
She spent the same amount of money on another 20 muffins. Each muffin cost $0.95 more than each bun. How much did Mdm Goh spend altogether? RG11S12 1
51. Mdm Lim bought some books and stationery. of all the items bought were
fiction 3
1
books, of them were non-fiction books and the rest were stationery. The prices of the 5
books and stationery were shown below: Items Cost of each item Fiction books $24.90 Non-fiction books $18.80 Stationery $0.60 Mdm Lim spent $723.60 on all the books. How much did she spend on the stationery? RY11S08 52. The ratio of the number of 20-cent coins to the number of 50-cent coins to the number of $1 coins in a bag is 2 : 6 : 7. Given that the total amount of money in the bag is $156, how many coins are there altogether? NH11S14 53. Jerry bought four times as many pencils as notebooks and spent a total of $21.60. He spent $2.40 more on the notebooks than the pencils. Given that a notebook costs $3.20 more than a pencil, find the cost of a pencil. CH11S16 54. Leon bought some terrapins and guppies for a total of $96. He bought 3 times as many guppies as terrapins. He paid $30 more for the terrapins than for the guppies. Each terrapin cost $10.40 more than each guppy. (a) How many terrapins did he buy? (b) What was the cost of each guppy? NY11C12 pslemathseries.com
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55. A cup of coffee cost $5 and a cup of tea cost 20% less. Mr Lim collected $925 from the sale of these two types of beverages. If 37.5% of the number of cups sold were tea, how many cups of coffee did Mr Lim sell? RS11C11 56. Jason spent $36 on some rulers, pencils and erasers. The ratio of the amount of money he spent on the rules, pencils and erasers was 3 : 2 : 4. Rulers were sold at 5 for $2. The 3
1
4
4
number of rulers he bought was the number of pencils. The number of pencils was the number of erasers. How many more erasers than rulers did he buy? RS11C17 1
1
4
2
57. Mr Yusoff had some stationery in his shop. of them were pencils, of the remainder were pens and the rest were pencil cases. The table below shows the price of the stationery. He sold some pencils, pens and pencil cases in the ratio of 3 : 4 : 5 and collected $52. 1
Given that he sold of the total number of pencils, how many pencil cases did Mr Yusoff 2
have at first? RY11C16 Price of Stationery 1 pencil 1 pen 1 pencil case
Price $0.40 $0.80 $1.20
58. At a party, the ratio of the number of boys to the number of girls is 3 : 4. If each boy is given 2 stickers while each girl is given 3 stickers, 1080 stickers are needed. How many boys are at the party? AT11C06 59. Mrs Koh bought some pens, files and erasers. The ratio of the number of pens to the number of files to the number of erasers she bought was 1 : 2 : 3. The cost of each pen and eraser is $2.50 and $0.50 respectively. If she spent $60 on the pens and the erasers, how many files did she buy? CH11P15 60. A train has a capacity of 154 seats. Tickets for seats are sold at $8 and $12. There are
1 5
more $8-seats than $12-seats on the train. During a trip, the amount collected from the sale of $8 tickets was twice the amount collected from the $12 tickets. The total amount collected was $540. How many $8-seats were not taken during the trip? NH11P14
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Unit 7.7 Ratio Changing Quantities
PSLE Math Series 2007 2
1. Derrick had as many stickers as Benedict. After Derrick bought another 8 stickers and 3
4
Benedict lost 5 stickers, Derrick now has as many stickers as Benedict. Find the number 5 of stickers Derrick and Benedict had at first. AC07P43 2. Siti had some red and blue marbles. 80% of the marbles were red. After she bought another 63 red marbles and 46 blue marbles, 75% of the marbles were red. Find the total number of marbles she had at first. HK07P48 3. The ratio of the number of Andrew’s stickers to the number of Eunice’s stickers was 1 : 5. Then their mother gave Eunice 12 more stickers and Andrew 5 more stickers. The ratio of the number of Andrew’s stickers to the number of Eunice’s stickers became 1 : 4. How many stickers did Andrew have in the end? PC07P(1)41 2
4. Joshua had as many game cards as Nat. After Joshua bought another 20 game cards 3
4
and Nat lost 29 game cards, Joshua now has as many game cards as Nat. How many 5
game cards did Nat have at first? NY07C48 5. There were some flowers at a flower shop. The ratio of the number of roses to the number of tulips was 2 : 3. When 50 more roses and 30 more tulips were added, the ratio of the number of roses to the number of tulips became 5 : 6. How many flowers were there at first? AC07S45 6.
𝟏 𝟓
𝟑
of the number of chickens that Farmer Wong had is equal to of the number of 𝟒
chickens that Farmer Zhang had. When Farmer Wong sold 150 of his chickens and Farmer Zhang bought another 160 chickens, the ratio of the number of chickens that Farmer Wong had to the number of chickens that Farmer Zhang had become 5 : 3. What was the total number of chickens that the 2 farmers have at first? NY07S48 7. The number of grey marbles to black marbles in a bowl was in the ratio of 4 : 5. Later, 8 grey marbles were taken out and 20 black marbles were added into the bowl. After that, the ratio of grey marbles to black marbles became 4 : 11. How many marbles of each colour were in the bowl in the end? RY07S44
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2008 8. The ratio of the amount of water in Bottle A to the amount of water in Bottle B was 2 : 1. After 60 mℓ of water was poured into Bottle A and 150 mℓ was poured out of Bottle B, the ratio became 4 : 1. What was the amount of water in Bottle A at first? RG08S42 9. The number of guppies Ali has is 25% that of the number of swordtails. After selling 3 of his guppies and 10 of his swordtails to his friend, the number of guppies left is 20 % of the number of swordtails left. How many fishes did Ali have at first? MG08S46 2009 10. The ratio of Jane’s allowance to Olivia’s allowance was 4 : 3. After Jane and Olivia were given $15 and $8 respectively, the ratio of Jane’s allowance to Olivia’s allowance became 3 : 2. How much allowance did Jane have at first? NY09C13 11. 75% of the children in the stadium were girls. After 52 girls and 4 boys left, the remaining children formed groups of 8. In each group, there were 3 boys. How many children were there in the stadium at first? AT09C17 𝟐
12. A librarian counted the number of adults in the library and found that of the number 𝟓
of women was equal to 2 times the number of men. When another 12 men entered the library and 45 women left the library, the ratio of the number of women to the number of men became 5 : 2. (a) What was the ratio of the number of women at first to the number of men at first? Give your answer in its simplest form. (b) Find the number of women in the library at first. HP09P15 13. The ratio of the number of pencils to the number of erasers in a box was 2 : 3. When 42 pencils were added and 15 erasers were removed, the ratio of the number of pencils to erasers became 3 : 4. How many erasers were there left in the box? AC09P08 𝟏
14. At first, 25% of Kumar’s money was the same as 33 % of Lily’s money. Lily’s father 𝟑
𝟏
gave her $80 later, while Kumar spent $325. In the end, Lily had 2 times as much 𝟐
money as Kumar. (a) How much money did Kumar have at first? (b) How much money did Lily have in the end? RG09P18
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2010 15. The ratio of the number of Daniel’s pens to the number of Eunice’s pens was 1 : 5. Then Daniel bought 12 more pens and Eunice bought 17 more pens. The ratio of the number of Daniel’s pens to the number of Eunice’s pens became 1 : 4. How many pens did Daniel have at first? PC10P05 16. In a school Art Club, the ratio of the number of boys to the number of girls was 3 : 2. After 2 boys and 3 girls joined the club, the ratio became 4 : 3. How many girls were there at first? NH10C13 17. Alina and Adeline had some stickers in the ratio of 3 : 5. When Alina bought 42 more stickers and Adeline bought 7 more stickers, the ratio became 6 : 7. Find the number of stickers Alina had at first. MG10S09 18. Lisa had 25% as much money as Ken at first. Lisa and Ken won $1304 and $10 respectively at a lucky drawn. In the end, Lisa had 20% more money than Ken. How much money did Lisa have at first? NY10S09 19. At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8 : 5. There was an equal number of male and female participants. (a) Find the ratio of male speakers to male participants at the conference. (b) Halfway, 40 male participants left the conference and another 60 female 𝟑
participants joined the conference. In the end, there were as many male 𝟒
participants as female participants remaining behind. How many speakers were there at the conference? CH10P18 20. An equal number of girls and boys went to a party. The ratio of the number of girls who wore spectacles to the number of boys who wore spectacles was 11 : 3. The ratio of the number of girls who did not wear spectacles to the number of boys who did not wear spectacles was 3 : 5. (a) Find the ratio of the number of boys who wore spectacles to the number of boys who did not wear spectacles. (b) There were 7 times as many girls as boys who left the party. The ratio of the number of girls to the number of boys who remained at the party became 35 : 38. If there were 560 girls remaining at the party, how many girls left the party? NY10S16
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21. There were a total of 480 pink and black pearls in a box. The number of pink pearls 𝟏
was 1 times that of black pearls. Some silver pearls and some white pearls were put 𝟐
into the box. For every 6 pink pearls that were already in the box, 13 white ones were added. Then the final number of black pearls and silver pearls was 25% of the final number of pink pearls and white pearls. What is the ratio of the number of silver pearls to the number of white ones? SN10P17 2011 22. The ratio of the number of sweets Abigail has to the number of sweets Ben has is 4 : 5 at first. After Abigail bought another 16 sweets and Ben ate 2 sweets, Abigail has thrice as many sweets as Ben. How many sweets did Ben have in the end? CH11P06 23. The ratio of Muthu to Ivan's marbles was 9:5 at first. After Muthu bought another 92 marbles and Ivan bought another 12, Muthu had four times the number of Ivan's marbles. How many marbles did Muthu have in the end? RY11S10 3
24. In an amusement park, there were as many girls as boys. After 20 boys left that park 8
3
and 12 girls entered the park, the ratio of boys to girls became . 7
(a) How many girls were at the amusement park at first? (b) How many children were at the amusement park at the end? MG11S16 25. In a cinema, the ratio of the number of girls to the number of boys was 3 : 2. The ratio of the number of women to the number of boys was 5 : 4. The ratio of girls to the number of men was 2 : 5. During the movie, 6 women and 27 men left the cinema. The ratio of the number of women to the number of men became 1 : 2. (a) Express the number of women as a fraction of the number of men at first. Leave your answer in its simplest form. (b) How many children were there in the cinema? NY11P18 26. Jane and Iris had 255 sweets altogether. Jane had 15 more sweets than Iris. Jane gave away 25% as many sweets as Iris. She was left with twice as many sweets as Iris? (a) How many sweets did Iris give away? (b) How many sweets did Jane have in the end? NY11C17 27. At Station A, the ratio of the number of children to the number of adults on a train was 4 : 5. At the next station, 12 children alighted and 10 adults boarded the train. The ratio of the number of children to the number of adults on the train then became 7 : 10. How many children were on the train at first? NY11S13
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28. In a club, the ratio of women to men was 2 : 3. 3 more women and 2 more men joined the club. The ratio of women to men then became 3 : 4. How many men were there in the club at first? NH11C13 4
29. Eric and Fandi had some stamps. Eric's number of stamps is of Fandi's number of 5
stamps. Eric gave away 12 of his stamps, while Fandi bought 5 more stamps. In the end, the ratio of Eric's stamps to Fandi's stamps is 2 : 5. How many stamps did Fandi have in the end? MG11P18 30. Amy’s saving was 40% less than Bao Yu’s savings at first. After Amy donated $52 and Baoyu donated $60, Bauyu’s savings became 5 times as much as Amy’s. What was their total savings at first? AT11C14 31. Mrs. Lee made some curry puffs and sardine puffs. The ratio of the number of the curry puffs to the number of sardines puff was 3 : 4. She made another 65 curry puffs and sold 27 sardine puffs. The ratio became 5 : 3. (a) How many curry puffs and sardine puffs did Mrs. Lee make altogether at first? (b) Mrs. Lee sold all the curry puffs and sardine puffs she made at $0.80 each. How much did she collect? HK11P18 32. The ratio of Garreth’s pocket money to Jin Bao’s pocket money was 6 : 5. After Garreth received $20 from his father and Jin Bao spent $9, the ratio of Jin Bao’s pocket money to Gareth’s pocket money was 1 : 4. How much money did Gareth have at first? AT11S09
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Unit 7.8 Ratio Overlapping Shapes
PSLE Math Series
2007 1. In the figure not drawn to scale, the ratio of the area of the bigger square to the smaller square is 8 : 4. If 25% of the larger square is shaded, what percentage of the whole figure is not shaded? RY07P38
