Primary 5 Mathematics Ace The Exams with My 24/7 Personal Tutor Detailed Explanation of ALL Questions by Tutor in Virtual Classroom
Consulting Editor: Dr Zhang Yong
© Outreach Edusys Pte Ltd
ALL RIGHTS RESERVED. No part of this book and the accompanying CDROM may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, CD duplication, replication, or by any information storage and retrieval system, without permission in writing from the Publisher.
First Published 2010
ISBN: 978-981-4275-16-3
Published by: Outreach Edusys Pte Ltd (CRN: 200006571H) Distributed by: Outreach System Pte Ltd 20 Shaw Road, #07-03 Singapore 367956 Tel: +65 91162024 Fax: +65 35107345 Email:
[email protected] Website: http://www.orlesson.org Please check URL regularly for new releases and promotions. Sample chapter and lesson for each title can be downloaded from above URL. Purchase online or call/SMS 9116-2024 today. FREE home delivery (one location within Singapore) for purchases above S$60/=.
ii
Preface This book is written to assist pupils in preparing for the Primary 5 Math examinations. There are a total of 10 specially crafted examination style papers. The main features of the papers are as follows. 1. Questions are modeled after examination papers set by top well known Singapore schools. 2. Questions are crafted to highlight common misconceptions in each of the topics. This book comes with a multimedia CDROM. The CDROM contains detailed explanation of each question in each paper by our teacher. These lessons ensure pupils understand the methods behind solving each question. Outreach Book Alive series brings the “tuition teacher” to you at zero cost. You may also want to try our online programme. These are interactive “diagnostic” modules consisting of multiple choice questions. The incorrect options to each question are carefully crafted using specific mis-conception in learners. If your child submit a wrong answer, our system will dynamically diagnose your child’s problem and bring him/her an explanation on why he/she is wrong, and what is the correct way to the solutions of such questions. Visit http://www.orlesson.org today.
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Contents Semestral Assessment 1 Mock Paper 1 Semestral Assessment 1 Mock Paper 2 Semestral Assessment 1 Mock Paper 3 Semestral Assessment 1 Mock Paper 4 Semestral Assessment 1 Mock Paper 5 Semestral Assessment 2 Mock Paper 1 Semestral Assessment 2 Mock Paper 2 Semestral Assessment 2 Mock Paper 3 Semestral Assessment 2 Mock Paper 4 Semestral Assessment 2 Mock Paper 5
Suggested Answers
Paper 1 Paper 2 Paper 1 Paper 2 Paper 1 Paper 2 Paper 1 Paper 2 Paper 1 Paper 2 Paper 1 Paper 2 Paper 1 Paper 2 Paper 1 Paper 2 Paper 1 Paper 2 Paper 1 Paper 2
1 8 15 23 30 38 45 53 60 67 74 80 88 94 101 108 115 122 129 137 144
Free Past Year School Exam Papers (from 2004 onwards) for download and print. Visit http://www.orlesson.org for links and download instructions. Subscribe to Outreach Lesson Online Access for hundreds of hours of lessons, and thousands of questions. Less than 70 cents a days for unlimited access to ALL subjects. For details, visit http://www.orlesson.org.
iv
Semestral Assessment 1: Mock Paper 1 Paper 1 (Duration: 50 mins) Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1.
2.
3.
Fill in the blank with an appropriate number that matches the pattern ______, 900 000, 800 000, 700 000 (1) 10 000 (2) 100 000 (3) 1 000 000 (4) 10 000 000 (
)
( 3 In order to have of the set below shaded, how many more squares must be 5 shaded?
)
1 How many quarters are there in 3 ? 2 (1) 3 (3) 10
(1) (3) 4.
5.
(2) (4)
9 7
(2) (4)
Find the value of 24 + 48 ÷6 – 6 (1) 6 (3) 26
(2) (4)
5 14
8 6 (
)
(
)
(
)
22 36
What is the correct numeral for the following statement? Six hundred and six thousand, six hundred and sixty six (1) (3)
606 606 666 606
(2) (4) 1
606 666 660 660
6.
How many lines of symmetry are there in this letter?
I (1) (3)
4 2
(2) (4)
3 1 (
7.
If the product of 124 and 19 is calculated and rounded off to the nearest hundred, what will be the final value? (1) 2000 (2) 2300 (3) 2400 (4) 2360 (
)
)
8.
A car can travel 9 230m with 1l of fuel. 300l of fuel was consumed in a month. How many kilometers did the car travel in that month? (1) 2 769 (2) 27 690 (3) 276 900 (4) 2 769 000 ( )
9.
Mary’s weight is 27kg. She is (1) (3)
3 as heavy as David. How much does David weigh? 5
15 kg 54 kg
(2) (4)
45 kg 84 kg (
10.
11.
Two numbers have a difference of 72 and a sum of 166. Find the bigger number. (1) 138 (2) 119 (3) 94 (4) 49 ( 1 2
)
)
5 8
Sarimah bought 3 kg of flour. She then used 1 kg to bake cakes. After that, her 1 4
mother gave her another 1 kg of flour. How much flour did she have eventually? (1) (3) 12.
7 3 kg 8 1 2 kg 4
(2) (4)
1 3 kg 8 7 1 kg 8
(
Caroline has 6 times as many stickers as Denise, but only half as many as Rachel has. If Denise has 154 stickers less than Rachel, how many stickers does Caroline have? (1) 14 (2) 77 (3) 84 (4) 160 (
2
)
)
13.
Examine the pattern below carefully. How many sticks are there in the 18th pattern?
? Pattern 1
(1) (3) 14.
15.
Pattern 2
Pattern 3
Pattern 4
37 57
(2) (4)
Pattern 18
47 67 (
)
(
)
Find the smallest value among the following expressions (1)
0.80
(2)
17 20
(3)
3 4
(4)
0.69
In the figure below, ∠ AOB = 93o. What is ∠BOC? Note that AOC is a straight line and the figure is not to scale. C O 93o
A
B (1) (3)
3o 90o
(2) (4)
87o 273o (
)
Questions 16 to 25 carry 1mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16.
Write 9 080 011 in words.
17.
Arrange these numbers in descending order. 8 883 008, 880 300, 8 880 003, 88 380
Ans: __________, __________, __________, __________ 3
18.
What is the correct value of A?
7 000 000 A
3 000
3 906
900
7 503 906
6
Ans: _____________________ 19.
Find the total of the first 6 multiples of 7
20.
49 Express as a mixed number 9
21.
5 Calculate x108 9
Ans: _____________________
Ans: _____________________
Ans: _____________________
4
22.
2 1 Calculate 3 +2 and simplify your answer. 5 2
23.
Ans: _____________________ What is the proportion of the shaded area compared to the whole square? Write the answer in fraction.
24.
Ans: _____________________ Find the largest possible odd number between 5 000 000 and 6 000 000 using all the digits given.
9
25.
0
1
7
2
6
5
Ans: _____________________ Write the following statement as a numeral Three million one hundred and forty-seven thousand six hundred and eighty-two
Ans: _____________________ 5
Questions 26 to 30 carry 2 marks each. Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
Mr. Ben chose a sofa set that cost $5 250. He paid the exact amount in 90 pieces of $100 and $50 notes. How many $50 notes did the cashier receive from Mr. Ben?
27.
10 tables and 20 chairs cost $650. 20 tables and 10 chairs cost $850. What is the cost of one table and one chair?
Ans: _____________________
28.
Ans: _____________________ Mr. Tan, a worker, had 850 long nails, 620 short nails and 930 medium nails in a 1 1 container. He gave of these nails to his colleague and used of these nails to 4 12 make tables. How many nails did he have left?
Ans: _____________________ 6
29.
30.
An oil producer is filling two empty barrels with oil. The first barrel fills at a rate of 90l per minute. After 1 minute, he starts filling the second barrel at a rate of 105l per minute. How many minutes will it take for the second barrel to contain the same amount of oil as the first barrel?
Ans: _____________________ Mary and John were given the same amount of money by their mother. After spending some of their money, Mary only has one-seventh as much money as John had. If John spent $1 572 and Mary spent $2 892, how much did each of them have at first?
Ans: _____________________
7
Semestral Assessment 1: Mock Paper 1 Paper 2 (Duration: 1 hr 40 mins) Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1.
2.
3.
In a donation drive, team A and team B collected a total of $12 795. Team C and team D collected a total of $17 245. Team A and team C collected the same amount of money. Team D collected 6 times as much money as team B. How much money did team D collect?
Ans: _____________________ 3 1 A shop is selling gloves for Christmas. of the pairs are red, of the pairs are 8 4 white and the remaining 114 pairs are dark blue. How many pairs of gloves does the shop have in total?
Ans: _____________________ 1 kg of pork cost $2 more than 1 kg of chicken. 1 kg of beef cost $3 more than 1kg of pork. Aunt Linda spent a sum of $99.60 on 6 kg of each type of meat. How much did she spend on the chicken and the beef?
Ans: _____________________ 8
4.
Cheese cakes are sold at $6.90 for 3. Curry puffs are sold at $5.20 for 4. (a) If Timmy could only spend $25 on each type of food, how many more curry puffs than cheese cakes could he buy? (b) Bobby paid $129.60 for an equal number of cheese cakes and curry puffs. How many cheese cakes and curry puffs did he buy altogether?
5.
Ans: _____________________ Peter wants to send a parcel to his friend in Indonesia. At the post office, he finds the following table which shows the postage rates: Mass not over
Postage
First 30g
$1.00
Next 50g
$1.70
Per additional step of 25g
$0.35
How much does Peter have to pay if his parcel weighs 197g?
Ans: _____________________ 9
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.
7.
Given that AB is a line of symmetry in the figure below. Shade the squares to complete the symmetric figure
Ans: _____________________[4] The average number of Peter’s stickers and Jordan’s stickers is 924. Peter has 232 more stickers than Jordan. Albert has 172 stickers more than Peter. What fraction of Albert’s stickers are Jordan’s stickers? Write your answer in its simplest form
Ans: _____________________[4]
10
8.
9.
Three years from now Dan’s father’s age will be thrice Dan’s age. How old is Dan’s father now if he was 34 years old when Dan was born?
Ans: _____________________[4] The houses along a road are numbered from 1 to 150. The house number signs are made of steel digits. How many digits are needed altogether to number the entire road?
Ans: _____________________[4]
8 cm A
B 13 cm
4 cm
9 cm
5 cm
Find the perimeter of the figure below. 5 cm
7 cm
10.
36 cm
Ans: _____________________[4] 11
11.
12.
13.
A shop sells carpets at $15 per square meter. Uncle Tay wants to buy a carpet for his living room, which is 10m by 7m. How much does he have to pay?
Ans: _____________________[4] When 60 packs of cookies are placed in a box, the total mass is 6 790g. When the same box contains 25 packs of cookies, the mass is 4 655g. Find the mass of the box in kg.
Ans: _____________________[4] Each tourist has to pay $1 215 for a 5-day tour to Vietnam. If there were 116 tourists who chose that tour last month, how much did the travel agency receive?
Ans: _____________________[3]
12
14.
15.
16.
Create a tessellation in the space provided by drawing 4 more unit shapes.
Ans: _____________________[4] Alex, Ben and Carl collected a total of 2 151 stamps. Alex collected 224 stamps fewer Carl. Ben’s collection was 3 times as many as Carl’s. How many stickers did Carl have?
Ans: _____________________[4] How many lines of symmetry are there in the figure below, given that all line segments are equal
Ans: _____________________[3] 13
17.
18.
A water tank 90 cm long, 40 cm wide and 15 cm high needed to be filled by two taps A and B. Tap A, which had a flow rate of 12l per minute, was turned on first. After 1 1 1 minutes, tap B, which can flow only as fast as tap A, was turned on and both 2 3 tap continued to fill the tank. Since both taps were turned on, how long did it take to fill the tank completely? Express your answer in minutes and seconds.
Ans: _____________________[4] A number of trees were planted around the perimeter of a rectangular parcel of land that was 49m long and 35m wide. There was a tree in each corner. On each side of the land trees were planted 7m apart. How many trees were there in total?
Ans: _____________________[4]
14
Semestral Assessment 1: Mock Paper 2 Paper 1 (Duration: 50 mins) Marks Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1.
76 x 50 can also be expressed as (1) 70 x 6 x 5 (3) 76 x 5 x 10
(2) (4)
7 x 6 x 5 x 10 70 x 6 x 5 x 10 (
2.
3.
4.
5.
Calculating 196 x 68 and rounding off to the nearest thousand, the result will be (1) 13 000 (2) 13 300 (3) 13 400 (4) 14 000 ( What is the best estimate of 635 ÷ 80? (1) 6.35 (3) 8
What is the value of 183 – 24 ÷ 3 x 4 + 12 (1) 139 (2) (3) 224 (4)
)
63.5 7.5 (
)
(
)
(
)
163 712
What value should be filled in the box to make the expression correct? 6.5 x 6 + (1) (3)
6.
(2) (4)
)
x 3 = 78
13 39
(2) (4)
14 41
Replace “?” with a correct number that fits the pattern below 0.7, 1.4, 0.8, 1.3, ___?___, 1.2 (1) 0.6 (2) 0.9 (3) 1.7 (4) 2.1
15
7.
MNPQ is a trapezium. Which of the following shows a parallel pair of lines? W T X N M
Q (1) (3)
Z
P
Y
MQ and XY WZ and YT
(2) (4)
WZ and XY MQ and WZ (
8.
9.
2 4 kg of meat. Aunt Irene bought kg of meat more than aunt 7 5 Sophie. How many kg of meat did both of them buy? 8 22 (2) (1) 35 35 34 13 1 (3) (4) 35 35 ( )
Aunt Sophie bought
Find one of the letters below that does not have any line of symmetry
(1)
(3)
T A
(2)
(4)
H Z (
10.
)
Muthu had 25 kg of sugar. He packed them equally into 7 bags. There was 2kg of sugar left over. How much sugar was there in each bag? (1) 3.28 kg (2) 3.29 kg (3) 3.57 kg (4) 3.58 kg (
16
)
)
11.
The graph below shows the number of customers visiting a shopping centre over a period of 5 months. How many customers visited the shopping centre from January to March? 4000
3500 3000
2500 2000
1500 1000
500 0 January
(1) (3)
February
March
7 200 7 400
(2) (4)
April
May
7 300 7 500 (
)
12.
A tank measures 45 cm by 30 cm by 10 cm is filled with 4.5l of water. What fraction of the tank is not filled? 1 2 (2) (1) 3 3 9 4 (4) (3) 13 13 ( )
13.
In 147 683, which digit is in the ten thousands place? (1) 1 (2) 4 (3) 6 (4) 3
14.
(
)
(
)
4 ten thousands + 4 thousands + 4 hundreds + 4 ones =? (1) 40 400 (2) 40 004 (3) 44 404 (4) 44 440
17
15.
Find the correct numeral for the following expression (1) (3)
Three hundred and three thousands, three hundred and three 303 303 (2) 330 330 330 303 (4) 333 000
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16.
17.
18.
Given that MN is the line of symmetry of the figure below, shade two more squares to complete the figure.
2 that of an adult ticket. Mrs. Lim and her 5 daughter paid $49 for their tickets. How much does a child ticket cost?
A child ticket to enter the zoo costs
Ans: _____________________ The price of a car is $180 000 when rounded off to the nearest $1 000. What could the lowest price of the car be? Provide your answer correct to the nearest dollar.
Ans: _____________________
18
19.
Form the biggest even number using all the digits given
3, 6, 9, 5, 1, 2 20.
Ans: _____________________ 1 3 Tony spent of his money on a shirt and of the remaining money on a pair of 4 5 jeans. What fraction of his money did he spend? (Use the simplest form for your answer).
Ans: _____________________ 21.
1 of the audience were children and the rest were adults. There were 5 144 more adults than children. How many people were there in the audience?
At a concert,
Ans: _____________________ 22.
What is the area of the triangle below?
Ans: _____________________
19
23.
7 of a cake to her 3 children to share. Each child had the same 9 portion. What fraction of the cake did each child get?
Mrs. Chan gave
Ans: _____________________ 24.
25.
Express the value of
14 100
+
8 10
+5+
32 1000
in decimal form.
Ans: _____________________ 3 Fann has 2 times the number of stamps that Alex has. What is the ratio of the 5 number of Alex’s stamps to Fann’s stamps?
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. (20 marks) 26.
In the space provided, construct a line PQ that is perpendicular to line MN
M N
20
27.
28.
There are 4 teams in the Federation Cup tournament. Every team has to play one match with each of the other teams. How many matches are there in the tournament?
Ans: _____________________ 5 Selina started doing her homework at 7:45 PM. It took her 3 hours to complete all 12 the homework. At what time did she finish the task?
Ans: _____________________ 21
29.
The table below shows the parking rates at a shopping mall. Vanessa parked her car from 3.40 PM to 5.25 PM. How much money did she pay more the parking?
Parking rates 1st hour
$2.50 $1.90
Every additional hour or part there of
30.
Ans: _____________________ In the figure below, ABCD is a rectangle, ST is a straight line. Calculate the difference between ∠x and ∠y A
B D 41o x
58o S
T
C
y
33o
80o
Ans: _____________________
22
Semestral Assessment 1: Mock Paper 2 Paper 2 (Duration: 1 hr 40 mins) Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. 1.
2.
3.
1 1 of the audience came by car, came by bus 25 4 and the rest came by train. If there were 180 people who came by car, how many people came by train?
A survey at a concert showed that
Ans: _____________________ Mrs. Ng had a rectangular parcel of land that is 9m wide. The area of the parcel is 108m2. She wanted to repaint the fence around the land. a) Find the perimeter of the land. b) The fence surrounds the whole perimeter of the land. She paid $126 for the painting cost. How much did she have to pay to paint 1 meter of the fence?
Ans: _____________________ Harry cycles to a basketball court every day. He can take either route 1 or route 2. He chooses route 1 from Monday to Friday and route 2 from Saturday to Sunday. If he takes route 1, he has to cycle 4 km 300m. The total length of route 1 and route 2 together is 8 km 200 m. What is the total distance that Harry travels to the basketball court in a week? Give your answer in km.
Ans: _____________________ 23
4.
5.
In a training field there is a starting position and several finish lines. The first finish line is 30m away from the starting point. Each of the finish line from the second one is twice as far from the starting point as the previous finishing line. Peter ran straight from the starting point to the first finish line and returned straight back to the starting point. He then ran straight to the second finish line and returned to the starting point again. He kept running, every time to the next finish line and returning to the starting line. If the last finish line is 240m away, how far did he run in total when he reached the starting point for the last time?
Ans: _____________________ The graph below shows the number of visitors who visited Science Centre in the period from July to December. a) What is the fraction of the number of visitors in the least visited month to the number of visitors in the most visited month? 2 b) If of the visitors in July were children and there were twice as many boys 3 as girls, how many girls were there? 2000 1800 1600 1400 1200 1000 800 600 400 200 0 Jul
Aug
Sep
Oct
Nov
Dec
Ans: _____________________ 24
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.
Study the figures below. The figure on the left shows a rectangular strip of paper. The figure on the right shows that strip when folded along the dotted line. It consists of 2 squares and 1 trapezium. a) Find the length of the paper strip. b) Find the area of the paper strip 7 cm
3 cm
7.
Ans: _____________________[4] 3 Jeffery spent of his money on 18 cakes and 21 toy robots. 5 The cost of a toy robot is 2 times that of a cake. How many more toy robots could he buy with the remaining money?
Ans: _____________________[3]
25
8.
9.
10.
Some girls bought a packet of strawberries to share among themselves. If each girl took 7 strawberries, there would be 4 extra strawberries. If each girl took 8 strawberries, there would be 4 strawberries short. a) How many strawberries did they buy? b) How many girls were there?
Ans: _____________________[4] 11 Freddie, Jason and Malik each had some toy cars. Jason and Malik had of what 14 7 of what Jason had. Freddie had, and Malik had 15 a) If Freddie had 56 toy cars, how many toy cars did Jason have? b) How many toy cars did they have altogether?
Ans: _____________________[4] Mary bought 7 similar notepads and 9 similar pens. Each notepad is $1.1 more expensive than a pen. If the total money Mary spent was $33.3, how much did she pay for the pens?
Ans: _____________________[3] 26
Ans: _____________________[4] Study the figure below. Note that it is not drawn to scale. Answer the following questions: a) What is the area of the unshaded part? b) What fraction of the whole figure is shaded?
18 cm
12.
Ross paid $85 for 10 notebooks and 4 files. Each notebook cost as much as 3 files. What is the price of a notebook?
10 cm
11.
30 cm
Ans: _____________________[4]
27
13.
14.
15.
2 of the fruits in a basket are pears. There are 30 more apples than pears. The rest of 7 the fruits are 90 oranges. How many more apple than oranges were there?
Ans: _____________________[4] At a museum, the body of the whale skeleton on display is as long as the total length of its head and tail. The head of the whale skeleton is 8m long. The length of the tail 1 is equal to that of the head plus that of the body. How long is the whale skeleton? 3
Ans: _____________________[4] 5 3 of the passengers were adults. of the A train departed from Clementi station. 11 4 1 children were boys. The number of adult men is that of women. There were 114 4 less girls than boys. At the next station, Dover, 9 women and 5 boys boarded the train. a) How many passengers were there altogether when the train left Clementi Station? b) How many male passengers were there on the train when it departed from Dover station?
Ans: _____________________[4]
28
16.
17.
18.
Mrs. Liu bought 5 packets of sugar, A, B, C, D, and E. The mass of sugar in each packet is 500g, 600g, 800g, 900g and 1kg, respectively. Mrs. Liu kept one packet for herself and sold the other packets to Mrs. Chan and Mrs. Lim. Mrs. Lim bought twice the amount of sugar that Mrs. Chan bought. Which packet did Mrs. Liu keep for herself if she kept more than 500g?
Ans: _____________________[4] Alex, Benny, Carol and Dean stand in a straight row. Alex is not standing next to Dean and Benny does not stand at the first position, how many possible ways are there to arrange the four pupils?
Ans: _____________________[4] 16 Seven years ago Mrs. Goh’s age was her son’s age. Now her age is three times 3 her son’s age. What is Mrs. Goh’s age now?
Ans: _____________________[4] 29
Semestral Assessment 1: Mock Paper 3 Paper 1 (Duration: 50 mins) Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1.
What is the result of (1) (3)
5 x 63 9
14 35
(2) (4)
28 42 (
2.
3.
4.
3 4 of the people at a cartoon movie show are children. of the children are girls. 5 9 What is the fraction of the number of girls to the number of people at the show? 1 7 (1) (2) 3 15 1 4 (3) (4) 2 15 (
)
)
The ratio of the number of boys to the number of girls in a class is 3:5. If there are 32 pupils in the class, how many boys are there? (1) 12 (2) 20 (3) 28 (4) 36 ( ) In the figure below, which line is the base of triangle XZT if XT is its height? Z
Y
X (1) (3)
T
XY YZ
(2) (4)
ZT YT (
30
)
In the following figure, the area of the shaded shape is 13 cm2. What is the area of the unshaded part of the triangle?
9 cm
5.
(1) (3)
2
23 cm 41 cm2
12 cm (2) (4)
30 cm2 60 cm2 (
)
6.
The Physics textbook of a university student weighs 3.9 kg. His Math textbook is 0.532 kg lighter than his Physics textbook. What is the total mass of the two books? (1) 3.368 kg (2) 4.432 kg (3) 7.268 kg (4) 8.332 kg ( )
7.
Find the value of 60 ÷ (14 – 4) x 3 (1) 2 (3) 25
(2) (4)
18 30 (
8.
9.
Patrick and Albert have 72 pokemon cards. Patrick has thrice as many as Albert. How many cards does Patrick have? (1) 18 (2) 24 (3) 54 (4) 63 (
)
)
3 8 of David’s weight. David’s weight is Peter’s weight. Express 4 9 Peter’s weight as a fraction of Irene’s weight. 11 59 (1) (2) 13 36 3 2 (3) (4) 2 3 ( )
Irene’s weight is
31
What is the area of the shaded triangle?
16 cm
10.
28 cm (1) (3) 11.
312 cm 210 cm2
(2) (4)
Which of the following is greater than (1) (3)
12.
2
(
)
(
)
(
)
(
)
2 ? 3
4 5 4 9
(2) (4)
4 7 4 11
What is ∠r in the figure below? XOY is a straight line.
r X
(1) (3) 13.
11 cm 224 cm2 88 cm2
29o
O
151o 61o
Y
(2) (4)
119o 29o
Which of the following is the best estimate for 605 x 48? (1) 600 x 40 (2) 600 x 50 (3) 700 x 40 (4) 700 x 50
32
14.
In a running competition, the total time taken by the 2 boys was 350 seconds while the total time taken by the 3 girls was 555 seconds. Find the average time that a child took to complete the race. (1) 102 seconds (2) 175 seconds (3) 181 seconds (4) 270 seconds ( )
15.
In 3 852 176, how many times is the value of digit 8 to the value of digit 1? (1) 8 (2) 80 (3) 800 (4) 8 000 (
)
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16.
17.
5 1 of his money. He bought a calculator with 7 5 of his remainder. If he had $112 left, how much was the calculator?
Kelvin bought a pair of skates with
Ans: _____________________ The figure below is made up of 8 identical squares. The total area is 32m2. Each corner of a square at a lower row is at the midpoint of the side of the square of the row above. What is the perimeter of the figure?
Ans: _____________________ 33
18.
19.
20.
While reading a book, Jerry noted that the product of the two facing pages that he was reading is 600. What are the page numbers of the two facing pages that Jerry was reading?
Ans: _____________________ Kathy bought a badminton racket for $199. She also bought 5 similar boxes of shuttlecocks. She gave the cashier $300 and was given a change of $41. How much was each box of shuttlecocks?
Ans: _____________________ Kelvin and Elizabeth shared some sweets. The ratio of Kelvin’s sweets to Elizabeth’s is 8:5. If they have 65 sweets in total, how many sweets did Elizabeth have?
Ans: _____________________ 21.
Find digits X and Y from 0 to 9 so that X
+
Y Y
Y
X
Ans: _____________________ 34
22.
23.
24.
25.
2 as many crayons as Ali. After Ali received 4 new crayons and 3 Jonathan received 10 new crayons, they have the same number of crayons. How many crayons did both of them have altogether before they received new ones?
Jonathan had
Ans: _____________________ Miss Lisa divided 300 paper clips to her pupils. Each pupil received 15 paper clips. The next day she divided some toy bricks to her pupils. Each pupil got 10 toy bricks. How many toy bricks did Miss Lisa gave the class?
Ans: _____________________ Gupta and Davis had a total of $300. If Davis gave Gupta $18, he would have twice as much money as Gupta. How much money did Gupta have at first?
Ans: _____________________ Mrs. Tan made 225 lollipops and packed them equally into some boxes, each have 15 lollipops. Each box was sold at $12.30. After selling all the boxes, how much did she earn?
Ans: _____________________ 35
Questions 26 to 30 carry 2 marks each Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 26.
Find the area of the figure below, which consists of a square, a rectangle, and 3 identical triangles.
7 cm 3 cm 4 cm
27.
Ans: _____________________ Ali counted his savings and noted that all of his money was in $2, $5 and $10 notes. 1 1 of the notes are $2, are $5 and the rest are $10. He had saved $1 794 in total. 3 6 What is the total value of $5 notes had he saved?
Ans: _____________________ 36
28.
29.
30.
1 Darren needed to run 10km for training. He had run 4 km. How many more 9 kilometres did he have to run to complete the training? Express your answer correct to 2 decimal places.
Ans: _____________________ Jimmy can make 30 paper birds every hour. Philip can make 50 paper birds every hour. After Jimmy had started making paper birds for 2 hours, Philip also started. How many hours would Philip take to make the same number of paper birds as Jimmy?
Ans: _____________________ The ratio of 2 whole numbers is 2:15. The bigger number is greater than 98 but smaller than 108. Find the smaller number.
Ans: _____________________ 37
Semestral Assessment 1: Mock Paper 3 Paper 2 (Duration: 1 hr 40 mins) Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated.
2.
2 5 Helen cycles 7 km to school. Jack cycles of that distance to school. What is the 3 8 difference in distance they have to cycle to school? Express your answer as a fraction in its simplest form.
Ans: __________________km Find the area of the shaded part in the figure bellow, given that ABCD is a rectangle and CN is 3 times as long as ND. A
B
M
24 m
1.
N D
C 96 m
Ans: _____________________
38
3.
4.
5.
The ratio of the amount of petrol Mr. Quek used in January to the amount of petrol he used in February was 4:7. He used 60l of petrol in January. How much did he have to pay for petrol in total if the price of petrol was $2.50 per litre during those two months?
Ans: _____________________ Nurbaya wanted to make 24l of strawberry drink from a 1.5l bottle of strawberry syrup. She mixed the syrup with plain water in the ratio of 1:5. a) How much strawberry syrup is she short of? b) After buying more syrup and made the desired drink, she added another 2l of syrup to make the drink sweeter. Find the new ratio of syrup to water in the new drink.
Ans: _____________________ A salesman earned $10 for each unit of product A and $4 for each unit of product B that he sold. In a month, he earned a total of $11 400. The ratio of the number of product B units to product A units that he sold was 3:14. a) How many units of product A did he sell? b) What is the difference between the amount of money he collected from selling product A and the amount of money he collected from selling product B?
Ans: _____________________
39
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.
Nancy had some stickers.
1 of them were used to make a scrapbook. She then 3
2 of the remaining equally to her three friends. After making the scrapbook 3 and sharing stickers to her friends she had 42 stickers less than what she had at the beginning. How many stickers did each of her friends receive?
divided
7.
Ans: _____________________[4] Suriyana and Fahan each had saved some 20-cent and 50-cent coins. Suriyana had a 3 total of 192 coins. The number of 20-cent coins that Suriyana had was the number 5 of 50-cent coins that she had. The ratio of the number of 20-cent coins to the number 1 of 50-cent coins that Fahan had was 1:2. Fahan’s total number of coins is only 4 that of Suriyana. a) What is the ratio of the number of 20-cent coins Suriyana had to the number of 50-cent coins that Fahan had? b) What is the ratio of the amount of money that Suriyana had to the amount of money that Fahan had?
Ans: _____________________[4]
40
8.
Find a number that gives a quotient of 189 and a remainder of 17 when divided by 55.
Ans: _____________________[3] 9.
Mr. Ong spent
5 of his working hours working with his computer. He worked for 12
1 of the day. How many minutes did he work with his computer? 3
10.
Ans: _____________________[3] Tom and Jerry have some money. If Tom gives Jerry $5, he will have half what Jerry has. If Jerry gives Tom $5, they will have the same amount. a) How much money does Tom have? b) How much money does Jerry have?
Ans: _____________________[4] 41
11.
12.
13.
A box of 16 Pelican pens (box A) is sold at $14.70. A box of 24 Pelican pens (box B) is sold at $22.50. Is box A or box B the cheaper buy?