2. In the figure below, 3 squares A, B and C overlap to form Squares X and Y. The perimeter of Square X is 20 cm.
𝟓 𝟏𝟔
of Square B is shaded. The areas of Squares A, B and
C are in the ratio 4 : 25 : 9 respectively. Find the total perimeter of the unshaded regions. NY07C47
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2008 1
3. In the figure below, not drawn to scale, the area of X is of the whole rectangle. The 4
ratio of Area Y to Area Z is 5 : 4. What is the ratio of Area X to Area Y to Area Z? RY08C41
4. The figure below consists of 2 squares, X and Y, and a circle Z. The ratio of the area of X : 1
Y : Z is 5 : 2 : 3. If of Y is shaded, what fraction of the figure is not shaded? SN08C42 6
5. The figure below consists of 3 overlapping squares A, B and C. The ratio of the area of A to the area of B to the area of C is 2 : 3 : 4. If 25% of both Squares A and C is shaded, find the ratio of the shaded area to the unshaded area in the figure. Please give your answer in the simplest ratio. NH08C41
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6. The figure below, not drawn to scale, is made up of two overlapping rectangles, A and B. The ratio of the area of Rectangle A to that of Rectangle B is 2 : 5. If 25% of Rectangle A is shaded, what fraction of the figure is unshaded? TN08S40
7. In the diagram below, 75% of square Z is not shaded. The ratio of the area of square X to the area of square Y is 9 : 4. The ratio of the area of square Y to the area of square Z is 4 : 1. (a) What is the ratio of the area of square X to the area of square Z? (b) Find the ratio of the unshaded area of square Y to the unshaded area of square Z. SC08P42
8. The figure below is made up of an oval and a triangle overlapping each other. The ratio of the area of the unshaded part of the oval to the area of the unshaded part of the triangle is 11 : 9. If 70% of the triangle is shaded, what is the ratio of the area of the shaded part to the area of the unshaded part of the whole figure? RS08S37
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9. The ratio of the areas of the rectangle to the triangle to the circle is 6 : 4 : 5. of the 3
1
rectangle and of the triangle are shaded. What is the ratio of all the shaded areas to all 4
the unshaded areas? (Express this ratio in simplest form). RY08S42
2009 10. The figure below is made up of 2 triangles. The ratio of the area of small triangle to the 𝟒
area of big triangle is 9 : 16. The shaded area is of the area of small triangle. The area 𝟗
of the unshaded part is 68 cm 2. Find the area of the big triangle. NH09P11
11. The figure shown below is not drawn to scale. It is made up of two overlapping triangles. The ratio of the shaded area to the area of triangle A is 8 : 13. The ratio of the shaded area to the area of triangle B is 4 : 5. What is the ratio of the shaded area to the total unshaded area in the figure? SC09S10
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12. The figure below is made up of 2 squares and a rectangle. The ratio of the area of A to the area of B to the area of C is 9 : 4 : 3. The ratio of the unshaded part of B to the unshaded part of C is 4 : 1. If the shaded part is 56 m 2, find the area of A that is not covered by B. SN09S12
2010 2
13. The figure shows 2 overlapping identical squares (not drawn to scale). of each square is 3
shaded. What is the ratio of the shaded area to the unshaded area of the figure? Express your answer in its simplest form. RY10C04
1
14. The figure below consists of two overlapping squares ABCD and BXYZ. Q is the mark of 5
the sides, DC and ZY. Express the shaded area as a fraction of the total unshaded area. (Give your answer in the simplest form.) AT10S12
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15. The figure below (not drawn to scale) is made up of three rectangles X, Y and Z placed such that they overlap at S and T. The ratio of the area of Rectangle X to the area of Rectangle Y to the area of Rectangle Z is 6 : 4 : 1. The ratio of the area of Rectangle S to the area of Rectangle T is 3 : 1. If the area of Rectangle Y is twice that of the area of Rectangle S, what is the ratio of the total area of shaded parts to the total area of the unshaded parts? Express the ratio in its lowest term. RY10S11
16. The figure below shows 3 different rectangles, A, B and C. 20% of rectangle A and 30% of rectangle C is shaded. The shaded area of A is the same as the shaded area of C. What fraction of the figure is shaded if 40% of rectangle B is shaded? CH10S14
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17. In the figure below, not drawn to scale, 40% of the triangle DEC is shaded. The ratio of the shaded part of circle to the unshaded part of the circle is 5 : 9. (a) What percentage of the rectangle ABCD is shaded? (b) If the area of the circle is 168 cm2 and AE = EB, find the area of the triangle ECB. RS10P15
18. The ratio of the area of the shaded region to the area of the triangle is 1 : 4. The ratio of the area of the shaded regions to the area of the rectangle is 1 : 9. Find the value of A. NY10S05
2011 19. The figure below, not drawn to scale, shows a square and a rectangle that are overlapping each other. The area of the square to the area of the rectangle is 2 : 5.
The ratio of the area of the square to the area of the shaded part is 5 : 2. If the shaded area is 10 cm2, find the area of the unshaded part of the figure. MG11S07
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20. The figure below is made up of a rectangle and a square. The ratio of the area of the rectangle to the area of the square is 5 : 2. After the shaded part is cut out, the ratio of the unshaded part of the rectangle to the unshaded part of the square becomes 3 : 1. Given that the length of the square is 6 cm, find the area of the shaded part. NH11S15
21. The figure below is made up of three triangles A, B and C. 50% of Triangle A is shaded. 𝟏 𝟒
of Triangle B is shaded.
20% of Triangle C is shaded. The total area of Triangle A and Triangle B is 125% of the area of Triangle C. Express the area of Triangle A as a fraction of the area of Triangle B. Leave your answer in its simplest form. NY11C18
22. The figure below shows 2 overlapping rectangles A and B. The area of
rectangle B is 20% more than the area of rectangle A. The unshaded, area of rectangle A is 80% of the unshaded area of rectangle B. What percentage of rectangle B is shaded? RY11P05
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23. The figure below is made up of a triangle and a rectangle. The ratio of the area of the triangle to the area of the rectangle is 9 : 20. 2
The shaded area is of the area of the triangle. 3
The unshaded area is 126 cm 2. Find the area of the triangle. RY11C12
1
24. Rectangle A overlaps with rectangle B. Rectangle A is twice the size of Rectangle B. If of 3
rectangle B overlaps with rectangle A, what fraction of rectangle A overlaps with rectangle B? NH11C11 25. The figure below is made up of a square and a rectangle overlapping each other. The ratio of area X to the area of square is 1 : 4. The ratio of area X to the area of the rectangle is 4 : 13. Find the length of each side of the square if the area of the rectangle is 52 cm2. HK11P09
26. The figure below shows 3 different rectangles, X, Y, and Z.
3 10
of X and 40% of Z is shaded.
The shaded area of X is the same as the shaded area of Z. What fraction of the figure is unshaded if 60% of Y is shaded? TN11S16
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Unit 8 Speed
PSLE Math Series
8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8
Basic Concept Model Method Logical – Same Direction Logical – Opposite Directions Catching up Meeting up Ratio Method Fraction Method
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PSLE Math Series
Unit 8.1 Speed Basic Concept
2010 1. Mr Yu travelled 180 km at 54 km/h. At what speed must he travel if he wanted to decrease his travelling time by 20 minutes? AT10S05 2. In a recent triathlon race, Ben swam, cycled and ran at an average speed of 21.5 km/h. He swam 1500 m in 34 minutes and took 11 minutes more to run 10 km. He managed to complete the whole race in 2 hours 36 minutes. (a) What was the distance that he travelled by cycling? (b) Find the average speed for the total distance at which he cycled and ran. (Give your answer in km/h and as a fraction in the simplest form.) MG10P14 3. Jack and Ken ran in a marathon covering 42 km. When Jack completed the distance in 𝟓
5 hours, Ken only covered of the distance. Find the average speed of Ken. RG10S03 𝟔
4. City A and City B was 300 km apart. Jason and Kevin were driving from City A to City B. in the journey, Jason passed a petrol kiosk 1 hour before Kevin while Kevin was 60 km away from the petrol kiosk. How long did Kevin take to travel from City A to City B? RG10P05 𝟏
5. Mrs Don drove at an average speed of 75 km/h for 1 h. She continued to drive at 15 𝟐
𝟏
km/h slower for another h. How far had she travelled altogether? SN10P04 𝟑
6. Mr Lim was travelling at a speed of 50 km/h for 1 h 30 min and completed the rest of his journey at 70 km/h for 30 min. Find the average speed of his whole journey. HK10P02 7. A motorcycle travels 3 times as fast as a bicycle. If the motorcycle travels 126 km at a speed of 63 km/h, how much longer will it take the bicycle to travel the same distance? SC10P04
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2011 8. Mr Woo travelled from Town Q to Town R. After travelling for 1 hour at an average speed of 80 km/h, he decreased his speed by 20 km/h to travel the remaining journey for 3 hours. Find his average speed for the whole journey. NY11S05 9. At 8 a.m., Kenny started travelling from Town A to Town B at 80 km/h. At 10 a.m., he was still 2 hours away from Town B.
Find the total distance from Town A to Town B. RG11S03 10. The graph below shows the total distance Sam jogged yesterday over a period of time.