Ans: _____________________[4] All the people at a party shake hands with one another. How many handshakes are there if there are a) 3 people? b) 5 people? c) 10 people?
Ans: _____________________[4] The ratio among 3 sides of a triangle is 4 : 2 : 5. The longest side is 300 cm. What is the perimeter of the triangle?
Ans: _____________________[4]
42
14.
15.
16.
Study the following pattern: 1 1 1 = − 2×3 2 3 1 1 1 = − 3× 4 3 4 1 1 1 = − 4×5 4 5 ... Use the above pattern to calculate 1 1 1 1 + ... + + + 2× 3 3× 4 4× 5 19 × 20 Give your answer in the simplest form.
Ans: _____________________[4] 3 Mr. Green needed to go from A to B. He had travelled of the distance and still 8 needed to travel another 480km. What is the distance from A to B?
Ans: _____________________[4] A rectangle water tank can contain a maximum of 105m3 of water. Its base is 5m wide and 7m long. What is the depth of the tank?
Ans: _____________________[4]
43
17.
What is the area of the right-angled trapezium ABCD as shown below?
14 cm
B
11 cm
A
D
18.
26 cm
C
Ans: _____________________[4] 36 chickens and dogs have a total of 100 legs. How many chickens are there?
Ans: _____________________[4]
44
Semestral Assessment 1: Mock Paper 4 Paper 1 (Duration: 50 mins) Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided. 1.
What is the area of triangle PQR? 14 cm S P
P
25 cm
Q
(1) (3) 2.
3.
66 cm2 225 cm2
(2) (4)
Find the value of 84 ÷ (5 + 2) – 2 x 5 (1) 2 (3) 60
(2) (4)
R 175 cm2 297 cm2 (
)
(
)
50 72
COD is a straight line. Find ∠x if ∠x is 180 less than ∠y. (The figure is not drawn to scale).
y
x (1) (3)
99o 36o
(2) (4)
81o 9o (
45
)
4.
What is the value of ∠a, given that AB and CD are straight lines? D a A
B
138o
C (1) (3)
o
(2) (4)
32 60o
o
48 122o (
)
5.
Nelson, Jordan and Joe had a number of cookies. Nelson had 2 times the number of cookies that Jordan had. Joe had the same number of cookies as Nelson. What is the ratio of the number of cookies that Nelson had to the total number of cookies of all three friend? (1) 1:5 (2) 2:5 (3) 3:5 (4) 4:5 ( )
6.
A triangle of height 8cm and base 6cm is cut from each corner of a square. The perimeter of the square is 80cm. Find the area of the remaining figure? (1) 208 cm2 (2) 250 cm2 2 (3) 304 cm (4) 352 cm2 (
7.
How many thousands are there in one and a half million? (1) 15 (2) 150 (3) 1 500 (4) 15 000 (
8.
9.
)
The difference between 430 000 and 550 000 is divided by 400. What is the final value? (1) 30 (2) 300 (3) 3 000 (4) 30 000 ( Round off 205 621 to the nearest thousand (1) 205 000 (2) (3) 206 000 (4)
)
205 600 206 621 (
46
)
)
10.
1 How many sixths are there in 3 ? 2 (1) 0 (3) 15
(2) (4)
5 21 (
13.
14.
2 of a Sunday practicing the piano. 3 How many hours did she spend on that Sunday practicing the piano? (1) 8 hours (2) 16 hours (3) 20 hours (4) 36 hours
Sally spent
(
)
(
)
(
)
Which of the following is not a symmetric figure? (1)
(2)
(3)
(4)
Find the area of the shaded figure. 28 cm
8 cm
12.
Mr. Koh’s garden is 25m long and 12m wide. The cost of mowing 1m2 of garden is $15. How much must he pay to mow his whole garden? (1) $20 (2) $555 (3) $1 110 (4) $4 500 ( )
19 cm
11.
)
(1) (3)
112 cm2 308 cm2
(2) (4)
47
266 cm2 420 cm2
15.
The graph below shows Mrs. Ong’s grocery expenses for her family from January to May. What is Mrs. Ong’s average grocery expense for the five months? $200 $180 $160 $140 $120 $100 $80 $60 $40 $20 $0 Jan
(1) (3)
Feb
Mar
$100 $150
(2) (4)
Apr
May
$125 $175 (
)
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated. 16.
17.
At a fruit stall, the ratio of apples to oranges is 2:3 and the ratio of apples to banana is 4:9. Find the ratio of oranges to bananas.
Ans: _____________________ Sylvia, Alan and Ronald are making paper stars together. Ronald and Alan made 221 paper stars altogether. Alan and Sylvia made 121 paper stars altogether. If Ronald made 5 times as many paper stars as Sylvia, how many paper stars did Alan make?
Ans: _____________________ 48
18.
19.
1 of the remaining pens are red, while 8 the remaining pens are black. If there are 210 more black pens than red pens, how many pens are there altogether?
Half of the pens at a stationary shop are blue.
Ans: _____________________ A drink stall had some cans of coke and soda water in the ratio 3:7. After selling 48 cans of soda and buying another 48 cans of coke, the shop had the same number of cans for each drink. How many cans of coke were there at first?
Ans: _____________________ In triangle XYZ below, XZ = YZ = 9cm. Calculate the area of the shaded area. X 4.5cm
20.
Y
Z 2 cm
Ans: _____________________ 49
21.
Danny and Fahan had $54 in total. If each boy was given another $8, the ratio of the amount that Danny had to the amount that Fahan had became 3:4. How much money did Fahan had at first?
22.
Arrange the following fractions in ascending orders 5 4 5 7 , , , 4 5 7 5
23.
How many two thirds are there in 18?
Ans: _____________________
24.
Ans: _____________________ Betsy had an average of 56 slices of fruit a month. 3 How many slices of fruit did she have in 2 months? 4
Ans: _____________________ 25.
Fill in the box with an appropriate number
8 2 = 12
Ans: _____________________
50
Questions 26 to 30 carry 2 marks each Show your workings clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
26.
27.
The number of chocolate candies in a box is between 60 and 100. If 4 or 7 children share the box, each of them can have the same amount of candies. How many chocolate candies are there in the box?
Ans: _____________________ Mr. Lee had a number of boxes. He packed them into 8 layers in a container. Each layer has 7 rows. Each row has 6 boxes. How many boxes did Mr. Lee have?
Ans: _____________________ 28.
1 5 Find A if A × 5 = 2 4 12
Ans: _____________________ 51
29.
30.
If a bus can carry 25 passengers, what is the minimum number of buses to carry 7 groups of passengers, each of which have 32 passengers?
Ans: _____________________ Two pumps are used to fill a swimming pool. Pump A can fill the pool completely in 3 hours. Pump B can fill the pool completely in 2 hours. How long will it take to fill the pool completely if both taps are turned on at the same time?
Ans: __________________hours
52
Semestral Assessment 1: Mock Paper 4 Paper 2 (Duration: 1 hr 40 mins) Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated.
1.
2.
1 of the 2 1 number of questions on the first day. On the second day he answered of the 10 1 number of questions. If he continued to answer of the number of questions every 10 day from the third day, on what day will he finish all the questions?
Wu Wei was given a number of questions as homework. He answered
Ans: _____________________ For every 5 hour of work, Daniel was paid $80. How many hours had he worked if he was paid $1440?
Ans: _____________________ 53
3.
4.
5.
What is the area of the shaded part in the figure below if each square has sides of 3 cm?
Ans: _____________________ 7 A piece of cloth is cut into two pieces. The area of the bigger piece is that of the 12 original piece. If the area of the bigger piece is 138 cm2 more than that of the smaller piece, what is the area of the bigger piece?
Ans: _____________________ Complete the figure below so that the dotted line is the line of symmetry
Ans: _____________________
54
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.
In the figure below, what is the area of the square if the averaged perimeter of the square and the triangle is 59 cm?
12 cm
28 cm
7.
Ans: _____________________[4] 1 The volume of petrol in barrel A is the volume of petrol in barrel B. 24l of petrol 4 1 is moved from barrel B to barrel A. The volume of petrol in barrel A is now the 2 volume of petrol in barrel B. How much petrol is there in barrel B in the end?
Ans: _____________________[4] 55
8.
Examine the pattern of the following figure. Find the missing number.
89
115
5
117
1020
12
258
4500
205
?
397
4816
9.
Ans: _____________________[4] A shop is selling toy robots at $20 and dolls at $50. There are 23 more dolls than toy robots. After selling some dolls for $900, the shop has 1.5 times as many dolls as toy robots. How many dolls did the shop have at first?
Ans: _____________________[3]
56
10.
Joey, Zhong Ren and Suriya had a total of $1 326. After Joey spent
2 of his money, 5
1 1 of his money, and Suriya spent of her money, all of them had 7 3 the same amount of money. How much did they spend altogether?
Zhong Ren spent
11.
12.
Ans: _____________________[4] Fred, George and Harry shared some pokemon cards. The number of cards Fred had 4 is the total of cards that George and Harry had. George had twice the number of 11 cards Fred had. a) If George had 104 cards, how many did Harry have? b) What was the number of cards three of them had altogether?
Ans: _____________________[4] 1 Jane had of his brother’s money. The product of their money is $400. How much 4 money did Jane have?
Ans: _____________________[3]
57
13.
14.
15.
A pair of shoes is 9 times as expensive as a pair of socks. If 3 pairs of shoes and 5 pairs of socks cost $192, how much is a pair of shoes?
Ans: _____________________[4] What is the area of the shaded part, if each small square is 4 cm x 4 cm?
Ans: _____________________[4] 1 A bag of rice is 2 times as heavy as a bag of powder. The average mass of the two 2 bags is 33.25 kg. What is the mass of the bag of powder?
Ans: _____________________[4] 58
Ans: _____________________[4] The figure below is not drawn to scale. Find the area of the shaded part. 19 cm
18.
15 cm
15 cm
17.
The ratio of the number of pencils to the number of pens in a stationary shop was 3: 7. The stall owner then sold 36 pens and the number of pens became equal to the number of pencils. How many pens were there in the shop at first?
7 cm
16.
Ans: _____________________[4] Alice had 9 notepads and Ronald had 6 notepads. Alice then bought some more notepads. After that the ratio of the number of notepads that she had to the number of notepads Ronald had is 7: 3. How many more notepads did Alice buy?
Ans: _____________________[4]
59
Semestral Assessment 1: Mock Paper 5 Paper 1 (Duration: 50 mins)
Marks Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.
1.
2.
3.
4.
Five pupils shared a 9l jug of orange juice. How many litres of orange juice did each pupil get? 5 8 l l (1) (2) 13 13 4 5 1 l l (3) (4) 5 9 ( ) Write 8.56 in fraction form 14 (1) 25 14 8 (3) 25
(2) (4)
98 125 8 8 25
(
)
(
)
Which of the following ratio is not equivalent to 5 : 13 (1) 15 : 39 (2) 30 : 78 (3) 35 : 91 (4) 40 : 84 In the diagram below, ABCD is a rectangle, AB = 7cm, AD = 5cm, BO = 4 cm, AO = 9.5 cm. What is the base and height of the shaded triangle? A B O
C
D (1) (3)
4 cm and 9.5 cm 5 cm and 9.5 cm
(2) (4)
4 cm and 7 cm 5 cm and 7 cm (
60
)
5.
Each worker in a factory was given 300 short nails, 700 medium nails and 600 long nails. Find the ratio of the number of long nails to the total number of nails (1) 3 : 13 (2) 7 : 16 (3) 3:8 (4) 3 : 16 ( )
6.
There were 45 strawberries in basket A. Basket B had 25 more strawberries than basket A. What was the ratio of the number of strawberries in basket B to basket A? (1) 14 : 9 (2) 9 : 14 (3) 4:9 (4) 9:4 ( )
7.
What is the value of (1) (3)
8.
9.
10.
13 8 × ? 4 9
26 9 104 9
(2) (4)
What is the value of 66 + 18 ÷ 3 + 4 x 5 (1) 48 (3) 116
(2) (4)
21 13 117 32
(
)
(
)
92 160
3 kg of candies. Mrs. Chua packed all the candies in the tin into 9 5 bags, each weighs the same. What was the mass of each candy bag? 27 4 kg kg (1) (2) 5 5 1 12 kg kg (3) (4) 15 5 (
A tin contains
A rectangle (1) (3)
)
3 m wide has an area of 9m2. What is its perimeter? 4
1 7 m 2 3 12 m 4
(2)
12m
(4)
1 25 m 2
(
61
)
11.
Ding Mei’s water bottle was full and had
3 3 l of water. She drank l and poured 2 10
1 l of water. What was the fraction of the amount of water left in Ding Mei’s 4 bottle to the full bottle? 19 19 (1) (2) 30 20 11 1 (3) (4) 20 20 ( )
away
12.
13.
14.
Miss Sally needed to use 85cm of ribbon to tie a present. If she had to make 25 similar presents to her pupils, how many meters of ribbon were used? (1) 1.1 (2) 2.125 (3) 3.4 (4) 21.25 (
)
Calculate the sum of 72.35 and 52.87. Round off your answer to 1 decimal place. (1) 124.2 (2) 125.2 (3) 126.2 (4) 127.2 (
)
Joey, Lucy, Michael and Sam attended a physics test. There scores are shown in the table below: Pupil’s name Joey Lucy Michael Sam
Test score 95 83 77 71
Who had the score that is closest to the average score of all 4 pupils? (1) Joey (2) Lucy (3) Michael (4) Sam ( 15.
)
Fatimah needed to walk 1.8 km to school. She had walked 216m. What percentage of the journey did she still have to walk? (1) 12% (2) 13.64% (3) 75% (4) 88% ( )
62
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
16.
Write 8 006 500 in words.
17.
What is the remainder when dividing 5603 by 7?
18.
Ans: _____________________ What fraction of 5km is 1300 m? Provide the simplest form for your answer.
Ans: _____________________ 19.
20.
Express
23 km in metres. 5
Ans: _____________________ In the diagram shown below, MNPQ is a rectangle; K and H are midpoints of MN and PQ respectively. What fraction of the figure is shaded? K M N
Q H
P
Ans: _____________________
63
21.
Mei Mei, Jing Jing and Hui Hui were given the same homework. Mei Mei had done 1 1 of the homework. Hui Hui had done of the homework. Jing Jing’s completed 4 2 portion of the homework is exactly midway between Mei Mei’s and Hui Hui’s. What fraction of the homework had Jing Jing done?
22.
Ans: _____________________ 1 carpenter can make 8 tables in a week. How many carpenters are required to make 40 tables in a week?
23.
A = 1 + 2 + 3 + … + 99 + 100.
Ans: _____________________ Find the value of A.
24.
Ans: _____________________ A carpenter completed a chair at 4.40 pm. It took him 2 hours 45 minutes to complete his work. What time did he start?
Ans: _____________________ 64
25.
At first, Davis, Feng Xue and Ann had 181 stamps in total. Davis had 37 stamps. Feng Xue and Ann had the same amount of stamps. A few weeks later, Ann collected another 29 stamps. How many stamps did Ann have in the end?
Ans: _____________________ Questions 26 to 30 carry 2 marks each. Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
26.
27.
Two numbers have a sum of 148.5 and a difference of 43.5. What are the two numbers?
Ans: ______________ 7 In the figure below, ABCD is a square of side 30 cm and DH = HC. Find the area 3 of the shaded triangle. A B
D
H
C
Ans: _____________________
65
28.
29.
4 2 of the apples and of the 7 9 pears were sold, the number of pears and the number of apples left are the same. How many pears were sold?
There were 592 apples and pears in a fruit shop. After
Ans: _____________________ At first, of a tank was filled with water. The total mass was 81.74 kg. Water was then taken out of the tank until it was half filled. The total mass was 59.8 kg. What was the mass of the tank? Round off your answer to 1 decimal place.
30.
Ans: _____________________ Of all the adults at a concert, were women. There were 114 more children than women. The ratio of the number of adults to the number of children was 3: 7. How many children were there at the concert?
Ans: _____________________
66
Semestral Assessment 1: Mock Paper 5 Paper 2 (Duration: 1 hr 40 mins) Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated.
1.
Grapes were sold at $0.65 per 250g in a market. Mr. Khoo bought 3.25 kg of grapes. How much did he have to pay?
2.
Find the area of triangle ACD in the figure below.
Ans: _____________________
A
7 cm
16 cm
D
8 cm
B
C
22 cm
Ans: _____________________ 67
3.
4.
5.
Three packets of candies had an average mass of 903.6g. The packet of apple candies weighed twice as much as the packet of strawberry candies. The packet of mango 4 candies is the mass of the packet of strawberry candies. What is the mass of the 5 packet of apple candies? Express your answer up to 2 decimal places.
Ans: ___________________kg 2 boxes of candies and 3 boxes of cookies have an average mass of 3.84 kg. 3 boxes of candies and 2 boxes of cookies have an average mass of 3.7 kg. The candy boxes are identical and the cookies boxes are also identical. What is the total mass of 2 boxes of candies and 1 box of cookies?
Ans: _____________________ There are two water taps, A and B. Tap A is used to fill in tank X and tap B is used to fill in tank Y. In every minute, tap A can fill 8l more than tap B. However, 56.5l of water is drawn from each tank in every minute. When tank X has 54l, tank Y has 22l. a) How much water does tank Y receive per minute? b) How much water is there in tank Y after 1 hour?
Ans: _____________________ 68
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.
7.
1 1 his salary. He then used of 7 4 the remaining amount plus $54 to pay his bills. After that, he spent half of the remainder plus $27 to buy a computer. Finally, he saved the remaining $846. How much was his salary?
When Tom received his salary, he gave his mother
Ans: _______________[4] In the tables and chairs section of a warehouse, the ratio of the number of chairs to that of tables is 5: 3. There are 64 wooden pieces of furniture and the rest are made of plastic. The number of plastic pieces is twice the number of wooden pieces. If there are 32 wooden chairs, what is the ratio of the number of plastic chairs to that of wooden tables?
Ans: _______________[4]
69
8.
9.
10.
1 1 m tall. Her brother is m taller than she is. What is the average height 2 6 of the two children? Round off your answer to 2 decimal places.
Betsy is 1
Ans: _______________[4] 1 1 Nicole read of a magazine on Friday and of the remaining on Saturday. On 5 4 Sunday she read twice as many pages as on Friday. What fraction of the magazine was not read?
Ans: _______________[4] 4 The ratio of the cost of an LCD monitor to that of a computer is . The computer 9 costs $900. What is the average cost of the two devices?
Ans: _______________[3] 70
11.
12.
13.
Ken bought 3 pairs of jeans and 2 shirts for $90. A pair of jeans was $5 more expensive than a shirt. How much did a pair of jeans cost?
Ans: _______________[4] The ratio of the number of Indian pupils to the number of Chinese pupils is 2: 7. The ratio of the number of Malay pupils to the ratio of Chinese pupils is 3: 4. What is the ratio of the number of Indian pupils to the number of Malay pupils to the number of Chinese pupils?
Ans: _______________[4] A bank paid a fixed 0.68% saving interest per year. Bill opened an account and deposited $172 000. How much interest would he earn after a year?
Ans: __$____________[4]
71
14.
15.
The total amount of money that Soo Hui and Margaret had is $630. If Margaret gave Soo Hui $52.70, Soo Hui would have eight times the amount that Margaret had. Initially, what was the difference in the amounts that they had at first?
Ans: _______________[4] The total volume of water in tanks A, B and C is 400l. If half of the water in tank A is taken away and the water in tank B is doubled, and 30l is added to tank C, the ratio of the volume of water in tank A to B to C will be 3: 2: 1. Find the amount of water in tank B initially.
Ans: _______________[4]
72
16.
17.
A set of furniture costs $3290. Mr. Tay bought the set with 20% discount. However, he had to pay 7% GST on the discounted price. How much did he have to pay for the set of furniture?
Ans: _______________[4] Use the following digits, each digit only once, to make the smallest even number that is greater than 250 000.
0, 3, 7, 2, 9, 6
18.
Ans: _______________[3] In a laboratory, the mass of some bacteria doubles every 12 minutes. If the mass is 128 mg at 5 p.m, what time was it when the mass was 0.5 mg?
Ans: _______________[4]
73
Semestral Assessment 2: Mock Paper 1 Paper 1 (Duration: 50 mins) Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.
1.
The digit 9 in 5 298 637 is the _________________________ place (1) hundreds (2) thousands (3) ten thousands (4) hundred thousands (
)
2.
Which of the following numbers will result in 555 000 when being rounded off to the nearest thousand? (1) 554 494 (2) 555 494 (3) 555 501 (4) 555 513 ( )
3.
45 x 100 = ____________________(1) 45 x 20 x 5 (3) 45 x 10 + 90
4.
6.
40 + 5 x 100 (45 x 20) + (45 x 5) (
)
(
)
(
)
3 hours. For how many minutes did he study? 10 258 minutes (2) 300 minutes 342 minutes (4) 400 minutes
Frank studied for 4 (1) (3)
5.
(2) (4)
Find the value of 650 – (27 + 123) ÷ 4 (1) 36.25 (3) 250
(2) (4)
125 612.5
2 1 of his money and used of his remaining 3 4 money to buy some toys. What is the fraction of money left? 1 3 (2) (1) 4 4 5 1 (3) (4) 12 12 (
Harry bought a pair of jeans with
74
)
Find the area of the figure below (not drawn to scale)
8 cm
7.
(1) (3)
9
2
(2) (4)
30 cm 42 cm2
36 cm2 49 cm2 (
8.
9.
What is the volume of a cube of side 4 cm? (1) 16 cm3 (2) 3 (3) 64 cm (4)
)
32 cm3 128 cm3
( ) What is the maximum number of 2-cm cubes that can be fitted into a rectangular box measuring 9 cm by 6 cm by 4 cm? (1) 9 (2) 24 (3) 27 (4) 54 ( )
10.
Annie was sitting in a concert. The chairs were arranged in rows in a rectangular manner. There were 6 chairs on Annie’s left and 8 chairs on her right. There were 10 rows in front of her and 11 rows behind her. How many chairs were there? (1) 294 (2) 308 (3) 315 (4) 330 ( )
11.
Mei Mei jogged for the same distance every night. After a week, the total distance 1 covered was 17 km. What was the distance that she jogged each day? 2 1 2 km (1) (2) 3km 2 1 10 km (3) 5km (4) ( 2
12.
)
3 5 of the participants are boys and of these 5 6 1 boys likes basketball. The survey also shows that of the girls like basketball too. 3 What fraction of the pupils like basketball? 19 11 (1) (2) 30 30
In a survey among pupils in a school,
(3)
14 15
(4)
75
7 6
(
)
13.
14.
15.
Express 21 km 3 m in km. (1) 21. 003 km (3) 21.3 km
(2) (4)
What is the product of 56.31 and 60? (1) 3.3786 (3) 333.86
(2) (4)
21. 03 km 210.3 km (
)
(
)
33.786 3 378.6
The average mass of two packets of rice is 4 kg. Which of the following are the likely mass of the two packets of rice? (1) 2.5 kg and 2.5 kg (2) 2.5 kg and 3.5 kg (3) 2.5 kg and 4.5 kg (4) 2.5 kg and 5.5 kg (
)
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
16.
What is the remainder when 3256 is divided by 19?
17.
Ans: _____________________ Write six hundred and eighty thousand, seven hundred and ninety-five as a numeral.
Ans: _____________________ 18.
What is the difference between and
19.
Calculate 290 – 36 ÷ 4 x (27 + 5) ÷ 2 + 115
?
Ans: _____________________
Ans: _____________________ 76
20.
21.
How many cubic centimetres are there in 1l 25 ml?
Ans: _____________________ 5 1 Pei Xin had l of milk in her bottle. She drank of the milk in the bottle. How 6 3 many liters of milk did she have left?
Ans: _____________________ 22.
X 2 Find x if × =5 4 3
Ans: _____________________ 23.
Express 63.08l in terms of milliliters.
24.
Ans: _____________________ The table below shows the prices of different fruits at a market. Fruit Apple Strawberry Kiwi Watermelon
Price (per kg) $3.65 $4.89 $5.99 $4.20
Uncle Tiong bought 2 kg of apple and 3 kg of kiwi. How much did he spend?
Ans: _____________________
77
25.
Find X and Y if X : 5 : 9 = 7 : Y : 63
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your workings clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
26.
27.
Mrs. Lim wants to give some pens to her pupils. If each pupil gets 7 pens, there will be 3 pens extra. If each pupil gets 8 pens, there will be 4 pens short. a) How many pupils are there? b) How many pens does Mrs. Lim have?
Ans: _____________________ 75% of the candies in a box are chocolate flavored. 40% of the remainder is mango flavored and the rest is strawberry flavored. a) Express the number of strawberry flavored candies as a fraction of the total number of candies in the box. b) How many more chocolate flavored candies than strawberry flavored candies are there if there are 20 mango flavored candies?
Ans: _____________________
78
28.
29.
30.
The breadth of a rectangular floor is 15% of its perimeter. The length of the floor is 760 cm longer than its breadth. What is the area of the floor in m2? a) b) The floor is used to store identical cartons each has a base measuring 30 cm by 30 cm. What is the maximum number of cartons that can be stored?
Ans: _____________________ The table below shows the water tariffs (charges) for monthly water consumption Volume consumed Charges per unit (dollars) First 40 units 1.17 Above 40 units 1.40 Mr. Choo’s family used 56 units in January. In February he paid $135 for his bill. a) How much water did Mr. Choo’s family use in February? b) On average, how many units of water were consumed by his family in a month over this period? c) On average, how much does Mr. Choo have to pay for water bill in a month?
Ans: _____________________ 2 Peter has a number of books. Lixiang has as many books as Peter has. Fahan has 3 half as many books as Peter has. If Lixiang has 32 books, how many books do they have altogether?
Ans: _____________________ 79
Semestral Assessment 2: Mock Paper 1 Paper 2 (Duration: 1 hr 40 mins) Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated.
1.
2.
3.
The maximum score for a physics test is 50 marks. What is the highest possible average score for 5 pupils who took the test, if it is known that one of them scored 15 marks?
Ans: _____________________ Fred and George folded a number of paper birds. Fred folded 35% of the birds. George folded 90 birds more than Fred. How many birds did George fold?
Ans: _____________________ Mary, Andy and Bob donated some money to a charity fund. Mary donated 40% what Andy donated and 50% less than what Bob donated. If they donated $660 altogether, how much did Andy donate?
Ans: _____________________
80
4.
In the figure below, ABCD is a rhombus. What is ∠ABE? The figure is not drawn to scale.
A 116o D
B
E
C
5.
Ans: _____________________ Kin Eu had collected some stamps. After collecting another 12 stamps, the number of stamps in his collection increased by 30%. How many stamps did he have at first?
Ans: _____________________ 81
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.
The table below shows the number of days pupils exercised in a week. What is the fraction of the number of pupils that exercise 2 days or more to the total number of pupils? Express your answer correct to 2 decimal places. No. of exercised days No. of pupils
7.
8.
0 5
1 9
2 7
3 16
4 5
Ans: _____________________[3] In a festival that has 2500 participants, there are 1100 females. How many percent more males than females are there? Round off your answer to 2 decimal places.
Ans: ____________________%[3] The number of exercise questions that 3 pupils have completed is in the ratio of 2: 4: 5. If the pupil who had done the least completed 6 questions, what is the total number of questions that they have completed?
Ans: _____________________[4] 82
9.
10.
There are approximately 3300 adults and 1700 children in a stadium. If both above figures are corrected to the nearest hundred, what is the largest possible difference between these 2 figures?
Ans: _____________________[4] 1 The area of the shaded part in the figure below is 54 cm2. SH = PK. 4 What is the area of triangle PQR? P
S Q
H
R
K
Ans: _____________________[4]
83
11.
The area of rectangle A is 3 times the area of square B. The unshaded area of rectangle A is 5 times the unshaded area of square B. If the shaded area is 27 cm2, what is the area of the square? The figure is not to scale. B
A
12.
Ans: _____________________[4] Miss Chua brought some lollipops to share equally among 36 pupils at the end of a camp. However, 9 pupils had to leave the camp early. Therefore, each of the remaining pupils received 3 more lollipops. How many lollipops did Miss Chua bring?
Ans: _____________________[4] 84
13.
In the figure below, ABC is a right angled triangle at C. Its height is 9 cm and its base is 12 cm. 4 such identical triangles are used to form the square MNPQ. Find the side of the square MNPQ. M
A
C
N
B
P
Q
14.
Ans: _____________________[4] In the figure below, a rectangle is divided into 4 smaller triangles A, B, C and D. The 1 area of triangle A is the area of triangle B. The ratio of area of triangle A to that of 3 triangle D is 3: 5. The width of the rectangle is 6 cm. The area of triangle D is 30 cm2. Find the perimeter of the rectangle.
A
C B D
Ans: _____________________[4] 85
15.
16.
In a second-hand bookshop, story books are sold at $12 each and comic books are sold at $8 each. At first, there were 50% more story books than comic books. After 2 of the story books and all the comic books were sold. The shop some time, 3 received $6400. When all the books were sold, how much would the shop receive?
Ans: _____________________[4] 1 Lucy had the money that Aaron had. After that Aaron spent $45 and Lucy’s 3 mother gave her $6. Aaron still had $3 more than Lucy. How much money did Lucy have at first?
Ans: _____________________[4] 86
17.
18.
3 2 of Joey’s marbles is equal to the number of marbles that Thomas has. Ben has 5 7 twice the difference between Thomas and Joey’s marbles. Joey has 48 marbles less than Ben. How many marbles do they have altogether?
Ans: _____________________[4] Tank A measures 4 m by 6 m at the base and is 1 m high. Tank B has the base dimensions of 5 m x 3 m and is twice as high as tank A. Both of them contain the same amount of water. The height of water level in tank A is half of its height. Find the height of water level in tank B.
Ans: _____________________[4] 87
Semestral Assessment 2: Mock Paper 2 Paper 1 (Duration: 50 mins) Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.
1.
The square below is divided into three parts, A, B and C. The ratio between the areas A and C is 8: 3. What is the ratio of the area of B to that of C?
(1) (3) 2.
3.
3:8 8:5
(2) (4)
5:3 8 : 11
(
The average weight of 3 pupils is 38 kg. Andy weighs 33.5 kg. John is 3.5 kg heavier than Bob. How heavy is John? (1) 42 kg (2) 38 kg (3) 33 kg (4) 30 kg ( ) Maria and Lily shared some money. Maria had of the total sum. Lily had $180 more than Maria. How much money did both of them have in total? (1) 72 (2) 90 (3) 360 (4) 420 (
4.
5.