What was Sam’s average speed for the whole journey? RY11P01
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Unit 8.2 Speed Model Method
PSLE Math Series
2007 1. A motorist wanted to travel from Town P to Town R via Town Q. On the first day, he travelled 70 km from Town P to Town Q. On the second day, he continued his journey 𝟏
from Town Q towards Town R and covered of the remaining journey. He was then 𝟒
halfway between Town P and Town R. If he had travelled at an average speed of 50 km/h, find the total time taken to travel from Town P to Town R. NY07S41 𝟏
𝟏
𝟑
𝟐
2. Neil made a journey from City X to City Y. He covered of the journey in 1 h. In the 𝟏
𝟐
𝟒
𝟓
next 2 h, he covered another of the journey. He then took 1 h 15 min to travel the remaining 96 km. Find his average speed in km/h for the whole journey. PC07P(2)46 3. Jane started driving at 9.30 a.m. from Town A to Town B. At 11.30 a.m., Jane had 2
covered only of the distance. She had to cover another 144 km before she reached 5
Town B. (a) What was the distance between Town A and Town B? (b) If Jane were to travel at an average speed of 72 km/h after 11.30 a.m., at what time would she reach Town B? (Express your answer using the 24-hour clock) RG07P41 2008 4
4. A car took 3 hours to complete the last of a journey at an average speed of 60 km/h. Its 5
average speed for the whole journey was 50 km/h. (a) Find the total distance of the whole journey. 1
(b) Find the time taken for the first of the journey. NH08S42 5
3
5. Mr Ng travelled a distance of 450 km on an expressway. He completed of the journey 5
in half the time taken for the whole journey and covered the rest of the distance at an average speed of 60 km/h. (a) What was the total time taken for his whole journey? (b) What was his average speed for the first part of his journey? RS08P38
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6. At 7.15 a.m., Mr Tan started driving from Town P to Town Q at a uniform speed of 60 km/h. 30 minutes later, Mr Lee started driving from Town Q to Town P. Mr Lee drove at a constant speed until he met Mr Tan at 9.45 a.m. along the way. At this point, Mr 𝟑
Tan had travelled of the journey. Mr Lee decreased his speed by 10 km/h after 𝟕
driving past Mr Tan, and he drove at the new speed for the remaining journey. What time did Mr Lee reach Town P? HK08P47 7. Andrew left Town X for Town Y which was 500 km apart. He travelled at an average 3
speed of 90 km/h for of the journey. He then increased his speed by 30 km/h for the 5
rest of the journey and reached Town Y at 2 pm. Richard also left Town X for Town Y at the same time as Andrew and he drove at an average speed of 100 km/h for the whole journey. (a) What time did Andrew leave Town X? (b) How far apart were they at 1 pm? SC08P44 8. Mark and Andre competed in a 1600 m race. When Mark finished the race, Andre had 3
completed only of the distance. Mark ran at an average speed of 200 m/min. 4
(a) How long did Mark take to complete the race? (b) What was Andre’s speed? MG08S45 9. Elijah participated in a 45-km marathon. For the first 3 hours, he ran at 8 km/h. He decided to change his speed for the remaining distance. It took him a total of 5 hours to complete the entire marathon. What was his average speed for the remaining part of the marathon? SN08S44 𝟒
10. Mr Yee took 3 hours to cycle from Town X to Town Y. He covered of the journey in 𝟗
𝟏
the first hour, of it in the second hour and the rest in the third hour. If his average 𝟑
speed for the first 2 hours was 14 km/h, find his average speed for the whole journey. MB08S48 2009 1
11. Ahmad left Town A and drove towards Town C. After driving for of the journey at an 4
average speed of 72 km/h for 40 mintues, he stopped at Town B to have a break for 20 min. Then he carried on with the journey at an average speed of 80 km/h. (a) What was the distance between Town A and Town C? (b) How long did Mr Ahmad take to travel from Town A to Town C? NH09P14
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12. The speed of a car when it started its journey is 90 km/h. After travelling at this speed 𝟑
for 2 h, it had completed of the journey. It then increased its speed by 30 km/h and 𝟒
travelled the rest of the journey at this new speed. What was the average speed of the car for the whole journey? SC09S14 13. A bus left Town X at 9.00 a.m. and travelled towards Town Y at a uniform speed of 60 km/h. Half an hour later, a car left Town Y and travelled towards Town X at an average 𝟐
speed of 100 km/h. When the car had travelled 350 km, the bus had only travelled of 𝟑
the whole journey. At what time did the bus reach Town Y? HP09S13 14. The distance between John’s home and the park is 4200m. He ran at a speed of 140 1
m/min for the first of the distance from his home and at a speed of 200 m/min for the 3
remaining distance. What was his average speed for the whole journey? Express your answer in kilometres per hour. NY09S10 2010 2
1
3
3
15. Royston cycled for 3 days. He cycled 6 km on the first day for h and of the remaining 1
journey on the second day. Then he had of the total journey left. If his average speed 2
for the entire journey was 12 km/h, find (a) the total distance; (b) his average speed for the last 2 days. SN10P09 16. The distance between Town X and Town Y was 875 km. Kenny started his journey from 𝟑
Town X to Town Y at an average speed of 70 km/h. After he had covered of the 𝟓
journey, he decided to increase his speed so that he could reach town Y one hour earlier. What was the increase in speed for the remaining part of the journey? NY10S08 𝟑
17. Mr Phua drove from Town A to Town B. He took 2 h to cover of the journey at an 𝟒
average speed of 60 km/h. He covered the remaining journey at an average speed of 50 km/h. If he arrived at Town B at 12 noon, what time did he leave Town A? AT10S17
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2011 18. At 8.30 a.m., Myke and Jerome set off at the same time from Town X to Town Y. At 𝟓
11.00 a.m., Myke completed his journey but Jerome had covered only of the journey. 𝟖
Jerome’s speed was 54km/h slower than Myke’s. (a) Find the distance between Town X and Town Y. (b) At what time would Jerome complete his journey? SN11P12 19. The distance between Town A and Town B is 116 km. A bus left Town A and headed for Town B. Some time later, a car left Town A and headed for Town B along the same route. Along the way, the car overtook the bus and arrived at Town B 45 minutes 𝟓
earlier than the bus. When the car arrived at Town B, the bus had travelled of the 𝟖
distance. What was the speed of the bus? MG11P12
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PSLE Math Series
Unit 8.3 Speed Logical (Same Directions)
2007 1. Rowena travelled from Higgety Town to Lollipop Town. She covered the first 135 km at 1
90 km/h and completed the remaining journey at 80 km/h for 1 h. Sabrina took another 2
route and she travelled 15 km less than the route Rowena travelled. If Sabrina’s average speed for her whole journey was 96 km/h, how much less time did Sabrina take to complete the journey than Rowena? PH07S43 2. Mabel and Nelly wanted to cycle to the library. 150 m Nelly’s house
900 m
Mabel’s house
Library
Mabel started cycling at an average speed of 50 m/min from her house. Nelly started from her house, which was 150 m behind Mabel’s house. She cycled at an average speed of 75 m/min. Both of them started cycling at the same time. (a) When Nelly reached Mabel’s house, how far was Mabel ahead of her? (b) The library was 900 m away from Mabel’s house. When Nelly reached the library, how far from the library was Mabel? PH07S47 3. Tom and David started travelling from Town A at the same time. Collin, who was travelling in the same direction, was some distance ahead when Tom and David started on their journey. After travelling for 12 minutes at an average speed of 70 km/h, Tom overtook Collin. 3 minutes later, David, who was travelling at an average speed of 58 km/h, overtook Collin too. What was the average speed of Collin in km/h? PH07P46 4. Town E and Town F were 240 km apart. Jason left Town E at 9.00 a.m. travelling at an average speed of 60 km/h. Karen left Town E some time later than Jason and overtook him at 11 a.m. Karen’s travelling speed was 90 km/h. (a) At what time did Karen leave Town E? (b) How long had Karen rested when Jason finally reached Town F? NH07P43
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5. Mr Goh was travelling from Town X to Town Y. After completing of the journey, he 𝟕
passed by Mr Lee travelling the same direction. Mr Lee was travelling at an average speed of 60 km/h. Mr Goh reached his destination 3 hours later, while Mr Lee was still 45 km away from Town Y. (a) Find the distance between the two towns. (b) If Mr Lee left Town X at 11.30 a.m., what time would he arrive at Town Y? AC07P48 6. Two motorists, X and Y, travelled on the same route from Town A to Town B. They each drove at a uniform speed but started their journey at a different time of the day. The table below shows some details of their journey. Motorist Distance from Town Time Distance from Town B A X 60 km 13 25 60 km Y 100 km 13 25 100 km If Motorist X reached Town B at 1625, find (a) the distance between the two towns and (b) the speed at which Motorist Y was travelling. MB07P44
Time 15 55 15 55
2008 7. At 8.30 a.m., Mrs Tan left Town A and drove towards Town B. 1 hour later, her husband left Town A and took the same route, driving towards Town B at an average speed of 80 km/h. When he reached Town B at 1.30 p.m., Mrs Tan was 20 km away from Town B. (a) Find Mrs Tan’s average speed. (b) At what time did Mrs Tan reach Town B? NH08S46 8. Ali and Dave cycled from Town A to Town B at 12 km/h and 10 km/h respectively. Ali left Town A at 8.30 a.m. and arrived at Town B at 9 a.m. When Ali arrived at Town B, Dave was 1.5 km away from Town B. What time did Dave leave Town A? AT08S42 𝟐
9. A car was on its way from Town Y to Town Z. After covering of his journey, it 𝟕
overtook a lorry which was travelling at an average speed of 65 km/h. 4 hours later, the car reached Town Z, but the lorry was still 60 km away from Town Z. (a) Find the average speed of the car. (b) Find the distance between Town Y and Town Z. NY08S45
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10. Desmond was travelling from Town K to Town L. After completing of the journey, he 𝟕
passed a truck travelling at an average speed of 70 km/h in the same direction. 3 hours later, Desmond reached Town L but the truck was still 65 km away from Town L. (a) Find the distance between Town K and Town L. (b) If the truck was travelling on the same route as Desmond and left Town K at 10 30, at what time would it arrive at Town L? RS08S46 11. Mr Tan and Mr Wong drove from Town K to Town H. They started their journeys at different times. Mr Tan drove at 66 km/h and took 50 min. Mr Wong drove at an average speed of 75 km/h and reached Town H the same time as Mr Tan. (a) What is the distance from Town K to Town H? (b) What was the time taken for Mr Wong’s journey? (c) If Mr Wong started the journey at 9.45 am, what time did Mr Tan start his journey? SC08S47 12. Mrs Lee and her children left home at 11.00 a.m. and drove to a holiday resort at an average speed of 48 km/h. Her husband left home for the same holiday resort half an hour later. They drove along the same route. Mr Lee managed to meet up with his family at 1.30 p.m. along the way. Find Mr Lee’s average speed. RS08S39 2009 Michelle’s house
Natasha’s house
Park
480 m 13. Michelle’s house and Natasha’s house are 480 m apart. Both girls walked from their house to the park at the same time. Michelle caught up with Natasha after 40 minutes. Given that Natasha’s speed is 68 m/min, find the time taken for Michelle to walk from her house to Natasha’s house. SC09P12 14. At 9.30 a.m., Mr Yeo left Town A for Town B driving at a speed of 75 km/h throughout his journey. At 10.30 a.m., Mr Lee also left Town A for Town B driving at a certain speed. He kept to the same speed throughout his journey. At 1.30 p.m., both of them passed a Shopping Mall that was 150 km away from Town B. How many minutes earlier did Mr Lee reach Town B than Mr Yeo? AC09P14
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15. At 7 am, a car started travelling from Town A towards Town B at an average speed of 64 km/h. At 10 am, a van started travelling from Town A towards Town B at an 𝟐
average speed of 56 km/h. By then, the car had already covered of the entire journey. 𝟓
(a) What was the distance between Town A and Town B? (b) How far from Town A had the van travelled when the car reached Town B? PL09P17 2010 16. Gary and Edwin started off together in the same direction from Town A and drove towards Town B at an average speed of 60km/h and 96 km/h respectively. How far apart would they be after 20 minutes? NH10S11 17. A car and a van started travelling from Town X to Town Y at the same time. The distance between the two towns was 225 km. Both vehicles did not change their speed. 𝟑
The car arrived at Town Y h earlier than the van. When the car reached Town Y, the 𝟒
van was still 45 km away from Town Y. What was the speed at which the car was travelling? HK10P15 18. A rabbit and a tortoise competed in a 5.2 km race. The rabbit ran at a speed of 20 km/h while the tortoise’s speed was 3 km/h. The tortoise ran continuously to complete the race. However the rabbit ran for 1 min and rested for 20 min. It ran for the next 2 min and rested for 20 min. It then ran for the next 3 min and rested for 20 min and so forth. At this rate, how many minutes more would it take the rabbit than the tortoise to complete the race? RV10P16 19. Nancy started cycling from Point X to the library at 9 a.m. at a uniform speed of 500 m/min. At 9.10 a.m., Nancy passed Sam as he started cycling from Y towards the library at a certain uniform speed. At 9.20 a.m., Sam was 1 km ahead of Nancy. They continued cycling towards the library and Sam reached there at 9.37 a.m. (a) What was Sam’s speed? (Leave your answer in km/h.) (b) What was the distance from Point X to the library? (Leave your answer in km.) NY10S14 20. Tony and Charles took part in a car race. Tony drove at a speed of 90 km/h. Both of them 1
did not change their speed throughout the race. When Charles had covered the 3
distance, Tony was 15 km in front of him. Tony reached the finishing line at 9.35 a.m. At what time did Charles reach the finishing line? AC10S14
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21.
Tom is travelling on a bus that is moving at a uniform speed of 30 km/h. If he alights at Bus Stop A, he will walk home by Route A which is 800 m away from his flat. He can also alight 1 km down the road at Bus Stop B and take the 730 m Route B home. If Tom walks at a uniform speed of 40 m/min, find: (a) The difference in time when he alights at the two different bus stops. (b) The earliest time he can reach home if he boards the bus from the interchange 20 km away at 13 05. MB10P18 22. A car and a lorry started a journey from a town at different times of the day. The lorry left the town at 12 noon and travelled at an average speed of 50 km/h. The car left the town at 1 p.m. but it caught up with the lorry after travelling 250 km. Assuming that both the car and lorry travel at a constant speed throughout the journey, how far apart were the lorry and the car at 6 p.m.? SC10P12 2011 23. Irfan and Jason jogged from the school to the swimming pool along the same route. Jason started his journey ten minutes later than Irfan.