)
)
Adil had 36 more stickers than Xiao Mei. Each of them then bought another 10 stickers. After that, Adil had 4 times as many stickers as Xiao Mei had. How many stickers did Adil have initially? (1) 38 (2) 40 (3) 58 (4) 108 ( ) 2 5 1 kg of sugar and Sarah bought 1 kg of sugar. They used 2 kg 10 5 6 to bake some cakes. How many kilograms of sugar did both of them have eventually? 3 7 (1) (2) 10 15 2 7 2 4 (3) (4) ( ) 15 30
Celine bought 2
88
6.
7 3 kg of charcoal for a BBQ but only used of them. How many 4 5 kilograms of charcoal were left over? 7 1 1 (1) (2) 10 20 3 7 1 1 (4) (3) 20 20 (
Ivy bought
)
7.
There are 32 students in a class. There are 24 students wearing spectacles. What is the ratio of the number of students who wear spectacles to the number of students who do not? (1) 1:3 (2) 3:1 (3) 3:4 (4) 4:3 ( )
8.
Ali is living in Singapore and he has collected stamps from Singapore, China and India. The ratio of the number of Singapore stamps to the number of China stamps to the number of India stamps that he collected is 1: 1: 2. Ali collected 108 foreign stamps in total. How many local stamps were there? (1) 27 (2) 36 (3) 81 (4) 144 ( )
9.
A container having a capacity of 33.5l is filled with lime juice drink. This container is dispersed into 100 similar glasses for guests. How many liters of juice drink is there in each glass? (1) 0.0335 l (2) 0.335 l (3) 3.35l (4) 3 350 l ( )
10.
Find the difference between 125.22 and 38.19. Express your answer as correct up to 1 decimal place. (1) 87.0 (2) 87.1 (3) 87.9 (4) 88.0 ( )
11.
A box containing 24 identical cans weighs 8.36 kg. What is the mass of the box (in kg) if each can weighs 340g? (1) 0.2 kg (2) 0.418 kg (3) 0.5 kg (4) 2 kg ( )
12.
The distance from Hassan’s house in Serangoon to Patrick’s house in Paya Lebar is 5 515 m. Write that distance rounded off to the nearest kilometer. (1) 5 km (2) 6 km (3) 5 500 km (4) 60 km ( ) 89
13.
What is the value of digit 3 in 238 962 (1) 30 (3) 3 000
(2) (4)
300 30 000
14.
Last month, a shop collected $65 098 from selling goods. Express this amount to the nearest hundred (1) 65 000 (2) 65 100 (3) 66 000 (4) 66 100
15.
1 Express 3 as a percentage 4 (1) 0.325% (3) 32.5%
(2) (4)
(
)
(
)
(
)
3.25% 325%
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
16.
17.
In an orchard there are apple trees and pear trees. The ratio of the number of apple trees to the number of pear trees is 5: 9. What is the ratio of the number of pear trees to the total number of trees in the orchard?
Ans: _____________________ A caterer mixed 2070 ml of orange syrup to 12.42 l of water to make orange juice drink. What is the volume of juice drink made? Express your answer in liters.
Ans: _____________________ 90
18.
How many percent of the figure below is shaded?
19.
8 Express in decimal form. 125
Ans: _____________________
20.
Ans: _____________________ 5 Kg of flour is divided equally into 10 bags. What is the mass of flour in each bag? 6 Give your answer in its simplest fraction form.
Ans: _____________________ 21.
3 years ago, Mohammed’s age is
2 that of his brother. He is 15 years old now. How 3
old is his brother now?
Ans: _____________________
91
22.
23.
What percentage of the number of days in 2009 is the number of days in September?
Ans: _____________________ Arrange these number in an ascending order 105 , 0.051, 0.501, 51 1000 100
Ans: _____________________ 24.
56 x 28 = 29 x 28 + 1 x 28 + ______ x 28
25.
Write 64% as a simplest fraction.
Ans: _____________________
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
26.
The price before tax of a plasma TV is $2100. A GST of 7% is charged on the price. How much does a buyer have to pay for the TV?
Ans: _____________________ 92
27.
28.
29.
30.
1 l of lime juice. 8 The third carton had 786 ml of lime juice. How many liters of lime juice are there in total? Round off your answer to 2 decimal places.
The first carton has 1.25 l of lime juice. The second carton has 2
Ans: _____________________ 5 Kavitha saved as much as Joshua saved. The two pupils saved $1053. How much 8 is Kavitha’s savings?
Ans: _____________________ A small swimming pool of dimension 20 m x 10 m x 1.5 m is half filled with water. 4 pumps, each is running at a rate of 375 l per minute, is used to pump the pool. How long will it take to fill the pool completely?
Ans: _________________mins A movie ticket for an adult is $8.50 and that for a child is $5. During a certain period, 126 more adults than children visited the cinema. The cinema collected $2907. How many adults visited the cinema in that period?
Ans: _____________________ 93
Semestral Assessment 2: Mock Paper 2 Paper 2 (Duration: 1 hr 40 mins) Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated.
1.
2.
3.
Two boys and eight girls have saved an average of $604. The two boys have saved an average of $592. What is the average of the savings of the girls?
Ans: _____________________ There are 1200 pupils in a school. 20% of them are Indian. 65% of the remaining pupils are Chinese and the rest are Malay. a) How many Chinese pupils are there? b) What percentage of pupils is Malay?
Ans: _____________________ Mr. Chan sold a number of balloons in a 3-day carnival. On the first day he sold 1 2 of the balloons. The number of balloons he sold on the second day is of what he 5 3 sold on the last day. 92 more balloons were sold on the last day than on the second day. Balloons are sold at $1.20 each. How much did Mr. Chan earn?
Ans: _____________________ 94
4.
Mr. Feng had 225 more tulips than roses in his garden to sell. After selling
3 of the 5
1 of the roses, he had 858 flowers remaining. How many flowers did he 3 have at first?
tulips and
5.
Ans: _____________________ The following figure is not drawn to scale. ABCD is a square. AEDF is a rhombus. Triangle DFG is isosceles. C, G, D are on the same line. F is the midpoint of AG. Find a) ∠ AFD ∠ EDC b) ∠ DAE c) A
B
E
F
40o G
D
C
Ans: _____________________ 95
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.
7.
8.
3 of 4500g and a box that weighs 48% 8 of 18 kg? Express your answer in kg correct to 2 decimal places.
What is the total mass of a bag that weighs
Ans: ___________________kg[3] There are 15 trees planted in a line. The distance between any two adjacent trees is the same. The seventh tree is 7920 cm away from the third tree. How far from the first tree is the last tree? Express your answer in meters.
Ans: _____________________[4] When dropping a tennis ball from a height of 15m to the ground, Johannes realized 4 that the ball went up to of the previous height for every bounce. Find the total 5 distance that the ball had travelled when it hit the ground the second time.
Ans: _____________________[4] 96
9.
10.
11.
Mr. Lee has 4 children. His age is 3 times that of his youngest child. Each child was born 3 years before the next one. The total age of the 4 children and the father is 193 years. Find the age of Mr. Lee’s first child.
Ans: _____________________[4] Each small truck has 10 wheels. Each large truck has 14 wheels. A truck manufacturer ordered 408 wheels for their 32 trucks. How many large trucks are there?
Ans: _____________________[4] Francis gave half of his salary plus $100 to his mother. He spent 25% of the 3 remaining plus $49 on furniture. He bought some books for $61. He gave of his 5 remaining sum plus $53 to his sister. He saved the final $443. How much is Francis’s salary?
Ans: _____________________[4] 97
12.
13.
14.
An elephant is 5.5 times as heavy as a zebra. The total mass of 2 elephants and 3 zebras is 1260 kg. What is the mass of 1 elephant and 4 zebras?
Ans: _____________________[4] From January to August, Phoebe earned an average of $2340 per month. From September to December, she earned some more money and the average earning over the entire year is $3290. What was the average amount of money that Phoebe earned a month in the period from September to December?
Ans: _____________________[4] In a charity event, 3 scouts Benny, Ray and Kathy raised $1459 altogether. Ray 1 raised $296 less than Benny while Katy raised an amount as much as Benny. How 4 much money did Kathy raise?
Ans: _____________________[4] 98
15.
16.
The ratio of the number of roses to the number of lilies to the number of tulips is 3:5:9. If there are 954 more tulips than roses, how many more lilies than roses are there?
Ans: _____________________[3] There are 20 more pages in a mathematics book than in a physics book. There are 70 more pages in a chemistry book than in a mathematics book. The total number of pages in 20 books of each type is 10 000. How many pages are there in a physics book?
Ans: _____________________[4]
99
17.
In the figure below, the rectangle on the left is made by bending a wire. Another wire with the same length is bent to make the two identical isosceles triangles on the right. What is the area of one isosceles triangle?
33 cm
36 cm
75 cm
18.
Ans: _____________________[4] The ratio of the amount of money Josh had to that Derek had was 3: 5. Derek spent 1 25% of his money on toys and on stationeries. He also bought two pairs of shoes 5 for $150. He saved the remaining $246. How much money did Josh have?
Ans: _____________________[4]
100
Semestral Assessment 2: Mock Paper 3 Paper 1 (Duration: 50 mins) Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.
1.
What is the ratio of (1) (3)
2.
3.
5 : 14 3:5
1 hours to 56 minutes? 3 (2) (4)
What percentage of 4 m is 25 cm? (1) 6.25% (3) 0.16%
(2) (4)
14 : 5 5:3 (
)
(
)
62.5% 16%
In a factory, soya drink is poured from a 5.2l tank to fill some identical cans, each of which has a capacity of 330ml. What is the maximum number of cans that can be filled using one tank? (1) 14 (2) 15 (3) 16 (4) 17 ( )
4.
Jane spent an average amount of $127 a month over 5 months. Find the total amount that Jane spent over 5 months. (1) $600 (2) $635 (3) $660 (4) $700 ( )
5.
John had some money. He used 25% of his money to buy furniture and used of the remainder to buy clothes. If the spent $300 on clothes, how much did he spend on furniture? (1) $240 (2) $500 (3) $1200 (4) $1500 (
6.
)
Jane bought some pieces of clothes for an average cost of $24. After that, she bought another piece that costs $96 and the average cost became $36. How many pieces of clothes did Jane buy altogether? (1) 5 (2) 6 (3) 8 (4) 4 ( )
101
7.
In the figure below, 1, 2, 3 and 4 together make a square. 2 and 3 are also squares and they contribute 50% of the area of the figure. Which of the following pair will 5 form of the figure? 8
1
4 (1) (3)
2 3
1 and 2 1 and 4
(2) (4)
3 and 4 2 and 3 (
)
8.
2 3 of what Harry had is equal to 5 4 of what Jack had. What fraction of the total number of cards are Jack’s cards? 8 15 (1) (2) 23 23 23 23 (3) (4) 15 8 ( )
9.
Find the value of 7 x (2 + 16 ÷ 2) – 1 (1) 14 (3) 62
10.
11.
Harry and Jack each had some Pokémon cards.
(2) (4)
Find the largest fraction of the following 7 (1) (2) 9 7 (3) (4) 11
21 69 (
)
(
)
7 10 7 12
The distance from A to B is eight times the distance from B to C. What is the ratio of the distance from A to B to the total distance? (1) 1:8 (2) 1:9 (3) 8:9 (4) 9:8 ( ) 102
12.
The volume of a tank is 56l when rounded off to the nearest litre. Which of the following is likely to be the actual volume of the tank in liter? (1) 55.05 (2) 55.49 (3) 56.45 (4) 56.51 (
)
13.
David had $32 left after spending $48. What percentage of his money did he spend? (1) 40% (2) 60% (3) 67% (4) 80% ( )
14.
What is the ratio of the shaded part to the whole figure below?
(1) (3)
1:4 4:9
(2) (4)
4:5 5:9 (
15.
)
What is ∠ h in the figure below? FG is a straight line. The figure is not to scale.
F
(1) (3)
35o
h
35o 55o
(2) (4)
G
45o 65o (
103
)
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
16.
17.
Write
12 in percentage form. 25
Ans: _____________________ A card board is 30 cm in length and 16 cm in breadth. What is the area of the card board?
18.
Ans: _____________________ Four cans of iced tea costs $6. How much is two dozen cans?
19.
Find ∠x given that ∠x = ∠y
Ans: _____________________
x 162o y
Ans: _____________________ 104
20.
In the figure below, ABCD is a rectangle, AI = ID, BJ = JC. What percentage of the whole area is the shaded area? A
J
I
C
D 21.
22.
23.
B
Ans: _____________________ A pencil case can contain 12 pencils. If there are 390 pencils, how many pencil cases are needed?
Ans: _____________________ 7 Angela has some short sleeved and long sleeved shirts. of the shirts are long 15 sleeved. What is the ratio of the short sleeved shirts to the long sleeved shirts?
Ans: _____________________ Brian has 50% more $2 notes than $5 notes. He has 45 notes in total. How much money does he have?
Ans: _____________________ 105
24.
What are the common factors of 18 and 45?
25.
Ans: _____________________ Kiara walked 55m in every minute. It took her 18 minutes to walk from home to school. How far is her school from her home?
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your workings clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
26.
27.
In 2009, Raphael is 9 years old. His father is 38 years older than he is. In how many years will his father’s age become three times his age?
Ans: _____________________ Find the volume of a bottle if 36% of it can fill a 72ml cup completely.
Ans: _____________________
106
28.
29.
Find the maximum number of 40 cm cubic boxes that can be stored in a storeroom that is 5m wide, 6m long and 3m high.
Ans: _____________________ Yvonne weighs 42.5 kg. Her bag weighs 4750g. If Yvonne wears her bag and stands on an electronic scale, what value will the scale indicate? The scale expresses mass in kg.
Ans: _____________________ 30.
Antoine needed to walk 1 for another
2 km. He had walked some distance and still had to walk 5
3 km. How far had he walked? Give your answer in meters. 4
Ans: _____________________ 107
Semestral Assessment 2: Mock Paper 3 Paper 2 (Duration: 1 hr 40 mins) Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated.
1.
2.
A water tank has dimensions 60 cm x 25 cm x 30 cm. Uncle Tiong is using a 3l pail to fill the tank. How many times does he use the pail?
Ans: _____________________ Study the figure below carefully. ABCD is a square piece of paper. If I fold the piece along the line IK and then cut away along the lines IJ and JK, what is the area of the remaining piece? 18 cm I A A B I J J
K D
K
2 cm C
D
25 cm
C
Ans: _____________________ 108
3.
4.
Mrs. Ong bought 2 kg of grapes at a price of $3.20 per 100g. Mrs. Choo bought the same kind of grapes with a discount of $0.70 per 100g. She paid the same amount of money as Mrs. Ong did. How many more kilograms of grapes did Mrs. Choo buy compared to Mrs. Ong?
Ans: _____________________ Fill in the blank with an appropriate number to complete the pattern.
1 , 4 , 9 , ________ , 25
5.
Ans: _____________________ The average distance that Mei Mei jumped over 5 attempts is 145 cm. The average distance of the first 3 attempts is 155 cm. What is the average distance of the last 2 attempts?
Ans: _____________________ 109
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.
The figure below is not drawn to scale. ∠MNQ is 29o. MNPQ is a rhombus. Find ∠ NMQ. a) If MN = NO, find ∠ NOP. b) M N
Q
O
P
7.
Ans: _____________________[4] 1 Guo Qi drank of the carton of milk on the first day. Over the next two days he 5 drank 75% of the remaining milk. There was still 750ml of milk left. What is the volume of the carton of milk? Express your answer in liters.
Ans: _____________________[4] 110
8.
9.
An apple drink is made by mixing apple syrup and plain water in the ratio 2: 5. How many milliliters of apple syrup is needed to make 1.4 l of apple drink?
Ans: _____________________[3] Study the pattern below. The shapes are made by using toothpicks.
1 shape a) b)
10.
3 shapes
2 shapes
How many toothpicks are needed to make 5 shapes? How many shapes can be made using 258 toothpicks?
Ans: _____________________[4] The number of stickers that Pamela had is 40% of the number of stickers that Zoe had. If the two children had 952 stickers altogether, how many stickers did Zoe have?
Ans: _____________________[3] 111
11.
12.
13.
5 that of Chek Khoon and Chek Khoon is 4kg more than Darren. If 6 the average mass of the three boys is 44 kg, what is the mass of Chek Khoon?
Bala’s weight is
Ans: _____________________[4] A restaurant had sold 3 times more honey roasted chicken than black pepper chicken. If 90 less honey roasted chicken had been sold, the number of black pepper chicken would have been twice the number of honey roasted chicken. a) How many honey roasted chickens were sold? b) How many black pepper chickens were sold?
Ans: _____________________[4] If Andy buys 3 story books and 5 comic books, he will have $24 left. If he buys 5 story books and 3 comic books, he will need $16 more. Given that a comic book is sold at $18, how much does Andy have?
Ans: _____________________[4] 112
14.
In the figure below, 1, 2, 3, 4 and 5 are all squares. What is the ratio of the total area of 1 and 2 to the total area of all the squares? 2
3
4
5
1
15.
16.
Ans: _____________________[4] Plastic tables were sold at $75 each and wooden tables were sold at $80 each. There were 150 plastic tables in a shop at first. After selling all the tables, the shop received $12850. How many wooden tables were sold?
Ans: _____________________[4] 1 1 In a class, of the pupils like basketball, of the remainder like chess, the rest like 3 4 swimming. There are 10 pupils who like chess. Each pupil only likes one sport. What is the number of pupils who like either chess or basketball?
Ans: _____________________[4] 113
17.
18.
Mr. Wong hired a transport company to deliver some glass products for him. For every safely transported product, the company charges $16.5. For every product that was broken on the way, the company compensates $66. Mr. Wong was charged $15,015 for the delivery. 90% of the products were delivered safely. How many products were broken on the way?
Ans: _____________________[4] Mindy and Ryan had an equal amount of cookies. Each day, Mindy ate 23 cookies and Ryan ate 8 more cookies than Mindy. a) How many days had passed when Mindy had 149 cookies left and Ryan had 53 cookies left? b) How many cookies did each of them have at first?
Ans: _____________________[4]
114
Semestral Assessment 2: Mock Paper 4 Paper 1 (Duration: 50 mins) Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.
1.
An equilateral triangle and a right-angled triangle are placed next to each other as in the figure below (not to scale). HAE is a straight line. Find ∠ EHB C
B
A
H (1) (3) 2.
4.
5.
30 120o
(2) (4)
o
60 150o
E (
)
Which of the following has the largest value? 1 5 24 (3) 0.26 (4) ( 1000 The average mass of a bag of rice and 3 bags of flour is 14 kg. If the bag of rice weighs 17 kg, what is the average mass of the three bags of flour? (1) 6 kg (2) 8 kg (3) 10 kg (4) 13 kg (
(1)
3.
o
25%
(2)
)
)
Amanda had 6 m of ribbon. She used 60% of the ribbon on the first day and of the remainder on the second day. How many centimeters of ribbon did she have left? (1) 60 cm (2) 90 cm (3) 180 cm (4) 240 cm ( ) 2 Sarimah bought two similar pizzas. She saved of a pizza for her mother and 3 shared the rest among herself and 5 friends. What fraction of a pizza did each child get? 1 2 (1) (2) 9 3 4 2 (3) (4) ( ) 15 15
115
6.
The table below shows the number of maximum marked papers scored by pupils in a class from August to November Month Number of maximum marked papers August 33 September 49 October ? November 52 The class scored an average of 46 maximum marked papers a month. How many maximum marked papers were there in October? (1) 48 (2) 50 (3) 134 (4) 184 (
7.
8.
9.
)
Knowing that 483 x 7 = 3381, find the value of 483 x 0.07 (1) 3381 (2) 338.1 (3) 33.81 (4) 3.381 (
)
Sally bought an LCD with a 30% discount and 7% GST for $749. What is the original price of the LCD? (1) $700 (2) $1000 (3) $1042 (4) $1200 (
)
Below is the parking charges at the car park of a shopping centre First 2 hours Subsequent 30 minutes or part thereof
$2.50 $1.50
Kelvin entered the car park at 3.45 pm. He paid $9.50 for parking charges when leaving the car park. What is the latest time possible that he left the car park? (1) (3)
7.15 pm 6.15 pm
(2) (4)
7.45 pm 6.45 pm (
)
10.
Josh wrote down two numbers on a piece of paper. 40% of the larger number is 84. The difference between the two numbers is 78. What is the smaller number? (1) 288 (2) 34 (3) 132 (4) 210 ( )
11.
How many eighths are there in (1) (3)
?
13 24
(2) (4) 116
16 26
(
)
12.
ABCD is a parallelogram. ∠ABD = 47o. ∠ BCD = 105o. What is ∠ BDA? A B
D (1) (3) 13.
14.
15.
o
(2) (4)
28 152 o
C 38 o 208 o (
)
(
)
3 sticks have a total length of 192 cm. What is the average length? (1) 32 cm (2) 64 cm (3) 96 cm (4) 576 cm There are 184 red, white and green marbles altogether. The number of green and white marbles is 54. There are 150 red and white marbles altogether. What fraction of the total number of marbles is the number of white marbles? 5 5 (1) (2) 36 46 5 5 (3) (4) 51 97 ( ) Mrs. Liu made 4.82 l of lemon tea in a container. She poured them into 8 cups, each of which had a capacity of 352 ml. What was the volume of lemon tea remaining in the container? (1) 2.004l (2) 2.04l (3) 2.24l (4) 2.4l ( )
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
16.
In an aquarium, the ratio of the number of goldfish to that of clownfish is 2: 7. The ratio of the number of clownfish to that of angelfish is 5: 2. What is the ratio of the number of goldfish to that of angelfish?
Ans: _____________________ 117
17.
18.
19.
20.
Calculate
17 3 . Remember to simplify your answer. × 9 34
Ans: _____________________ 1 Uncle Tan kept some milk in the fridge. After his children drank 1 l of milk, there 2 5 was 1 l left. How much milk was there in the fridge at first? 6
Ans: _____________________ If a pen costs $1.20 and I have $11, how many pens can I buy at most?
Ans: _____________________ The following diagram is not drawn to scale. Find ∠ i, given that WSX and YSZ are straight lines. Z W 154o S i
87o
X
Y Ans: _____________________ 118
21.
The average of the two numbers A and B is 80. The average of those two numbers and a third number C is 85. What is the value of C?
Ans: _____________________ 22.
23.
9 x 5.6 = 5.6 + 5.6 + 5.6 + 5.6 x A Find the value of A.
Ans: _____________________ Benjamin received 72 marks for Mathematics, 83 marks for Physics and 67 marks for Chemistry. What is his average score for the three subjects?
Ans: _____________________ 24.
What are the common factors of 24 and 36?
Ans: _____________________
119
25.
A convenience store collects an average of $5839 a day. How much does the store collect in a week?
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
26.
27.
The sum of the area of all the faces of a solid cube is 54 cm2. What is the volume of the cube?
Ans: _____________________ A journey 12.8 km long was divided into 9 parts. Of these 9 parts, there were 5 parts that were 0.91 km long each and 3 parts that were 1.32 km each in length. What was the length of the remaining part?
Ans: _____________________
120
28.
29.
There are 10 200 people in a village. 30% of the villagers are children and the rest are adults. 40% of the adults are working outside the village. How many adults are working outside the village?
Ans: _____________________ Calculate ∠ ABD in the figure below. Note that it was not drawn to scale. A 93o
B
30.
D
43o
37o
C
Ans: _____________________ Lucy bought 6 similar skirts and 4 similar shirts for $162. The price of 2 shirts is equal to the price of 3 skirts. How much is a shirt?
Ans: _____________________
121
Semestral Assessment 2: Mock Paper 4 Paper 2 (Duration: 1 hr 40 mins) Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated.
1.
2.
3.
Stanley withdrew some money from the bank to purchase some goods. He spent 1 $1144 to buy a new laptop and of the remainder on a game console. He still had 4 half of what he withdrew from the bank. How much did Stanley withdraw from the bank?
Ans: _____________________ 5 similar bags of potatoes have a total mass of 86.25 kg. A porter can carry a maximum of 60 kg. How many porters are needed to carry 20 of such bags?
Ans: _____________________ The distance from Mary’s house to her grandmother’s house is 14 km. Mary had cycled 3.115 km from her home to her grandmother’s. What percentage of the journey had she covered?
Ans: _____________________ 122
4.
5.
In the figure below, there are two adjacent squares and the shaded shape overlaps both. The larger square has a side of 36 cm and the smaller square has a side of 20 cm. What is the area of the shaded shape?
Ans: _____________________ The ratio of Charles’ stamps to Mark’s stamps to Shawn’s stamps is 3: 7: 9. Mark has 168 stamps. a) How many stamps do the boys have altogether? b) After Mark gives some stamps to Charles, the two boys have the same number of stamps. How many stamps did Mark give Charles?
Ans: _____________________
123
For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.
7.
There are some flowers in a garden. 0.2 of the flowers are daisies and the remaining 5 flowers are roses. of the roses are red and the rest are white. There are 24 more red 7 roses than white roses. a) How many white roses are there? b) How many daisies are there?
Ans: _____________________[4] In the figure below, AB = BC = CA. FCD, BCE and ACG are straight lines. The figure is not to scale. Find a) ∠ CED ∠ ACF b) A
B
F
42o
C 31o D
G E
Ans: _____________________[4] 124
8.
9.
10.
Mrs. Foo bought 3.3 kg of fish at $1.59 per 100g, 2.8 kg of beef at $4.89 per 500 g, and 7 packages of vegetable at $0.86 per package. How much did she pay for all the goods?
Ans: _____________________[4] The ratio of the number of curry puffs to the number of cakes in a shop is 1: 4. A curry puff costs $2. Each cake is sold at $5. The total amount that the shop will receive from selling all the cakes and curry puffs is $1892. How many cakes are there?
Ans: _____________________[4] A shop had 280 pens. 70% of the pens were blue. A week later, a number of blue pens were sold and 60% of the remaining pens were blue. How many pens altogether were there in the shop a week later?
Ans: _____________________[4]
125
11.
12.
13.
A textbook and a bag cost $30. A textbook and a comic book cost $22.5. David bought 4 textbooks, 2 bags and 1 comic book for $100. What is the cost of a comic book?
Ans: _____________________[3] Marion and Nina had some beads in the ratio 5: 7. If Marion gave Nina 24 beads, Nina would have three times as many beads as Marion had. How many beads did Marion have at first?
Ans: _____________________[4] What fraction of 4l is 350ml? Express your answer in the simplest form.
Ans: _____________________[3]
126
14.
15.
16.
40% of the fruits in an orchard are apples, 80% of the remainder is oranges and the rest are mangoes. There are 648 more oranges than apples. After some apples have been sold, 10% of the remaining fruits in the basket are apples. How many apples have been sold?
Ans: _____________________[4] A salesman’s salary is $1575 a month. Apart from the salary, he earns a commission of $1.20 for every $5 of sales he makes. In 8 months, the total sales he makes is $72000. What is his average earning a month over these 8 months?
Ans: _____________________[4] 1 A rectangular tank measures 60 cm by 43 cm by 24 cm is filled with water up to 3 its height. At 1.p.m, water from a tap started to flow into the tank at a rate of 1.8 l per minute. How much water is in the tank at 1.20 pm?
Ans: _____________________[4] 127
17.
18.
Three identical squares, each is made up of 9 identical squares, are overlapped as in the figure below. Find the ratio of the shaded portion to the total area of the figure.
Ans: _____________________[4] Joanne thinks of a number. The difference between thrice that number and of that same number is 36 more than that number. What is the number that Joanne thinks of?
Ans: _____________________[4]
128
Semestral Assessment 2: Mock Paper 5 Paper 1 (Duration: 50 mins) Questions 1 to 10 carry 1 mark each and Questions 11 to 15 carry 2 marks each. For each question, write the number corresponding to the correct option in the bracket provided.
1.
The figure below is made up of 2-cm cubes. How many more cubes are needed to make it into a larger cube with sides 6 cm?
(1) (3)
10 17
(2) (4)
12 20 (
2.
3.
4.
)
3 of them are 10 cent coins. 8 The remainders are 50 cent coins. All the 10 cent coins together are worth $2 more than all the 20 cent coins together. How many 50 cent coins does Johan have? (1) 40 (2) 80 (3) 120 (4) 160 ( )
Johan has some coins. 12.5% of them are 20 cent coins.
The ratio of the number of orangees to the number of mangoes in a basket is 4: 5. If there are 5 more mangoes than oranges, how many oranges are there in the basket? (1) 20 (2) 25 (3) 45 (4) 5 ( ) Which of the following statements is true? If one of the angles in an (2) (1) isosceles triangle is 60o, the triangle is equilateral. No angle can be 60o in a right(4) (3) angled triangle.
129
A rhombus has all the properties of a square. The sum of all the angles in a foursided figure is always different. ( )
5.
6.
Three pupils shared a number of books. Katrina contributed 0.5 of the number of 3 and Patrick contributed the rest. What percentage of books, Melisa contributed 10 the number of books is Patrick’s contribution? (1) 20% (2) 35% (3) 53% (4) 80% (
)
Sally read 40% of her book and had 120 pages left. How many pages were there in the book? (1) 200 (2) 280 (3) 300 (4) 520 ( )
The following graph shows the number of students in different grades in a secondary school. Study the graph carefully and answer the questions below.
7.
8.
What is the difference between the number of Sec 3 and the number of Sec 1 students? (1) 30 (2) 40 (3) 70 (4) 80 (
)
What fraction of the total number of students is the number of Sec 1 students? 14 16 (1) (2) 57 57 29 25 (3) (4) 114 114 (
)
130
9.
10.
4 3 hours. However, she only used of 5 4 the time intended. How much time did she save? 1 1 h h (1) (2) 20 5 11 3 h h (4) (3) 20 5 ( )
Sabrina planned to complete her drawing in
3 boys shared 1
1 of a pizza equally. What fraction of a whole pizza did each boy 4
get? (1) (3)
11.
12.
5 12 1 12
(2) (4)
Find the missing value 8.507 = ________ x 1000 ÷ 100 (1) 0.8507 (3) 85.07
(2) (4)
Which of the following is not equal to (1) (3)
12 5 15 4
(
)
(
)
(
)
8.507 850.7
5 ? 9
15 27 25 36
(2) (4)
45 81 35 63
13.
The average of 3 numbers is 27. Two of the numbers are 19 and 25. What is the third number? (1) 17 (2) 37 (3) 59 (4) 81 ( )
14.
Find a number between 40 and 50 that has a remainder of 2 when divided by either 4 or 5. (1) 42 (2) 46 (3) 47 (4) 49 ( )
131
15.
Study the figure below. ABC is an isosceles triangle at A, CDE is an isosceles triangle at D. Find the value of ∠x. The figure is not to scale. A
B
C
E
x
(1) (3)
144o
D (2) (4)
o
25 55 o
36o 70 o (
)
Questions 16 to 25 carry 1 mark each. Write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
16.
17.
1 of the chocolates for her brother. She 3 divided the rest of the chocolates equally among herself and her 5 friends. What fraction of the total number of chocolates did each of Alice’s friends get?