Irfan jogged 4 km at an average speed of 3 km/h for the whole journey.
Both of them arrived at the swimming pool at the same time. What was Jason's average speed? MG11S05
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24. Devi and Laura took part in a cycling competition. Devi's average speed was 400 m/min. When Devi completed the journey in
45 minutes, Laura still had 900 metres to cover. a) What was the distance of the cycling competition? b) What was Laura's average speed? NH11S10 25. Sue drove past Orchard Mall travelling at an average speed of 80 km/h to Maple Mall. Derek left Orchard Mall one hour earlier than Sue and took 5 hours to reach Maple Mall, travelling at an average speed of 72 km/h. Derek reached Maple Mall at 6 p.m. (a) At what time did Sue leave Orchard Mall? (b) How far was Sue from Maple Mall when Derek reached the destination? RG11S16
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Unit 8.4 Speed Logical (Opposite directions)
2007 1. At 8 am, a van left Town A and travelled towards Town B at 70 km/h. At the same time, a lorry left Town A and travelled in the opposite direction towards Town C. When the lorry reached Town C at 10 am, the van was 10 km away from Town B. If the distance between Town B and Town C was 270 km, what was the average speed of the lorry? NH07S46 2. Town X and Town Y were 350 km apart. At 11.30 a.m., a van started travelling from Town X towards Town Y at 80 km/h. Two hours later, a truck started travelling from Town Y towards Town X at 54 km/h. (a) How far from Town X was the van at 3.30 p.m.? (b) What was the distance between the van and the truck at 3.30 p.m.? HP07S45 3. A bus was travelling at a constant speed from Town A to Town B. It passed a car 𝟏
travelling at a constant speed of 90 km/h in the opposite direction. 1 hours later, the 𝟐
bus reached Town B but the car was still 25 km away from Town A. If the bus took 4 hours to complete the whole journey, what is the distance between the two towns? RY07P48 4. At 8.30 a.m., Tom drove from Town P to Town Q at an average speed of 80 km/h. After 𝟐
driving of the journey for 4 hours, he passed Paul who was traveling along the same 𝟓
road in the opposite direction. Paul was traveling at a speed which was 20 km/h slower than Tom. At what time did Paul leave Town Q? HK07P46 2008 5. At 7.30 a.m. a bus left Town S for Town R travelling at an average speed of 60 km/h. 15 minutes later, a car left Town R for Town S. The car reached Town S at 10.45 a.m. The bus reached Town R at 12 noon. (a) How far apart were the two towns? (b) What was the average speed of the car? (c) How far apart were the two vehicles at 9.45 a.m.? MG08P45
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2009 6. Ahmad started travelling from Town P towards Town Q at 7 a.m. After travelling for some time, he passed Steve who was travelling at an average speed of 80 km/h in the opposite direction. After travelling for another 2 hours, Ahmad reached Town Q while Steve was still 40 km away from Town P. (a) If Ahmad reached Town Q at 1.00 p.m., what was his average speed? (b) If Steve started his journey from Town Q, at what time did he leave Town Q? NY09P17 7. At 8 a.m., Richard left Town A in his car and travelled towards Town B at 90 km/h. At the same time, Kenny left Town A in his car and travelled in the opposite direction towards Town C. When Kenny reached Town C at 10.30 a.m., Richard was 15 km away from Town B. (a) What was the distance from Town A to Town B? (b) If the distance between Town B and Town C was 440 km, what was Kenny’s average speed? NH09S16 2010 8. At 10 am, Mandy set off from Town X to Town Y at a constant speed of 70 km/h. At the same time, Nora drove off from Town Y to Town X. After some time, they drove past each other. Later at 1 pm, they were 40 km apart. Mandy reached Town Y at 3 pm. (a) How far from Town Y was Nora at 1 pm? (b) What time did Nora reach Town X? MG10S13 9. At 08 00, a van left Town Y and travelled towards Town Z at an average speed of 70 km/h. At the same time, a lorry left Town Y and travelled in the opposite direction towards Town X. When the lorry reached Town X at 10 00, the van was 10 km away from Town Z. Town X and Town Z were 270 km apart. (a) Find the speed of the lorry. (b) Find The time taken for the lorry to travel from Town X to Town Z. NH10P18 2011 10. A bus travelled at a uniform speed from Sunshine Town to Happy Town. It passed a car which was travelling at a uniform speed of 80 km/h in the opposite direction. 4 hours after they had passed each other, the bus reached Happy Town and the car was 30 km away from Sunshine Town. If the bus took 9 hours to travel from Sunshine Town to Happy Town, find the distance between the two towns. RG11P15
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11. At 9.30 a.m., a car left town X for town Y at a speed of 60 km/h for the whole journey. At 11 a.m., a lorry started from town Y and travelled towards town X. The speed of the lorry remained the same until it passed the car at 12.30 p.m. The lorry passed the car at midpoint between town X and town Y and decreased its speed by 20 km/h. It travelled at the new speed for the rest of the journey. What time did the lorry reach town X? CH11P11 12. A car left Town A at 08 00 and travelled to Town B at an average speed of 60 km/h. At the same time, a lorry left Town B for Town A. At 11 30, the car and the lorry were 85 km apart after passing each other earlier. If the car arrived at Town B at 13 00, at what time would the lorry arrive at Town A? NH11P15
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Unit 8.5 Speed Catching Up
PSLE Math Series
2007 1. A kangaroo chases a rabbit which starts 135 m ahead of the kangaroo. For every 4.7 m leap of the kangaroo, the rabbit makes a 1.7 m leap. How many leaps will the kangaroo have to make to catch up the rabbit? NH07C39 1
2. Ben travelled at an average speed of 70 km/h from Town A to B. James started off h 2
later and travelled at an average speed of 80 km/h from Town A to B. At the end, both of them reached Town B at the same time. Find the distance between Town A and Town B. PH07P39 3. A cyclist travelled from Town A to Town B at the speed of 29 km/h. After he had travelled 116 km, a motorist whose speed was 3 times that of the cyclist left Town A and travelled along the same route to Town B. How far did the motorist travel when he met the cyclist? RY07S43 4. Yen Ming started driving his car from Town X to Town Y at 13 40 at an average speed of 70 km/h. Leon started driving his sports car from Town X to Town Y at 15 10 at an average speed of 100 km/h. (a) At what time did Leon pass Yen Ming on the road? 3
(b) 14 h after Leon passed Yen Ming on the road, Leon reached Town Y. At what time did Yen Ming reach Town Y? NY07S46 5. Last Monday morning Edward walked from home to school. For the first 2 minutes, he was walking at an average speed of 40 m/min. When he realised that he was going to be late by 3 minutes, he quickly increased his speed by 10 m/min. As a result, he was early by 1 minute. Find the distance between his home and school.AT07S46 6. A bus and a car travelled from Town X to Town Y. The bus left Town X at 1 0.48 p.m. and it took 5 hours to reach Town Y. The car started 30 minutes later than the bus and it took 4 hours to reach Town Y. At what time did the car catch up with the bus? NY07P48
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2008 7. A kangaroo is trying to chase a rabbit which is 45 m in front of it. For every 3.8 m leap of the kangaroo, the rabbit makes a 2.3 m leap. How many leaps will the kangaroo have to make in order to catch up with the rabbit? AT08S43 8. Adrian tries to catch a frog which is 180 m away from him. For every 10 m Adrian runs, the frog jumps 7 m. How much further must Adrian run before he can reach the frog? MB08S40 9. At 2 pm, a motorist left Town A travelling towards Town B at a uniform speed. Two hours later, a lorry driver started from Town A and travelled along the same road. The lorry driver overtook the motorist at 7 pm. The speed of the lorry driver was 30 km/h faster than the speed of the motorist. (a) What was the speed of the motorist? (b) What was the distance between Town A and Town B if the lorry was 60 km away from Town B at 7 pm? RS08P43 10. Alice left Town X at 8.30 a.m. and travelled towards Town Y at an average speed of 90 km/h. Belinda left Town X 45 minutes later and travelled towards Town Y along the same route at an average speed of 84 km/h. (a) How far apart were they at 10 a.m.? (b) If Belinda increased her speed by 18 km/h after 10 a.m., how long would it be before she overtakes Alice? NH08P43 2009 11. Tommy and Wilson jog on a hexagon track (6 equal sides) at 8 a.m. Tommy starts at point C while Wilson starts at point F. Both job in the direction as shown by the arrows. Tommy’s speed is 1.5 times Wilson’s. (a) At which point will they meet? (b) If they meet at 8.20 a.m., find Tommy’s speed. AT09S15 B
C
0.5 km A
D
F
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and it took 5 hours to reach Town B. The car started 30 minutes later than the coach and it took 4 hours to reach Town B. At what time did the car catch up with the coach? HK09P15 2010 13. Jason left Town A at 1 p.m. travelling at 64 km/h towards Town B. Half an hour later, Ben left Town A, travelling at 80 km/h towards Town B. (a) How far ahead was Jason when Ben left Town A? (b) At what time would Ben be 8 km ahead of Jason? RG10P17 14. A tour bus which left Kuala Lumpur at 10.30 a.m. was scheduled to reach Singapore by 5 p.m. After travelling for 2 hours at its usual speed, the bus stopped for 30 minutes due to some problems. In order to reach Singapore punctually, the bus increased its speed by 8.5 km/h. Given that the bus took 4 hours to complete the rest of the journey, find the distance between Kuala Lumpur and Singapore. RY10P17 15. Sarah started driving from Town A to Town B at 4.30 a.m. travelling at constant speed. James left Town A for Town B three hours later than Sarah travelling at a constant speed of 120 km/h. When James arrived at Town B, Sarah was still 160 km away from Town B. Two hours later, Sarah reached Town B. (a) Calculate Sarah’s average speed. (b) What time did James overtake Sarah? RG10S18 2011 16. A bus, which left Terminal Y, was scheduled to reach Terminal Z at a certain time. After travelling for an hour at its usual speed, the bus stopped for 30 minutes due to an engine problem. In order to reach Terminal Z at the scheduled time, the bus travelled the remaining journey at a speed which was 6 km/h faster than the usual speed. The bus took 4 hours to cover the remaining journey. (a) Find the usual speed of the bus. (b) Find the distance between the two terminals. NY11S18