Alice bought some chocolates. She saved
Ans: _____________________ Mr. Smith had dinner at a restaurant. The cost of the food was $150. If he had to pay 7% GST and 10% service charge on the cost of the food, how much more did he have to pay?
Ans: _____________________
132
18.
Calculate the sum of the first 7 multiples of 9 that are larger than 90.
19.
Express 20.08l in litres and millilitres.
20.
Ans: ________l________ml A container measures 20 cm by 15 cm by 10 cm. Another container measures 15 cm by 7 cm by 5 cm. What is the total volume of the two containers?
21.
Ans: _____________________ Draw the corresponding height to base BC for the triangle ABC below. A
Ans: _____________________
B
C 22.
Calculate 199 – 53 x 2 + 14 ÷ 7
Ans: _____________________ 133
23.
What is the smallest positive common multiple of 36 and 48?
24.
Calculate 2215 ÷ 9, corrected up to 2 decimal places.
25.
1 How many seconds are there in 1 hours? 3
Ans: _____________________
Ans: _____________________
Ans: _____________________ Questions 26 to 30 carry 2 marks each Show your working clearly in the space below each question and write your answers in the spaces provided. For questions which require units, give your answers in the units stated.
26.
Find the missing numbers. _____ : 18 : 22 = 28 : ______ : 77
Ans: _____________________ 134
27.
The table below shows the prices of air ticket to country X
AIR TICKET TO COUNTRY X Adult
Child (below 12 years old)
(price per person)
(price per person)
Economy
$900
$450
Business
$1200
$600
First class
$1600
$800
Ticket class
Mr. Mohammed, his wife, 9-year-old daughter and 15-year-old son travelled to country X. How much did they pay altogether if they chose Business class?
Ans: _____________________ 28.
10% of a number is less than
2 of that number by 33. What is the number? 5
Ans: _____________________
135
29.
30.
Refer to the figure below. Three identical squares are arranged in a row. If the area of each square is 144 cm2, what is the perimeter of the rectangle that is made by the three squares?
Ans: _____________________ The time on the clock is exactly 9 a.m. When the minute hand turns 450o clockwise, what time will it be?
Ans: _____________________
136
Semestral Assessment 2: Mock Paper 5 Paper 2 (Duration: 1 hr 40 mins) Questions 1 to 5 carry 2 marks each. Show your workings clearly in the space below each question and write your answers in the space provided. For questions which require units, give your answers in the units stated.
1.
2.
Swee Swee had a saving account of $30 000 in a bank. The interest rate is 3.75% per year. How much interest will Swee Swee receive after a year?
Ans: _____________________ Construct a line that goes through M and is perpendicular to AB. M
. B
A 3.
Below is the menu at a restaurant: Appetizer Main course Tom Yam soup Grilled fish Spring roll Beef stew Mango salad Roasted chicken
Dessert Banana split Ice cream Cheese cake
How many different combinations could a person choose if he wanted to have an appetizer, a main course and a dessert?
Ans: _____________________ 137
4.
What is the average of the first 8 multiples of 9?
Ans: _____________________ 5.
4 7 kg of meat and cooked kg for dinner. What is the quantity of 5 10 meat that has not been cooked? Give your answer in decimals.
Nicolas bought
Ans: _____________________ For Questions 6 to 18, show your workings clearly in the space provided for each question and write your answers in the spaces provided. The number of marks awarded is shown in brackets at the end of each question. (50 marks) 6.
Mrs. Khoo mixed 6l grape syrup with 9l of water. After that, she used some rectangular containers to store the drink. Each container measures 12 cm by 7 cm by 5 cm. Each container is filled completely. a) How many containers could be filled? b) What is the volume of the drink that was left over?
Ans: _____________________[4] 138
7.
Find ∠ x in the figure below. AOB, COD, EOF are straight lines. E D
78o
A
33o x
C
8.
B
O
F
Ans: _____________________[4] 3 In the figure below, the breadth of the rectangle is its length. What is the area of 4 the shaded portion? The figure is not drawn to scale. 6.5 cm
17.5 cm
Ans: _____________________[4]
139
9.
10.
11.
Michael participated in a swimming competition. On average, he completed a lap in 3.2 minutes. He needed to swim 8 laps to complete the race. What was the total time he took to complete the race? Give your answer in minutes and seconds.
Ans: _____________________[3] 5 A farmer planted 400 flowers in his garden. of them were roses. The farmer then 8 3 sold some roses. The remaining number of roses was then of the total number of 8 flowers remained in the garden. How many roses were sold?
Ans: _____________________[3] The figure below is made up of two adjacent squares and a shaded triangle. The smaller square has an area of 16 cm2. The larger square has an area of 49 cm2. What is the area of the shaded triangle?
Ans: _____________________[4]
140
12.
Find ∠z in the following figure. AOB and COD are straight lines. ∠y = ∠z. ∠x = 12o. The figure is not to scale. D A 142o O C
x
y
z
B
Ans: _____________________[4] 13.
1 Peter studied Physics for 2 hours on Monday. On Tuesday he spent some time to 2 continue his Physics study. On Wednesday, he spent twice as many hours as on Tuesday to finish his Physics lesson. Over those 3 days, Peter spent an average of 138 minutes a day studying Physics. In how many hours did Peter study Physics on Wednesday?
Ans: _____________________[4]
141
14.
Jordan is a basketball player. On the first match of the 2009 league he scored 7 goals. In every later match he scored 2 more goals than the previous match. He played 7 matches altogether in the league. a) How many goals did he score in total? b) What is his average number of goals per match?
15.
Nelson’s height is 152 cm. Nelson’s sister is 0.2 m shorter than he is. What fraction of Nelson’s height is his sister’s height? Express your answer in the simplest form.
16.
Ans: _____________________[4] In a volleyball tournament, there are 10 school teams. Each team has to play one match against each of the other teams. How many matches will be played between the teams?
Ans: _____________________[4]
142
17.
18.
Mr. Teo bought a table and two chairs for $300. The two chairs were sold at the same price. The table’s price is twice as much as a chair’s. What is the price of the table?
Ans: _____________________[4] Peter wrote all the number from 1 to 100 continuously 1234567891011121314……979899100 How many digits did he write?
Ans: _____________________[4]
143
Answers to Semestral Assessment 1: Mock Paper 1 Paper 1 Q1 Q2 3 4
Q3 4
Q4 3
Q5 2
Q6 3
Q7 3
Q8 1
Q9 2
16 18
Nine million eighty thousand and eleven 3 906 = 3 000 + 900 + 6 7 503 906 = 7 000 000 + 500 000 + 3 906 The value of A is 500 000
17 19
20
5 94
21
22
5 109
23
24
5 976 201
25 26
3 147 682 If 90 pieces were in $100 notes, the money would be 90 x 100 = 9000 The number of $50 notes (9000 – 5250) ÷ 50 = 75 The cashier received 75 notes of $50 from Mr. Ben.
27
10 tables and 20 chairs cost $650 Thus 20 tables and 40 chairs cost $1300 20 tables and 10 chairs cost $850 Therefore 30 chairs cost $450 The cost of a chair is 450 ÷ 30 = 15 The cost of 1 table is (650 – 20 x 15) ÷ 10= 35 The cost of 1 table and 1 chair is 35 + 15 = 50 The cost of one table and one chair is $50 850 + 620 + 930 = 2400
28
2400x
29
Q11 2
Q12 3
Q13 1
Q14 4
Q15 2
8 883 008, 8 880 003, 880 300, 88 380 The first 6 multiples of 7 are 0, 7, 14, 21, 28 and 35. 0 + 7 + 14 + 21 + 28 + 35 = 105 The sum of the first 6 multiples of 7 is 105 60
Equal areas
Equal areas
The two shaded triangles at the bottom are equal to the two unshaded triangle at the top. So they and the shaded trapezium add up to a rectangle that is
1 3
of the big square. The shaded area is
1 3
of the
total area. 30
1 1 =600, 2400 x =200 4 12
2400 – 600 – 200 = 1600 He had 1600 nails left. 90 x 1 ÷ (105 – 90) = 6 It takes 6 minutes.
Paper 2 1
One equal part is (2892 – 1572) ÷ 6 = 3112 Each of them had $3112 at first 3
Value of 1 equal crossed part (17245 – 12 795) ÷ 5 = 890 Team B collected $890 890 x 6 = 5340 Team D collected $5340 2
Q10 2
1 − 83 − 14 = 83 ,
4
114 ÷ 83 = 304 The shop has 304 pairs of gloves in total.
144
The total price of 1 kg of each type 99.60 ÷ 6 = 16.60 The price of 1 kg of chicken (16.60 – 5 – 2) ÷ 3 = 3.20 The price of 1 kg of beef 3.20 + 5 = 8.20 (3.20 + 8.20) x 6 = 68.40 She spent $68.40 on the beef and the chicken. One cheese cake: 6.90 ÷ 3 = 2.30 One curry puff: 5.20 ÷ 4 = 1.30 25 ÷ 2.30 = 10.87 => 10 cheese cakes 25 ÷ 1.30 = 19.23 => 19 curry puffs 19 – 10 = 9 (a) Timmy could buy 9 more curry puffs than cheese cakes. (b) number of cheese cakes and curry puffs altogether is =129.6 /(2.3+1.3) x 2 = 72
808 1212
=
2 3
Jordan’s stickers are 8
2 3
of Albert’s.
Three years later: Dan’s age: 34 ÷ (3 – 1) = 17 Dan’s father’s age: 17 x 3 = 51 Now: Dan’s father’s age: 51 – 3 = 48 Dan’s father is 48 years old now.
10
9
9 cm
From 1 to 9: 9 x 1 = 9 From 10 to 99: 90 x 2 = 180 From 100 to 150: 51 x 3 = 153 9 + 180 + 153 = 342 342 steel digits are necessary.
14
5 cm
8 cm 7 cm
6
A
B 13 cm
4 cm
7
197g > 30g => $1.00 for the first 30g, left 197g – 30g = 167g. 167g > 50g => $1.70 for the next 50g, left 167g – 50g = 117g. 117 ÷ 25 = 4.68 => pay for 5 steps of 25g. $0.35 x 5 = $1.75 $1.00 + $1.70 + $1.75 = $4.45 Peter has to pay $4.45 Total of Peter’s and Jordan’s stickers: 924 x 2 = 1848 Peter’s stickers: (1848 + 232) ÷ 2 = 1040 Jordan’s stickers: 1040 – 232 = 808 Albert’s stickers: 172 + 1040 = 1212
5 cm
5
36 cm
11 12
13
16
A = 36 – 13 – 8 – 5 = 10 cm B = 7 + 9 – 4 – 5 = 7 cm 7 + 10 + 9 + 5 + 5 + 8 + 7 + 13 + 4 + 36 = 104 cm The perimeter is 104 cm 10 x 7 = 70 m2 70 x 15 = $1050 The difference in the number of bags 60 – 25 = 35 bags The mass of one bag (6790 – 4655) ÷ 35 = 61 g The mass of the box is 6790 – 60 x 61 = 3130g = 3.13 kg The box weights 3.13 kg. $1 215 x 116 = $140 940 The agency received $140 940 The figure has 5 lines of symmetry
15
17
If Alex had 224 more stamps, there would be five equal parts. Value of one equal part (2151 + 224) ÷ 5 = 475 Carl had 475 stamps. Tank’s volume: 90 x 40 x 15 = 54000 cm3 = 54l
12 × 1 12 = 18 l 54 – 18 = 36l Rate of tap B 12 ×
18
1 3
= 4l in a minutes
Total rate 12 + 4 = 16l in a minute Time taken: 36 ÷16 = 2.25 minutes = 2 minutes 15 seconds. 4 trees in the corners. Along the length: 49 ÷ 7 – 1 = 6 trees. Along the breadth: 35 ÷ 7 – 1 = 4 trees. Total: 6 x 2 + 4 x 2 + 4 = 24 trees. There were 24 trees in total
145
Answers to Semestral Assessment 1: Mock Paper 2 Paper 1 Q1 Q2 3 1
Q3 3
Q4 2
Q5 1
Q6 2
Q7 2
Q8 4
16
Q9 4
Q10 2
21
22
12 x 9 ÷ 2 = 54 cm2 The area is 54 cm2
24
0.14 + 0.8 + 5 + 0.032 = 5.972
25
1 : 2 53 = 1 : 135 = 5 : 13
27
The first team will play 3 matches with the 3 remaining teams. The second team already played 1 match with the first team, so it will play only 2 matches with 2 remaining teams. Similarly, the third team will play 1 match with the last team. The last team already played 3 matches with the 3 teams. 3 + 2 + 1 = 6, There are 6 matches in total.
23
1 4
Q14 3
Q15 1
− 53 (1 − 14 ) = 107 7 10
of his money
Number of children: 144 ÷ 3 = 48 Total: 48 x 5 = 240 There were 240 people in the audience 7 9
÷3 =
7 27
Each child got
7 27
of the cake
26
3 125 hours = 3 hours 25 minutes
7:45 + 3:25 = 11:10 Selina finished the task at 11:10 PM 30 x = 180o – 90o – 58o = 32o y = 180o – 33o – 80o = 67o y – x = 67o – 32o = 35o , The difference is 35o Paper 2 1 Total audience: 180 ÷ 1 = 4500 25
M N 29
5:25 – 3:40 = 1:45 Vanessa parked her car for 1 hour 45 minutes. So she will pay $2.50 for the first hour and $1.90 for the second hour. $2.50 + $1.90 = $4.40 Vanessa paid $4.40
2
108 ÷ 9 = 12 (12 + 9) x 2 = 42 The perimeter is 42m 126 ÷ 42 = 3 She paid $3 for each meter of the fence.
4
First finish line: 30m, Second line: 60m Third line: 120m, Fourth line: 240m Peter ran (30 + 60 + 120 + 240) x 2 = 900 m in total. a) Length: 7 + (7 + 3 + 7) + 7 = 31 cm b) Breadth: 7 cm Area: 31 x 7 = 217 cm2
People came by train:
4500 × (1 − 251 − 14 ) = 3195
5
Q13 2
Cost of a child ticket 49 ÷ (2 + 5) x 2 = 14 A child ticket costs $14 $179 501 965312
He spent
3
Q12 2
17
18 19 20
28
Q11 3
There were 3195 people who came by train From Mon to Fri (5 days), Harry travelled on route 1. Total distance on route 1: 4.3 x 5 = 21.5 km Length of route 2: 8.2 – 4.3 = 3.9 km. Total distance travelled on route 2: 3.9 x 2 = 7.8 km Total distance: 21.5 + 7.8 = 29.3 km Harry travels 29.3 km to the basketball court in a week.
6
a) Least visited month: Sep, 1200 visitors. Most visited month: Dec, 1900 visitors. Fraction b) Children visitors in July:
1800 × 23 = 1200 . Number of girls: 1200 ÷ 3 = 400 146
1200 1900
= 12 19
7
Cost of a toy robot is 2 times that of a cake. Cost of 18 cakes is 18 ÷ 2 = 9 times that of a toy robot. Therefore, with the amount spent, Jeffery could have bought 21 + 9 = 30 toy robots. With
3 5
With
2 5
56 x
11
10
Each notepad is $1.1 more than a pen. So 7 notepads is $7.7 more than 7 pens Cost of a pen (33.3 – 7.7) ÷ (7 + 9) = 1.6 9 x 1.6 = 14.4 Mary paid $14.40 for the pens.