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17. Mr Tok left Town A for Town B at 11.30 am. He travelled at an average speed of 75 km/h. At 12.15 pm, Ms Selva left Town A for Town B, travelling on the same route at an average speed of 100 km/h. (a) At what time would Ms Selva overtake Mr Tok? (b) After Ms Selva had overtaken Mr Tok, she took another 2 hours to reach Town B. What was the distance between Town A and Town B? AC11S13 18. Abdul, Bernard and Chi Hao were all standing in a straight line waiting for the race to start. Chi Hao was 300 m ahead of Bernard and Bernard was 100 m ahead of Abdul. At 9 a.m., they started the race. Abdul overtook Bernard in 5 mins. In another 5 mins, Abdul overtook Chi Hao. If Bernard's speed is 150 m/min, at what time did Bernard overtake Chi Hao? RY11P18
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PSLE Math Series
Unit 8.6 Speed Meeting Up
2007 1. The distance between Town A and Town B was 558 km. Mr Chan started from Town A and drove towards Town B at an average speed of 80 km/h. 30 min later, Mr Ho started from Town B and drove towards Town A at a speed of 68 km/h. (a) What distance had Mr Chan travelled when he met Mr Ho? (b) At what speed should Mr Ho increase by in order to reach Town A in 4 hours’ time after meeting Mr Chan? AC07S47 2. At 8.30 am, a car started from Town A and travelled towards Town B at an average speed of 90 km/h. At the same time, a bus travelled from Town B to Town A at an average speed of 60 km/h. If the distance between Town A and Town B was 600 km/h, what time would they pass each other? NH07S42 3. Town A and B are 484 km apart. A truck leaves Town A for Town B at 10 45 at an average speed of 64 km/h. At 14 15, a motorcyclist leaves Town B for Town A at an average speed of 40 km/h. At what time will the two vehicles meet each other? SC07S47 4. A lorry, a van and a car set off at the same time travelling at a constant speed of 60 km/h, 80 km/h and 120 km/h respectively. The lorry and the van were travelling from Town G to Town H while the car was travelling from Town H to Town G. The car passed the lorry 2 minutes after passing the van. (a) Find the ratio of the distances travelled by the lorry to the van to the car at the moment when the car passed the van. (b) Find the distance between Town G and H. HP07P48 5. At 7 a.m., Car A left Town X for Town Y while Car B left Town Y for Town X. At 3 p.m., the two cars passed each other. 5 hours later, Car A reached Town Y but Car B was still 150 km away from Town X. Find the distance between Town X and Town Y. SC07P47
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2008 6. The distance between Town A and Town B was 360 km. At 9.30 a.m., a lorry left Town A for Town B travelling at a constant speed. At the same time, a van travelling at a constant speed set off from Town B towards Town A. The two vehicles met each other at 12.30 p.m. The van was travelling at 20 km/h faster than the lorry. What was the speed of the van? AC08S48 7. Town X and Town Y are 600 km apart. At 2 p.m., Mr Tan left Town X for Town Y, travelling at a uniform speed. At the same time, Mr Ong left Town Y for Town X travelling at a uniform speed which was 12 km/h faster than Mr Tan. Find the average speed of Mr Tan if the two men met at 5 p.m. TN08S47 8. At 09 00, a van left Town P for Town Q. After some time, a car left Town Q for Town P. The two vehicles met at 11 30. The ratio of the average speed of the van to the average speed of the car is 3 : 5. (a) What time did the car leave Town Q? (b) If the distance between Town P and Town Q is 150 km, calculate the average speed of the van. RG08S48 9. A car started from Town A and headed towards Town B. At the same time, a van started from Town B and headed towards Town A. The speed of the car was 16 km/h greater 1
than the speed of the van. After 1 hours, they were 280 km apart. After another 2 2
hours, they passed each other. What is the speed of the car? RY08S46 10. The distance between Vovo Town and Domi Town was 1200 km. Mr Mong drove from Vovo Town to Domi Town at 72 km/h. He started on his journey at 11 a.m. Mr Sahu 𝟏
left Domi Town h later and drove towards Vovo Town at 75 km/h. If they were to 𝟑
continue driving at the same speed without stopping, at what time would they meet each other? Leave the answer in 24-hour clock. SN08S45 11. Car A left Town X for Town Y at the same time when Car B left Town Y for Town X. The average speed of Car A was 56 km/h and the average speed of Car B was 72 km/h. The two cards passed each other at a point 24 km from midway of the two towns. What is the distance between Town X and Town Y? AC08P43
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12. Ning and Zongwei jogged to and fro repeatedly along a straight path in a park between two points A and B. Ning jogged at a uniform speed of 4 m/s and Zongwei jogged at a uniform speed of 6 m/s. They started jogging from opposite directions at the same time as shown below. Ning A
Zongwei B X
Y
They first met one another at point X. The second time they met was at point Y. (a) Given that the distance between X and Y is 160 m. Find the distance between A and B. (b) If they started jogging at 8 a.m., how long did they take to meet again for the third time? (Express your answers in minutes and seconds) RY08P48 2009 13. The distance between Town G and Town H was 240 km. At 12 30, Mr Koh left Town G travelling at a constant speed towards Town H to meet his wife. At the same time, Mrs Koh who was at Town H travelled towards Town G at a constant speed. Mr and Mrs Koh met each other at 14 30. Mrs Koh was travelling at 20 km/h faster than Mr Koh. What was the speed Mrs Koh was travelling at? RS09S17 14. At 10.30 am., a car started from Town X and travelled towards Town Y at an average speed of 100 km/h. At the same time, a bus travelled from Town Y to Town X at an average speed of 70 km/h. If the distance between Town X and Town Y was 425 km, what time would they pass each other? NH09S12 15. Ben drove from Town X to Town Y and Carl drove from Town Y to Town X. Ben was driving at a constant speed of 80 km/h. At 2.30 p.m., they were 180 km away from 𝟏
each other. They passed each other 1 h later. 𝟒
𝟏
(a) Carl took 6 h to travel from Town Y to Town X. What was the distance between 𝟐
the two towns? (b) At what time did Ben reach Town Y if he left Town X at 12.15 p.m.? NY09S18 16. A van travelled from Town A to Town B at an average speed of 55 km/h. A car started its journey from Town B to Town A at the same time as the van, travelling at an average speed of 90 km/h. The two vehicles passed each other 70 km from the middle of the whole journey. Find the distance between the two towns. HP09P13
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17. At 9.30 a.m., Train A which was 200 m long, pulled out of Nanas Station and travelled towards Dadas Station at a uniform speed of 80 km/h. Half an hour later, Train B which was 150 m long, left Dadas Station and travelled towards Nanas Station at an uniform speed of 90 km/h. (a) How far has Train A travelled when Train B left Dadas Station? (b) The two trains met each other in a tunnel. Both trains took 15 minutes completely out of the tunnel. Calculate the length of the tunnel. RG09P17 2010 18. Kitty Town and Melody Town are 234 km apart. Danny left Kitty Town for Melody Town at 8.42 a.m. travelling at an average speed of 85 km/h. At the same time, Jasmine left Melody Town for Kitty Town. They met each other at 10.30 a.m. (a) What was Jasmine’s average speed when she met Danny? (b) If Jasmine were to increase her speed by 26 km/h before meeting Danny, how much less time would she take before meeting him? SN10P15 19. The distance between Town U and Town V is 374.25 km. A car left Town U at 21 15 for Town V, travelling at 85 km/h. A van left Town V at 22 45 for Town U on the same road, travelling at a certain speed. The two vehicles met at 276.25 km from Town U. What was the speed of the van in km/h? PC10P16 20. A car and a lorry which were 80 km apart started to travel towards each other at the same time. The car was 40 km/h faster than the lorry. They went past each other after
2 5
hours. (a) How far did the lorry travel when it went past the car? (b) Find the speed of the lorry. NH10S17 21. A car left City A for City B at 8 am travelling at an average speed of 60 km/h. One hour later, a bus started its journey from City B for City A. At 11.30 am, the two vehicles were 35 km apart after passing each other earlier. If the car reached City B at 1 pm, at what time would the bus arrive at City A? HP10P13 22. At 9.30 a.m., Train A left Station A and travelled towards Station B at a uniform speed of 80 km/h. Half an hour later, Train B left Station B and travelled towards Station A at a uniform speed of 90 km/h. (a) How far has Train A travelled when Train B left Station B? (b) If the distance between Station A and Station B is 635 km, at what time would the 2 trains pass each other? AC10P15
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23. At 9 a.m., John was cycling from Point A to Point B. At the same time, Mary was cycling from Point B to Point A using the same route as John. Cycling at a speed of 4 km/h faster than Mary, John would pass Mary 300 m away from the midpoint. (a) What time did they pass each other? (b) If John took another 3 minutes to reach Town B, what time would Mary reach Town A? CH10P15 24. John travelled from Town Q to Town R at an average speed of 72 km/h. He travelled
7 12
of the journey at an average speed of 70 km/h. After that, he decided to increase his speed to travel the remaining 450 km to Town R. (a) Find John’s speed in the last 450 km of the journey. (b) If Kenny started his journey from Town R to Town Q at the same time as John at a constant speed of 90 km/h, how far would he have travelled before he met John? NY10S17 2011 25. The distance between Town A and Town B was 520km. At 8.30 a.m., a van left Town A for Town B travelling at a constant speed. At the same time, a car travelling at a constant speed set off from Town B towards Town A. The two vehicles met each other at 12.30 p.m. The car was travelling at 20 km/h faster than the van. What was the speed of the car? AC11P15 26. At 6 a.m., a car left Town A for Town B at a speed of 65 km/h. At the same time, another car left Town B for Town A at a speed of 55 km/h. The distance between the two towns was 720 km. At what time did the 2 vehicles pass each other? SN11P05 27. Sunshine City and Moon Town were 361 km apart. At 06 00, Azman started travelling from Sunshine City to Moon Town at a constant speed of 80 km/h. 45 minutes later, Baoming left Moon Town and travelled towards Sunshine City at a constant speed of 60 km/h. At what time did Azman and Baoming pass each other? NY11S10 28. Ali and Ben started jogging from Park X to Park Y at the same time. Ali jogged at an average speed of 7.5 km/h while Ben jogged at an average speed of 4.5 km/h. After jogging for 1.2 h, Ali decided to turn back and jog towards Ben. Ali met Ben at Point Z which was halfway between Park X and Park Y. Ali and Ben then continued their jog together towards Park Y at an average speed of 4.5 km/h. What was the distance between Park X and Park Y? NY11P10
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29. Town A and Town B are 760 km apart.
At 9.40 a.m., Gopal set off from Town A to Town B at a constant speed of 80 km/h. Half an hour later. Baron set off from Town B to Town A at a constant speed which is 10 km/h slower than Gopal’s speed. What time will they meet each other along the way? MG11S15 30. Town A and Town B were 395 km apart. At 6 a.m., a car started travelling from Town A to Town B at a constant speed of 60 km/h. At 6.20 a.m., a motorcycle started travelling from Town B to Town A at a constant speed of 90 km/h. (a) At what time did they pass each other? (b) How far away was the car from Town B when it passed the motorcycle? NH11S18 31. A car left Town X for Town Y at the same time when a motorcycle left Town Y for Town X. The average speed for the car is 88 km/h while the average speed of the motorcycle was 64 km/h. The two vehicles passed each other at a point 33 km from the midpoint between Town X and Town Y. What was the distance between Town X and Town Y? RS11S17 32. A car left Town A for Town B. At the same time, a lorry left Town B for Town A. The average speed of the car was 90 km/h while the speed of the lorry was 70 km/h. The two vehicles passed each other at a point 36 km away from the mid-point between Town A and Town B. What was the distance between Town A and Town B? HK11P15
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PSLE Math Series
Unit 8.7 Speed Ratio Method
2007 1. Edward, Felix and George took part in a 60-metre race. When Edward crossed the finish line, he was ahead of Felix by 10 m and ahead of George by 20 m. Felix and George continued to race to the finish line without changing their speed. How far was George from the finish line when Felix completed the race? AT07S45 2. It takes courier A 10 hours to deliver a parcel from Town X to Town Y. Courier B takes 12 hours to deliver the parcel along the same route. If the speed of courier A is 9 km/h faster than courier B, find the speed of courier A. RG07S48 3. Najip, Kumar and Gurmit started jogging at the same time from the same starting point round a circular track. Najip and Kumar jogged in a clockwise direction and Gurmit jogged in an anti-clockwise direction. Gurmit took 5 minutes to complete each round. Gurmit met Najip after every 3 minutes. Gurmit met Kumar after every 2 minutes. The jogging speed of each person remained the same throughout. (a) What was the ratio of Gurmit’s speed to Najip’s speed to Kumar’s speed? (b) When Gurmit and Najip met again at the starting point after 15 minutes, Kumar had already jogged 3.6 km. What is the circumference of the circular track? PC07P(1)47 2008 4. John jogged at an average speed of 4 km/h from Point A to Point B and back to Point A at a speed of 3 km/h. He took a total of 1 h 10 min. How long did he take to jog from Point B back to Point A?TN08S41 5. Theodore, Gareth and Linus took part in a 100-metre race. When Theodore completed the race, Gareth and Linus were 15 m and 30 m away from the finishing line respectively. How far was Linus from the finishing line when Gareth finished the race? (note: all the boys were travelling at a constant speed throughout the race) SN08S37
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6. Chester cycles from his place to the community centre for his yoga class every Sunday. If he were to cycle at 10 km/h, he would reach the community centre at 3 p.m. If he were to cycle at 15 km/h, he would reach there at 1 p.m. (a) How far does Chester have to cycle from his place to the community centre? (b) At what average speed must he cycle if he wants to reach the community centre at 2 p.m.? SN08P44 1
7. Lily is meeting a friend at a certain time. If she drives at 80 km/h, she will be hour late. 3
3
If she drives at 60 km/h, she will hour late. How long will the journey take if she drives 4
at 90 km/h? NY08P47 8. Azman and Dollah took part in a cross-country race. Azman’s average speed was 72 m/min faster than Dollah. 𝟏
𝟒
𝟑
𝟕
When Azman completed the whole race in h, Dollah had only completed of the race. Find a) Dollah’s average speed and b) the time taken by Dollah to complete the race. MB08P48 9. Two motorists competed in a race. When motorist X completed the race in 4 hours, motorist Y covered only 75% of the race. Motorist X was driving at 40 km/h faster than motorist Y. (a) What is the total distance of the race? (b) Find the average speed that motorist Y was travelling at for the whole journey. SN08S47 10. Zhiyong and Muthu took part in a marathon. When Zhiyong finished the marathon in 3 3
hours, Muthu had completed of the race. Zhiyong’s speed was 4 km/h faster than 5
Muthu. Find the distance of the race. NY08S36 2009 11. Mr Fernandez drove from home to work at 60 km/h. After work, he needed to rush home for dinner and increased his speed on his way home by 30 km/h. As a result, he took 5 minutes less than what he had taken on his way to work. What was the distance between his house and office? RS09S09 2010 12. Kingsley planned to cycle from Town P to Town Q. If he were to cycle at 10 km/h, he would reach Town Q at 7.45 p.m. If he were to cycle at 12 km/h, he would reach Town Q at 7.15 p.m. What was the distance between Town P and Town Q? NY10P10
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13. A man travels from City X to City Y at 4 km/h and from City Y to City X at 6 km/h via the same route. The whole journey took 1 hour. Find the distance from City X to City Y. CH10S11 2011 14. Mr. Tan sends his son to school every morning at 6.15 a.m. If he drives at an average speed of 60 km/h, his son will be 10 minutes late for school. If he speeds at an average speed of 120 km/h, his son will arrive in school 10 minutes early. What should Mr. Tan’s average speed be if he wants his son to arrive in school on time? AT11S18
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PSLE Math Series
Unit 8.8 Speed Fraction Method
2008 1. A car, travelling at a constant speed, took 9 hours to travel from Town Y to Town Z. A lorry, travelling at a constant speed, took 18 hours to travel from Town Z to Town Y. Both vehicles started at the same time and they met when they were 180 km from Town Z. (a) Find the distance between the two towns. (b) Find the speed of the car. RG08P45 2009 2. A bullet train took 5 hours to travel from Patient Town to Honest Town while an electric train took 4 hours longer to travel from Honest Town to Patient Town. Both trains set off at the same time and moved towards each other. Two hours later, they were 255 km apart. What was the speed of the electric train? SN09P15 3. Mr Tan took 6 h to drive from Town A to Town B. Mr Lim, who started at the same time as Mr Tan, took 4 h to drive from Town B to Town A. When they met each other, they were 48 km away fro the midpoint of Town A and Town B. (a) Calculate the distance between Town A and Town B. (b) Calculate the speed of Mr Tan. CH09P17 4. Aaron and Kumar took part in a 24-km marathon. Aaron ran half the distance at a speed of 10 km/h and jogged the rest of the way at a speed of 8 km/h. Kumar ran half of his total time at 12 km/h and jogged the rest of the time at 6 km/h. If they started the marathon at 8 am, at what time would each of them finish? RY09P18 2011 5. Mr Lee took 7 hours to travel from Town A to Town B while Mr Wong took 8 hours to
travel from Town B to Town A. Both of them did not change their speed throughout the journey. Both of them started off at the same time and moved towards each other. 3 hours later, they were 110km apart. What was the speed Mr Lee was driving? HP11P16
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pslemathseries.com Unit 1 Whole Numbers Unit 1.1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42.
PH07C37/186 NH07C40/16.65 RY07C40/39 HK07P36/6 RG07P39/270/135 NH08C38/30 TN08S36/310 MB08S38/4.60 AT08S37/186 RY08P37/1.5 RY08S36/app AC09P07/115 HK09P06/1.90 HK09P17/app RS09P06/684 RY09C10/app SN10C05/89 AT10C12/app RY10S07/17 NH10S010/1250 AT10S07/5 AT10S11/June2013 NY10S12/app RG10S09/10 AC10P08/435 SN10P07/423.65 SN10S15/70/app SN10S09/108 CH10P10/app NY10S02/805000 SN10P02/26 HK10P03/800 MB10P08/5/30 HP10P05/46 AT10S04/88800 CH10P05/app RY10C03/69 RG11S11/65/61.75 NY11C02/5.8 NY11C05/14 RY11C01/117,4 SN11C13/188
43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54.
HK11P03/0.12 TN11S05/1.5 HP11P04/283 SN11C01/73 NH11S03/51 NY11C07/app CH11P05/12 NH11P02/8 RG11P04/5 NH11P05/0.65 MG11P06/app RS11P01/95
Unit 1.2 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
RY07C42/29/13 NH07C43/app AC07S38/156 NH07P40/84 SC07P37/72 MG08C48/26/130 RG08S44/2.50 NY08P37/8 NY08S42/app NH10C15/app MG10S07/12 CH10S06/50 AT10S10/app HK10P05/21 CH10P04/114 RY10S13/4/28 AT11C03/144 AT11C12/516/96 CH11S09/208 AC11P11/app
Unit 1.3 1. 2. 3. 4. 5. 6. 7. 8.
RY07C46/app RG07S41/120 HP07P45/7/1100 AC08S42/3/app NY08S39/10.50 AC10S15/app NY10S06/app NY11S01/8
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9. RY11C13/8/app Unit 1.4 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
AT08S40/app NY08P36/app RY08P44/app NY08P41/56 MG08P40/120 SC09S13/app NY10P02/11 SN11C06/8/34 NH11P04/24 HP11P11/app
Unit 1.5 1. 2. 3. 4. 5. 6. 7. 8. 9.
NY07C43/290/app HP07S48/app PC07P(1)37/105/42 RG08S38/383 AT09C14/app SN09C16/125 SN10S10/app NH10P09/app NY10P07/274.80
Unit 1.6 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
PH07C48/180/app PH07S48/app SC08P43/app HP09S06/app RY10P05/app NH10P03/app RS10P02/app RG11S14a/308 HK11P02/app RY11S13/app AC11P13/app
Unit 1.7 1. 2. 3. 4. 5.
AC07S39/7 NH07S43/15 NH07P39/7 NY07P41/18 PC07P(2)45/app i
pslemathseries.com 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
RY07C45/630/app NH07C37/app RY07S41/app NH08S43/26 NY08S43/app MB08S39/34 MG08S42/7 AT08S36/7big3small HP09P09/5 RS09P18/app SC09S08/54 NY09C14/app
18. NH10C14/
7
11
19. 20. 21. 22. 23. 24. 25. 26.
RG10P07/46 PC10P07/3090/13 AT10C13/app MGS11P01/5 NH11C15/app TN11S08/3 RY11S06/52 MG11S10/app
Unit 1.8 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
NH07C36/8 PH07C43/265 RY07C39/701 AT07S37/app AT07S38/0.45/4.95 NH07S36/45 AC07P41/1.60 SC07P45/app MB08C38/4.50 AT08C41/1.81 HK08P36/1087 NY08C41/2.40 SN08C37/9.60 MB08S36/1080 MB08S46/0.7/app AC08P42/0.4/2 MG08S39/99 SC08P38/30 SN08P39/518 RY09C18/app RG09S12/13
22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.
RG09P06/145 HP09S10/0.6 RG09S08/12.50 HP09S08/app HP09P07/19.80 AC10P07/78.75 AT10C18/app RY10C10/400 AT10S06/1200 SN10S12/116.80 HP11P06/app TN11S06/1.50 AC11S02/18 TN11S10/201 SN11S08/378 SN11C03/22.7 NY11S16/797/app RY11P13/1048/app RG11S13/app
Unit 1.9 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
AC07S42/70/140 SC07S37/app HP07P40/app NH08P44/app AC09P11/app PL09P07/app RV10P02/app RY10P18/app AT11C01/2880 RY11C09/633 RY11P06/app NY11P17/app RS11P15/app
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pslemathseries.com Unit 2 Patterns Unit 2.1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
AC07S48/13/21/201/50 HP07S37/24/96/10 HP07P41/1 NH07C46/8/14/32/19 PC07P(2)48/32/50/300 /app RG07S38/31/84 RG07P42/41/161/app SC07P42/124/app RG08S43/102/42 AC08S46/10/202/250 NY08S48/17/95/app NH08S45/6/10/10/22/7 0 HK08P45/9/19/354 SC09P10/52/app SN09P14/333/app AT09C10/64 RY09C12/16/51/5n+1 HK10P12/14/app RY10P12/25/app RG10S08/17/350 HP11P08/45/18/324 AC11S15/9/11/13/201/ 300 CH11S13/36/221 SN11C18/116/62/app AT11S13/41/app CH11P13/24,9/43 RS11S14/51/199 RY11S18/28/36/236/10 04
Unit 2.2 1. AT07S44/20/16/app 2. NH07P47/15/21/36/12 1 3. NY07C46/11/569/app 4. SC08S42/5/9/7/16/9/25 /11/36/11 5. NH08P47/7/16/9/25/62 5/11
6. SN09C18/12321/app 7. NH09C18/1+3+5+7+9/2 5/80/10and11 8. AT09S13/25/16641/15 9. CH09P14/21/421/app 10. PC10P18/41/14965/ap p 11. CH10P12/2551/app 12. CH10S18/16/121/15 13. NY11S14/55/112/app 14. RG11P10/9/81/app 15. RY11C11/25/144/app 16. NH11P17/16/11/32/40 0/34/app Unit 2.3 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
HK07P47/30/app MB08C48/28/15/app AT08C47/41/181/app SN08C48/6/7/12/14/22 /2550 NY09S15/56/app NY09P15/21/34/app NH09S15/15/45/12/3& 8 HP09P17/10/7/app RG09P15/45/15/app RY09P12/16/19/app NY11C15/21/7/app TN11S18/45/40/app
Unit 2.4 1. 2. 3. 4. 5. 6. 7.
PH07C41/app SC07S42/130 AC07P40/app RY07S46/1m/495m SC08P45/app SC08S41/15 AT09C09/5
8. NH09P09/ 9. 10. 11. 12.
Unit 2.5 1. 2. 3. 4. 5. 6.
RG08S37/4/9/7 RG08P47/app RG09S11/app RG09P14/100/app MG10P06/app SN10C16/app 5
7. AT11C18a/
6
Unit 2.6 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
PH07C47/29 PH07P42/46/21 RS08P47/32/192/app AT08S46/app RS08S48/14/42/16 PL09P15/7/8/app HP09S18/20/148/app SN10P18/20 NY10S15/399/199,200/ app NH10C17/2/3/4/5/5/4/ 3/2/30/2550 NY10P15/3/7/app NH10S14/398/app NH10P06/30/20/420 MG10P01/4.07 RY10P01/13×14/14×15 SC10P03/5 AT11C18b/app HK11P05/F NH11C16/23/25/33/ap p NY11P14/16,17,18,19,2 0,21/55/app
3 85
RY09P07/1,5/4,3/2,6 NY11C08/4 NH11C09/app SN11S10/app
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pslemathseries.com Unit 3 Algebra Unit 3.1 2𝑦−25
1. NY07C36/
3
/18
2. RY07C37/3y/57 3. AC07S36/18m 4. HP07S41/app 15−3𝑛
5. NH07S39/3n/
2
30−𝑘
6. PH07S36/
20
7. SC07S41/app 𝑦 +20
8. HK07P41/ 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
3
/16
HP07P36/6m SC07P36/8k+3/12:13 MB08C40/8m-4/20 RS08C42/4x+80/3.40 NY08C40/app RY08C39/2m–6/2 MG08C41/y+53/61 NH08S37/app TN08S38/24n AC08S37/15w+500/650 0 RG08S36/170–14y SC08P37/2x+36 RG08P36/28n SN08P37/4n+4.30/32.3 0
38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.
MB10P04/12p+10 CH10P02/4n+12 SC10P01/400–p RS11C01/100+28x NY11S03/2640 NH11P01/app RG11S02/25+42w 3000 −𝑤 SN11S03/ 5 CH11S02/5p RG11P01/12k NY11P01/app TN11S04/29m
Unit 3.2 𝟐𝟔𝟒−𝒌
1. AC07P39/
/app
𝟒 126 −3𝑘
2. AC08P36/ 3. 4. 5. 6. 7. 8.
4
/96
HK08P40/7k+8/app NY09C06/18x–3/app AC10S13/7p–8/32 SN10S11/7h+20/69 RG10S07/app HP10P09/8m–8/37 2
9. RY11S01/ c 3
10. 11. 12. 13. 14.
19𝑞
MG11S12/ /1900 7 SN11S07/5k+17 NH11S07/16p–7/40p–7 NY11C06/101h/app RY11C06/4w+5/4w+35
Unit 3.4 6𝑑
1. PH07C38/ 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
5
PH07C40/4h/app RG07S37/app PH07P41/app RS08C36/6y+10/46 MG08S36/30+3t NY08S40/8p/48 SC08S40/6h/app NY08P40/40+0.5x/app MG08P36/14g/90 NY09P12/6:7:11:15/6:7 AT09C13/6p/app NH10C10/147–15u MG10S11/app SN10S04/8r RY10S04/6x RG10S02/28y MG10P10/12a RS10P04/1.50+0.05x RY11S03/app AC11S06/3y/72 RS11S03/9y RS11P05/app TN11S07/app
𝑛 24
23. NH09S09/ /
4 𝑛
24. SC09S07/15b/168 5−0.4𝑚
25. HP09P06/ 26. 27. 28. 29. 30. 31. 32. 33. 34.
3
/1
SN09P08/20+r HP09S09/app RG09P07/app SN10S03/15k+42 RG10P01/505 SN10C09/app RG10P08/4y+0.20 SN10P10/app RY10S05/3k+30 30
35. CH10S01/
Unit 3.3 1. NY07P36/app 25𝑦 +67
2. RG07P36/
7
3. RY07P36/9w 4. SN08S38/53e–288/app 5. RG09S07/app 480
6. RY10C06/
𝑤
/40
7. SN10P05/app 8. MG11P08/12d+150/70. 62 9. HP11P07/3x–24/15 𝟑𝒚+𝟏𝟕𝟐
10. RG11P06/
𝑦
𝟓
/app
36. NY10S04/21 38−28𝑝
37. PC10P02/
3
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pslemathseries.com Unit 4 Data Analysis Unit 4.1 1. NY07C44/140/
5
35. AT11C09/4/30.31 36. AT11S01/110/Nov Unit 4.2
12
5
2. SC07S36/45
6
3. 4. 5. 6. 7.
AT07S36/1300/12.5 NH07S38/28/app SC07S38/A and B/app HK07P38/90/Sunday HP07P38/20/20 9
1. PC07P(2)36/15/42 2. RG07P38/app 3. AC07S40/750/app 3
4. HP07S38/2:5/1
5
5. PC07P(1)39/30/20 𝟐𝟏
6. HK08P38/ /app 𝟒𝟎
8. NH07P44/40/ /127
7. RG08P40/app
9. PC07P(2)38/750/1500 10. PH07P43/faster/slower /250 11. AC07P42/195/20 12. SC07P38/April/400
8. MB08P40/1200/
20
1
13. SC08P36/3/33
3
14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.
AC08P40/45/60/187.50 SC08S36/250/app SC08S37/Friday/544 MB08S44/90/app NH08S36/14/70 AC08S40/Feb and June/100/3:5 HK09P08/140/1200 NH09S08/300000/app MB10P09/4/app NY10P14/Year1/102000 0/1320000 CH10P09/175/75 CH10S09/300/165 AT10C07/220/app NH10S08/50/Sunday MG10P12/40/40/app NY10P05/13 RY10P03/2006– 2007/50 HP11P09/app NY11P04/50 NY11P12/600/900/300/ 900/1000/2300/251 RY11P09/Tuesday&Frid ay/Thursday/app
4
31
9. MG08P37/100 10. RY08P38/16/315 16
11. NY08P39/ /324 25
12. 13. 14. 15. 16.
AC09P09/60/app PL09P10/210/245 RY09P11/18 SN09P11/5/104/29 CH09P10/app 1
17. RG09P10/ /200 5
18. RG10P06/40 19. RS10P14/10/app 1
20. PC10P11/2:3:6/
4
21. HK10P08/10/1350 22. RY10P07/app 1
23. RV10P11/3200/ /800 16
24. RY10S12/72/216 2
25. NH10S05/16
3
26. NH10S18/300/125 27. RY10P04/78 28. SC10P06/1200 𝟓
29. AC11P10/ /app 𝟐𝟒 4
30. RY11S11/ /16:55 5
31. 32. 33. 34.
RY11P04/160 MG11P17/21/app HK11P08/801/14418 NH11P08/5
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pslemathseries.com 𝟐
Unit 5 Fractions
18. RY08P45/ /app
Unit 5.1
19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.
MG08P48/ /45 3 NH08P42/80 NY09C08/20 SN09C10/0.56/2.548 SN09C17/41715 RY09CR10/1197 AT09S07/300 RG09S16/13/app RY09C15/20 NH09S18/7/app SN09P12/350 SN10P06/702 HP10P08/48 RG10S12/548.10 RY10S02/1278 NH10C04/600 5 SN10C08/
36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60.
SN10S01/758 3 SN10S08/15 RV10P05/78 RV10P03/75 AC11P07/1596 RY11S04/20 AC11S16/225/app SN11S01/390.4 SN11S11/150 SN11S15/1740 SN11S16/app NH11S06/50 NY11P16/app RG11P13/14 RS11P06/50 RS11C10/408 RY11C02/255 1 RY11C03/4 15 RY11C04/540 RY11P07/550 MG11P15/48/72 CH11P17/app AT11C10/1164 HP11P13/680/310 RG11S17/app
1. 2. 3. 4. 5. 6. 7. 8.
MG08S38/app SN09C07/app 1 NH09C06/3/ 12 RY09C08/2/app NH10C01/0.8 2 SN10S02/ 9 RG10P10/app 1 RY10S06/8/
9. 10. 11. 12. 13. 14.
NH10S07/ 5 PC10P03/app AC11S03/app 2 SN11S14/5/ 7 NH11S02/11 11 SN11C02/7
2
15. AT11C05/ 16. 17. 18. 19. 20. 21. 22.
56
20 4
77 9
SN11P01/3 32 NY11C09/app SN11C07/20/app RY11P02/app RS11P07/ app NH11C02/0.625 1 NY11C01/9/ 20
5
3
4
4
23. RG11P03/1.22, , 1 ,2 Unit 5.2 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
NH07C38/550 AC07S37/3.50 31 RG07P44/140/ 32 MB07P41/app MB07P43/20 RY07C43/122 NH08C40/5 NY08C42/6 RY08C38/15 SN08C40/860 SN08P46/app RY08C42/2212 MG08C42/36 RY08C43/240 NY08C45/5.6 MB08C37/28 8 MB08P41/ 19
𝟗 1
18
1
Unit 5.3 1. 2. 3. 4.
RG07S44/app NH07S40/3 TN08S45/app NH09S10/5
pslemathseries.com
5. 6. 7. 8. 9.
SN09C08/app 2 RY09C06/3 3 RS09P07/app CH10S07/app RS11C04/800
Unit 5.4 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
1
RG08P42/ /2800 7 SN08C41/app NH08C45/app AC08S38/54 NH08S38/60 SN09S08/app NH10S13/app RS10P07/40.80 RV10P06/560 CH11S07/324 SN11C10/64/176 TN11S13/app
Unit 5.5 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.
RG07S36/560 NY07P38/100 RG07P47/app RY07S39/27 NH07P42/app RS08S44/360/app NH08C39/70 HK08P42/app PL09P12/5512.50 RG09P09/15 SN09C15/app SN09C14/4/app SN10P01/72 SN10C15/app 4 RY10C02/ 9 RY10S08/app CH11P07/96 RY11C14/app RG11S06 /7014 RG11P09/app NH11P07/12
Unit 5.6 1. 2. 3. 4.
NH07S37/600 RY08S37/126 MB08S37/750/app MG08P44/app
vi
pslemathseries.com 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
SN08P47/32:12:33/app CH09P07/app RY09P10/app NH09S07/app AT10C04/5:6 NH10S01/60 PC10P08/app RY10C12/8250/app RG10S13/app MG11S06/Raju/app
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pslemathseries.com Unit 6 Percentage Unit 6.1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.
NY07P37/3.75 PH07S46/app NH08S47/210/app MG08P42/48 HK08P44/app NH08S40/app SN08C44/255.10 SN09C13/Z/12 AT09S09/50 SN10C12/32.1 SN10C14/10/app AC10S01/525 RY10S03/1200 AC10S11/720 MG10P05/12.60 RG10S01/20 NH10C02/137.5 RG10S05/10 NY10P01/900 RV10P01/24 MB10P02/1.05 AC11P09/15 RY11S02/187.5 MG11S17/2250/app SN11S12/36.80/app NH11S05/70 RS11S10/app CH11S01/2000 NY11C03/15 NH11C05/1280 SN11C04/12.24 CH11P01/150 RG11S05/6.72 AT11C11/app NH11P09/440 RG11S15/app
Unit 6.2 1. 2. 3. 4. 5. 6. 7. 8. 9.
NY07S37/400 RY07S42/app NY07C38/6 AT07S48/app RS08P46/3250/app MB08P47/app TN08S42/40 AC08S47/app RS08S45/280/app
10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
NH09C16/3:3:5/60 CH09P16/app CH09P08/150 RS09P15/app SN09S14/28.14 PL09P13/435 HK09P16/330 RY10P10/275 NH10P14/75/2000 SN11P15/1440/app RY11S07/500 AC11S04/40 NH11C07/180 SN11C15/45 AT11C16/200 TN11S11/app
Unit 6.3 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.
NY07S45/app PH07S44/60 NH07S47/1600/app PH07P48/810/app RG07S46/85 NH07C44/5760/6912 PH07S45/34/3:5 NY07P46/app MB08C45/990/693 NH08C36/1000 TN08S44/34.65 AC08S44/600 SN08S43/app NH08P40/612 MB08S47/890/267 NY08C43/186000/1075 AT08C48/30/240 RS09S11/84 SC09S06/325 SN10C10/62675.20 SN10C17/1818 NH10C07/720 AT10C09/5 CH10P11/600 CH10P17/app MG10P15/20:25:36/ap p HK10P16/app RY11S09/1875 RS11S04/18 RG11S02/6750 RS11P10/20:25:16/40 NH11C12/625
pslemathseries.com
33. 34. 35. 36. 37. 38.
AT11C02/50 CH11P03/45 AC11S17/120/12 MG11S03/25 RY11P16/app AT11S17/app
Unit 6.4 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.
PH07S38/500/50 RG07P48/500/app NY07P39/2500/18 PH07P36/14 MB07P42/20/5 AC07P44/400 PC07P(2)47/300/app MG08C47/app NY08P44/decrease/–20 MB08C46/20/app SC08S39/50 RY08P46/1350/4770 AC08P46/app RS08S38/75 RY08S41/750 NH09C13/2310 AT09S16/120000 SN09S10/27 RG09S06/700 AC09P17/app HP09S14/147/20 NH10C06/800 NH10S02/75 AT10S16/35/40 NY10S18/45/17:20 RS10P18/app SN10P16/app RY10S10/51 NH10S16/144 RG10S16/80 NY11S09/62.5 AC11S10/189 AC11S18/847/app NH11S16/app NY11P03/25 NH11C01/18.75 TN11S12/32 CH11P08/25
Unit 6.5 1. MB08C41/527 2. NY08C39/360
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pslemathseries.com 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
MB08P37/100 SN08S39/app RG08S46/2.20/app RY08S44/18/app RS09P08/30 NY09S08/1600 SC09S12/480 AT09C11/2000 PC10P06/45 RY10S14/700/app RG10S11/app MG11P07/3 MG11S13/60
Unit 6.6 𝟖
1. NH07P48/ /24/app 2. 3. 4. 5. 6. 7. 8.
𝟏𝟓 𝟖
SC08S48/ /app 𝟏𝟓 RG08P39/app NH10C05/120 MG10S02/40 RG10P02/275 MB10P10/app CH11P16/2405/app
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pslemathseries.com Unit 7 Ratio Unit 7.1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.
PH07C44/48 1 MB07P45/75/1 3 RY07S48/336/app NH07C47/9/app AC07P47/89M/54F AC07S43/115 AT07S43/7:11:9/168 NH07S48/app NH07S44/630 PC07P(2)44/12 MB07P47/18/app AT08S41/10 AC08P48/20/app RS08P39/312 RS08C39/80 RS08C46/1800/90 RY08C48/95/20 SN08C45/8 MG08S47/60 RS08S42/5500 MG08P46/171/app SN09C09/351 1 SN09C12/ 6 NH09C07/240 SN09S13/17010 RY09P17/app SN09P17/app RY09C09/6:7 RY09C11/280 HK10P01/270 NH10C03/7:4 SN10S05/1656 SN10S14/2190 NY10S07/825 HP10P17/app HK10P09/30 AT10C14/25 RY10C08/75 RG10P14/356 PC10P12/8:9:2/1440 HP10P16/42/45 AC10P06/156 CH10P06/5 NH10C12/34 NH10S15/13.10/47.16 MB10P05/6:7 RG11S01/5:7
48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67.
NH11C03/13:5 SN11S04/96 8 NH11S11/ 9 RS11S07/42 RG11P11/169/832 RS11P08/50 RS11P17/270 RY11P12/450 CH11P02/11:13 NY11S04/2:3:5 HP11P02/24 AC11S05/1:3 AC11S11/280 RS11P02/88 NH11C17/A20/B25/C30 RS11C03/100 RS11C08/56 RY11C18/456/app RS11S01/3:11 SN11C08/120
Unit 7.2 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
RY07C48/9 HP07S40/256 RY07C36/app RG07P46/36:35/app RY07S37/364 NH08C44/9:20:15/app AT08C39/750 SN08S40/320 MG08C36/450 RS09P09/30 NH09P07/50 SN09S11/app PL09P06/5585 HK09P09/125 RY10C11/app NH10S03/9:25 RG11S04/24:5 SN11S13/app NH11S12/12/app CH11S15/app NH11C14/app 9 MG11P10/49 55 AT11C07/27 HK11P12/375/app
Unit 7.3 1. HK07P42/18 2. AT07S40/app pslemathseries.com
3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.
PC07P(1)43/27/app RS08P36/44 NY08S46/app TN08S37/51 AC08S43/80/90 SC08P40/24 MB08P45/decreased/1 68 AT08C40/35 RY08C45/44 RY08S48/11/app NY09C12/3 SN09P13/app SC09P06/36 NH10S09/6 HP10P03/18 MG10S12/42 AT10C15/20 AC10S06/35 RV10P17/app AT10C05/9 RG10S04/10:3 SC10P05/app SN11S09/462 RG11P07/6 NH11C10/7 RY11C05/app TN11S01/25 AT11S07/app AT11S16/app
Unit 7.4 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
PH07C42/24 RY07C41/2754 RY07S40/240 RG07P43/45 NY07S47/app RG07S43/1500/app NH08P48/360/app SC08P48/app SN08S41/220 SN08C38/48 RY08P36/150 NH08C47/app NY08S47/app MB08C44/186/18:13 AC08P41/400 NH09P17/app RY09P13/132 SN09S09/240 RS09S07/54
x
pslemathseries.com 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52.
AT09C15/630 SC09P09/5 RG09S09/240 NY09S09/2300 RY09C07/414 NY09C16/8:3/480 SN09S15/30 SN09S17/295 2 SN09S18/75/14 7 PL09P16/2:11/5982 NY09S14/app RS10P01/36 SC10P08/50 RY10S15/1020/6800 AT10C06/138 RS10P09/75 RY10P06/30 NY10P09/125 AC10P17/28:1/100 MG10S16/720/90 SN11P16/510 SN11P17/1100 NY11S08/567 RG11S09/100 NH11S08/54 CH11S14/480 RS11C16/42/app RY11C08/325 RY11C10/28 AT11C15/276 HK11P06/176 NH11P13/20 RY11S15/1:4/app
Unit 7.5 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
HP07S43/1920 PH07S37/30 RG07S47/880/app 11 HP07P43/24/ 15 HP07P47/120/app RY07C44/32/3:4 PC07P(1)40/120 AT08S48/180 MG08C45/app NY08P42/360 NH08S44/80 AT08S45/200/50 RS08C47/378 MG08C37/360 RG08P46/8:3/640
16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.
SN08C47/4:3/app AT09S17/app RG09P16/app HP09S16/38 1 HP09S07/ 7 NH09C10/112 NY09S12/36/57 NH09C14/108/24 AT09C16/325 RY09C13/540 RY10P11/120 RV10P14/app RY10C16/F39/L65 AC10S12/182 RY10S09/128 RY10C18/app CH10S12/360 NY10S11/51/68 1 NH10S16/33 /48 3 MG10P11/156 MG10P18/198/2 6 RG11S10/114/42 7 RY11S12/2700 SN11S17/app CH11S12/148 NY11P07/238 NY11C16/147/97 NH11C04/20 RY11P11/35:51 AT11C13/120 AT11C17/app AT11S10/21
Unit 7.6 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
NY07P44/AT10C10/800 AC07S44/264 AT07S41/27 NY07S38/190 SC07S48/app RY07P46/16 PC07P(1)48/app RY08C46/20 NH08C42/300/100 MB08C47/28 NH08C46/450 NH08S48/270 AC08S45/app RY08S47/32 MB08S45/900 AC08P45/app
pslemathseries.com
17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60.
RY08P47/16 MB08P42/21780 RG08P48/66.50 5 SN08P45/1350/ 9 NY08P45/120/app NH09S14/120 RY09P15/3.20 NH09C15/1200 NH09P13/264 SC09P14/42 NY09C18/app NY09P18/app SC09S17/120 RG09P11/14 RY09C16/100/120 AT09S11/67.5 HP10P01/105 SN10C07/24 RV10P09/205 NY10P16/app HP10P15/app MB10P12/26 SN10S16/192/201 SN10S17/1640 RY10C14/278.10 RY10C15/130 AT10S15/2880 MB10P06/12 AC10P13/9 SC10P07/420 RY10C13/111 NY11S11/60/200 HP11P15/app RG11S12/68.40 RY11S08/16.80 NH11S14/225 CH11S16/0.80 NY11C12/5/2.20 RS11C11/125 RS11C17/130 RY11C16/45 AT11C06/180 CH11P15/30 NH11P14/8
Unit 7.7 1. 2. 3. 4.
AC07P43/150 HK07P48/app PC07P(1)41/13 NY07C48/324
xi
pslemathseries.com 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.
AC07S45/250 NY07S48/app RY07S44/20G/55B RG08S42/660 MG08S46/app NY09C13/24 AT09C17/app HP09P15/5:1/app AC09P08/624 RG09P18/510/app PC10P05/31 NH10C13/12 MG10S09/84 NY10S09/18 CH10P18/4:5/app NY10S16/3:20/app SN10P17/app CH11P06/8 RY11S10/128 MG11S16/144/520 𝟏 NY11P18/ /app 𝟑 NY11C17/60/120 NY11S13/152 NH11C13/18 MG11P18/40 AT11C14/160 HK11P18/210/220 AT11S09/24
20. 21. 22. 23. 24.
NH11S15/app NY11C18/app 2 RY11P05/16 3 RY11C12/54 1 NH11C11/ 6
25. HK11P09/8 31
26. TN11S16/
43
Unit 7.8 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
RY07P38/app NY07C47/app RY08C41/3:5:4 22 SN08C42/ 23 NH08C41/app 12 TN08S40/ 13 SC08P42/app RS08S37/21:20 RY08S42/1:3 NH09P11/app SC09S10/8:7 SN09S12/app RY10C04/1:3 1 AT10S12/ 8 RY10S11/app CH10S14/app RS10P15/20/75 NY10S05/27 MG11S07/67.5
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xii
pslemathseries.com 8. AT08S42/8.33 9. NY08S45/80/app 10. RS08S46/385/app
Unit 8 Speed Unit 8.1
11
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
AT10S05/app MG10P14/44.4/app RG10S03/app RG10P05/app SN10P04/app HK10P02/app SC10P04/app NY11S05/app RG11S03/app RY11P01/app
Unit 8.2
11. SC08S47/55/ /10.29 15
12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
RS08S39/60 SC09P12/6 AC09P14/app PL09P17/480/app NH10S11/12 HK10P15/app RV10P16/app NY10S14/36/21.2 AC10S14/10.05 MB10P18/40/1405 SC10P12/12.5 3
1. NY07S41/app 2. PC07P(2)46/360/app 3. RG07P41/240/1330
23. MG11S05/3
7
24. NH11S10/1800/app 25. RG11S16/2pm/app
1
4. NH08S42/225/1
2
5. 6. 7. 8. 9. 10.
RS08P38/6/90 HK08P47/app SC08P44/9/20 MG08S45/8/150 SN08S44/10.5 MB08S48/app 4
11. NH09P14/192/2
5
12. 13. 14. 15. 16. 17. 18. 19.
SC09S14/app HP09S13/app NY09S10/10.5 SN10P09/24/13.5 NY10S08/app AT10S17/app SN11P12/360/app MG11P12/app
Unit 8.3 1
1. PH07S43/
2
2. 3. 4. 5. 6. 7.
PH07S47/100/200 PH07P46/app NH07P43/9.40/40 AC07P48/315/app MB07P44/420/88 NH08S46/60/1.50
Unit 8.4 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
NH07S46/app HP07S45/320/78 RY07P48/app HK07P46/app MG08P45/270/90/app NY09P17/50/app NH09S16/240/app MG10S13/180/app NH10P18/60/app RG11P15/app CH11P11/2.18 NH11P15/app
Unit 8.5 1. 2. 3. 4. 5. 6. 7. 8. 9.
NH07C39/45 PH07P39/280 RY07S43/174 NY07S46/1840/2110 AT07S46/app NY07P48/app AT08S43/30 MB08S40/600 RS08P43/45/app
pslemathseries.com
10. 11. 12. 13. 14. 15. 16. 17. 18.
NH08P43/72/app AT09S15/F/app HK09P15/app RG10P17/32/4pm RY10P17/app RG10S18/80/app NY11S18/48/app AC11S13/2.30/425 RY11P18/app
Unit 8.6 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.
AC07S47/320/app NH07S42/12.30 SC07S47/app HP07P48/3:4:6/60 SC07P47/app AC08S48/app TN08S47/app RG08S48/10/30 RY08S46/78 SN08S45/app AC08P43/384 RY08P48/400/app RS09S17/70 NH09S12/1pm NY09S18/416/app HP09P13/580 RG09P17/40/42.15 SN10P15/45/18 PC10P16/56 NH10S17/32/80 HP10P13/3pm AC10P15/40/1.30 CH10P15/9.09/9.36 NY10S17/75/607.5 AC11P15/75 SN11P05/12 NY11S10/0854 NY11P10/app MG11S15/2.58 NH11S18/8.50/225 RS11S17/418 HK11P15/app
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pslemathseries.com Unit 8.7 1. 2. 3. 4.
AT07S45/12 RG07S48/app PC07P(1)47/6:4:9/app TN08S41/40 11
5. SN08S37/17
17
6. SN08P44/60/12 1
7. NY08P47/1
9
8. 9. 10. 11. 12. 13. 14.
MB08P48/96/app SN08S47/640/app NY08S36/30 RS09S09/15 NY10P10/30 CH10S11/2.4 AT11S18/app
Unit 8.8
1. 2. 3. 4. 5.
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