12
a) Area of the shaded part: 30 x 10 ÷ 2 = 150 cm2 Total area: 30 x (10 + 18) ÷ 2 = 420 cm2 Area of the shaded part: 420 – 150 = 270 cm2
of his money, the number of toy robots he 3 5
x
2 5
= 20
Jeffery could buy 20 more toy robots with the remaining money. Total number of toy cars that Jason and Malik had 11 14
If each girl had 7 strawberries, there would be 4 strawberries extra. To give each girl one more strawberry so that each would have 8 strawberries, the 4 extra strawberries would be given to 4 girls first. There were 4 strawberries short so there were 4 girls left. Therefore, there were 8 girls. Number of strawberries 7 x 8 + 4 = 60 a) There were 60 strawberries b) There were 8 girls
of his money, he could by 30 toy robots
could buy is 30 ÷
9
8
= 44
Number of toy cars that Jason had 44 ÷ (7 + 15) x 15 = 30 Number of toy cars that Malik had 44 – 30 = 14 Total number of toy cars 30 + 14 + 56 = 100 a) Jason had 30 toy cars b) They have 100 toy cars altogether 1 notebooks = 3 files 10 notebooks = 30 files Cost of a file 85 ÷ (30 + 4) = 2.5 Cost of a notebook 2.5 x 3 = 7.5 The price of a notebook is $7.50
b)
13
= 145 of the whole figure is shaded.
14
Value of one equal part (90 + 30) ÷ 3 = 40 Number of apples 40 x 2 + 30 = 110 110 – 90 = 20, There were 20 more apples than oranges. 15
16 At Clementi: Number of girls 114 ÷ 2 = 57 Number of boys 57 x 3 = 171
17
10 10+18
Body = Head + Tail, 3B = 8 + B + 8 = B + 16 B=8 Body = 8 x 3 = 24, Tail = 8 + 8 = 16 8 + 16 + 24 = 48m The whale skeleton is 48m long Total amount of sugar: 500 + 600 + 800 + 900 + 1000 = 3800g The total mass of sugar in the sold packages must be a multiple of 3. Mrs. Liu did not keep packet A since she kept more than 500. So she must have kept packet C.
18 Number of children 171 + 57 = 228 Number of adults 228 ÷ 6 x 5 = 190 Number of men 190 ÷ 5 = 38 Number of women 38 x 4 = 152 From the diagram Total number of passengers 228 + 190 = 418 7 = 13u ÷ 2 – 3u, u = 2 At Dover: Mrs. Goh’s age 7 years ago The number of male passengers. 171 +5 + 38 = 204 2 x 16 = 32, 32 + 7 = 39 a) There were 418 passengers altogether when the Mrs. Goh is 39 years old now. train left Clementi Station b) There were 204 male passengers when the train left Dover station. There are 3 ways to arrange the first pupil: Alex, Carol and Dean (Benny does not stand at the first position). If Alex is at the first position, there are 2ways to arrange the second position (Benny and Carol) since Alex is not standing next to Dean. For each of the case, there are 2 ways to arrange the remaining 2 pupils. If Carol is at the first position, Benny cannot be at the second position since Alex and Dean have to be next to each
147
other then. Therefore, there are only two ways to arrange the second position (Alex and Dean). For each of the case, there are only one way to arrange the third and last position, since the third position must be Benny. If Dean is at the first position, there are two ways to arrange the second position (Benny or Carol). For each of the case, there are two ways to arrange the remaining pupils. The number of possible ways is 1 x 2 x 2 + 1 x 2 x 1 + 1 x 2 x 2 = 10 There are 10 ways to arrange these pupils. Answers to Semestral Assessment 1: Mock Paper 3 Paper 1 Q1 Q2 3 4 16
18
20
Q3 1
Q4 2
Q5 3
Q6 3
Q7 2
Q8 3
1 − 75 = 72 , 15 × 72 = 352 , 1 − 72 − 352 = 358 112 ÷ 358 = 490 , 490 × 352 = 28 The calculator cost $28 600 = 2 x 2 x 2 x 3 x 5 x 5 The two page numbers are two continuous factors of 600. 2 x 2 x 2 x 3 = 24, 5 x 5 = 25 The two pages are 24 and 25 8 + 5 = 13 65 ÷ 13 x 5 = 25 Elizabeth had 25 sweets.
22
24
26
Q9 3
Q11 1
Q12 3
Q13 2
Q14 3
17
Area of one square: 32 ÷ 8 = 4m2 Side of each square is 2m. Perimeter 32m
19
Total cost 300 – 41 = 259 Cost of 5 boxes of shuttlecocks 259 – 199 = 60 Cost of 1 box, 60 ÷ 5 = 12. Each box is $12.
21
X + 1 = Y, Y + Y = 10 + X X + 1 + X + 1 = 10 + X X = 8, Y = 9, 89 + 9 = 98 300 ÷ 15 = 20 There were 20 pupils. 10 x 20 = 200 Miss Lisa gave the class 200 toy bricks.
23
Total number of crayons at first (10 – 4) x 5 = 30 They had 30 crayons altogether at first. After David gave Gupta, the amount that Gupta had was 300 ÷ (2 + 1) = 100 The amount Gupta had at first was 100 – 18 = 82 Gupta had $82 at first. Area of one triangle: 3 x 4 ÷ 2 = 6 cm2+ Area of 3 triangles:3x6=18 cm2 Area of the square: 4 x 4 = 16 cm2 Area of the rectangle: 4 x 7 = 28 cm2 Total area: 18+ 16 + 28 = 62 cm2
Q10 2
25
225 ÷ 15 = 15 15 x 12.30 = 184.5 Mrs. Tan earned $184.50
27
Fraction of $10 notes
1 − 13 − 16 =
Q15 4
1 2
Ratio of $2 notes to $5 notes to $10 notes 2 : 1 : 3 Ratio of total amount $2 to that of $5 to that of $10 4 : 5 : 30 Amount of $5 notes 1794 ÷ 39 x 5 = 230 The total value of $5 notes Ali saved is $230 29 After 2 hours, Jimmy already made 28 10 − 4 1 = 5 8 ≈ 5.89 9 9 30 x 2 = 60 paper birds Darren had to run 5.89 km more. So the time that Philip would take is 60 ÷ (50 – 30) = 3 hours 30 108 ÷ 15 = 7.2, 98 ÷ 15 = 6.53, Therefore the bigger number is 15 x 7 = 105. The smaller number is 105 ÷15 x 2 = 14 Paper 2 19 7 2 CN = 96 ÷ 4 x 3 = 72 cm 2 1 7 23 × 85 = 4 19 24 , 7 3 − 4 24 = 2 8 Area of triangle MNC is 72 x 24 ÷ 2 = 864 cm2 The difference in their distances is 2 78 km 3
60 ÷ 4 x 7 = 105l (105 + 60) x 2.50 = 412.50 Mr. Quek paid $412.50
4
148
Volume of strawberry syrup needed 24 ÷ 6 = 4l Volume of strawberry syrup short: 4 – 1.5 = 2.5l Original volume of water 24 – 4 = 20l New ratio (4 + 2) : 20 = 6 : 20 = 3 : 10
5
7
Ratio of number of units of product A to that of product B 14 : 3 Ratio of total amount received from product A to that of product B 14 x 10 : 3 x 4 = 35 : 3 Total amount from selling product A 11400 ÷ (35 + 3) x 35 = 10500 Total amount from selling product B 10500 ÷ 35 x 3 = 900 Number of product A 10500 ÷ 10 = 1050 10500 – 900 =9600 a) He sold 1050 units of product A b) The difference between the amount of money collected from product A and B is $9600 Number of 20-cent coins that Suriyana had 192 ÷ (3 + 5) x 3 = 72 Number of 50-cent coins that Suriyana had 192 – 72 = 120 Suriyana had 72 twenty-cent coins and 120 fifty-cent coins.
6
Fahan’s total number of coins:
10
Fraction of stickers left after making scrapbooks
1 − 13 =
2 3
× 23 = 94 Fraction of stickers each friend received 94 ÷ 3 = Fraction of stickers left 1 − 13 − 94 = 92
Fraction of stickers given to friends
2 3
4 27
Number of stickers at first 42 ÷ (9 – 2) x 9 = 54 Each friend received
54 × 274 = 8 stickers
8
189 x 55 + 17 = 10 412 The number is 10 412
9
24 × 13 × 125 = 3 13 3 hrs 20 mins Mr. Ong worked with his computer for 3 hours 20 minutes
192 × = 48 coins 1 4
Number of 20-cent coins Fahan had 48 ÷ 3 = 16 coins Number of 50-cent coins Fahan had 16 x 2 = 32 coins a) Ratio of the number of 20-cent coins Suriyana had to the number of 50-cent coins that Fahan had 72 ÷ 32 = 9:4 b) Ratio of the amount of money that Suriyana had to the amount of money that Fahan had (72 x 20 + 120 x 50) : (16 x 20 + 32 x 50) = 31 : 8
11 13 14
15
12
Cost of a pen in box A: 14.70 ÷ 16 ≈0.92 Cost of a pen in box B: 22.50 ÷ 24 ≈ 0.94 Box A is the cheaper buy The length of the shortest side: 300 ÷ 5 x 2 = 120 cm The length of the last side: 300 ÷ 5 x 4 = 240 cm Perimeter 120 + 240 + 300 = 660 cm
+ 3×14 + 41×5 + ... + 19×120 = 12 − 13 + 13 − 14 + 14 − 15 ... + 191 − 201 = 12 − 201 = 1 2×3
1 − 83 = 85 , 480 ÷ 85 = 768
9 20
16
The total distance from A to B is 768 km 17
(14 + 26) x 11 ÷ 2 = 220 cm2
18
149
1 equal part = 5 x 4 = 20 Tom: 20 + 5 = 25 Jerry: 20 x 2 – 5 = 35 a) Tom had $25 b) Jerry had $35 a) The first person shakes hand with the other 2 people. There are 2 handshakes. The second person already shook hand with the first, so there is one more handshake. The last person already shook hand with the other two people. The number of handshakes is 2 + 1 = 2 b) Similarly, the number of handshakes when there are 5 people is 4 + 3 + 2 + 1 = 10 c) N umber of handshakes when there are 10 people is 9 + 8 + 7 + 6 + 5 + 4+ 3 +2 + 1 = 45 Base area: 5 x 7 = 35 m2 Depth: 105 ÷ 35 = 3 m The tank’s depth is 3 m. If all the animals were dogs, the number of legs would have been 4 x 36 = 144 Number of chickens (144 – 100) ÷ 2 = 22 There are 22 chickens.
Answers to Semestral Assessment 1: Mock Paper 4 Paper 1 Q1 Q2 2 1 16
Q3 2
Q4 2
Q5 2
Q6 3
Q7 3
Q8 2
Q9 3
Fraction of red pens
17
19
21
24
Sylvia made (221 – 121) ÷ 4 = 25 stars Alan made 121 – 25 = 96 stars The difference in the number of cans of coke and soda at first was 48 + 48 = 96 cans Number of cans of coke 96 ÷ (7 – 3) x 3 = 72 There were 72 cans of coke at first. If each boy was given $8, the total of their money would be 54 + 8 + 8 = 70 Amount that Fahan had at the end 70 ÷ (3 + 4) x 4 = 40 Amount Fahan had at first 40 – 8 = 32 Fahand had $32 at first.
54 × 2 34 = 154
26
30
In one hour pump A can fill
1 3
Q13 3
Q14 4
Q15 2
1 8
Area of the triangle XYZ 9 x 9 ÷ 2 = 40.5 cm2 Area of the unshaded part (9 – 4.5) x (9 – 2) ÷ 2 = 15.75 cm2 Area of the shaded part 40.5 – 15.75 = 24.75 cm2
20
22
5 7
, 54 , 54 , 75
18 ÷ 23 = 27
23
There are 27 two-thirds in 18. 8 12
=
2 3
The value of the box is 3.
2 34 months.
The number of candies in the box is a common multiple of 4 and 7. The smallest multiple of 4 and 7 is 4 x 7 = 28 We have 28 x 2 = 56 < 60 28 x 3 = 84 and 60 < 84 < 100 28 x 4 = 112 > 10 So the number of candies in the box is 84.
Q12 2
Ratio of blue pens to red pens to black pens 8 : 1 : 7 Number of red pens 210 ÷ (7 – 1) = 35 Number of black pens 35 x 7 = 245 Number of blue pens 35 x 8 = 280 Total number of pens 35 + 245 + 280 = 560
25
Betsy had 154 slices of fruit in
Q11 4
(1 − 12 ) = 161 1 Fraction of black pens 1 − 12 − 16 = 167
18
Apples : oranges = 2 : 3 = 4 : 6 Apples : bananas = 4 : 9 Oranges : bananas = 6 : 9 = 2 : 3
Q10 4
27 28
6 x 7 x 8 = 336， Mr. Lee had 336 boxes.
29
32 x 7 = 224 224 ÷ 25 = 8.96 9 buses are needed.
the pool and pump B can fill
5 A= 2 12
1 2
÷ 5 14 = 29 63
the pool.
The time taken for both pump to fill the pool completely is 1 / (1/2 + 1/3)= 1.2 hours。 Paper 2 2 1440 ÷ 80 x 5 = 90 1 The fraction of the number of questions remained Daniel had worked for 90 hours. after the second day 3 The shaded area can be divided into two parts: a 1 − 12 − 101 = 25 triangle at the top and a rectangle at the bottom. Number of days to answer these questions: The area of the shaded part is 2 1 3 x 3 ÷ 2 + 3 x 1 = 7.5 squares ÷ = 4 days 5 10 The area of each square is 3 x 3 = 9 cm2 So on the sixth day he finishes all the questions. So the area of the shaded part is 9 x 7.5 = 67.5 cm2 5 4 Fraction of the area of the smaller piece is
1 − 127 = 125 Area of the bigger piece 138 ÷ (7 - 5) x 7 = 483 The area of the bigger piece is 483 cm2 6
Total perimeter 59 x 2 = 118 cm Perimeter of the triangle 30 + 12 + 28 = 70 cm Perimeter of the square 118 – 70 = 48 cm Side of the square 48 ÷ 4 = 12 cm Area of the square 12 x 12 = 144 cm2
150
7
8
9 Volume of barrel A at first 24 x 3 ÷ 2 = 36 Volume of barrel B in the end 36 x 2 + 24 x 2 = 120 There is 120l of petrol in barrel B in the end. 10
11
(89 + 115) x 5 = 1020 (117 + 258) x 12 = 4500 So (205 + 397) x ? = 4816 ? = 4816 ÷ 602 = 8, The missing value is 8. Number of dolls sold: 900 ÷ 50 = 18 Number of dolls more than toy robots at the end 23 – 18 = 5 Number of dolls in the end 5 ÷ (1.5 – 1) x 1.5 = 15 Number of dolls at first 15 + 18 = 33 There were 33 dolls at first The number of cards Fred had: 104 ÷ 2 = 52 Total number of cards that George and Harry had 52 ÷
14
From the figure we can see that 1 equal part in Joey’s money is 2 equal parts in Zhong Ren’s money (2 squares) and 1 equal part in Suriya’s money is equal to 3 equal parts in Zhong Ren’s money. Total number of squares 2 x 5 + 7 + 3 x 3 = 26 Value of one square 1326 ÷ 26 = 51 Joey spent 51 x 2 x 2 = 204 Zhong Ren spent 51 x 1 = 51 Suriya spent 51 x 1 x 3 = 153 Total amount spent 204 + 51 + 153 = 408 They spent $408 altogether. Area of the shaded parts 2 x 4 ÷ 2 + 3 x 4 ÷ 2 = 10 squares Area of each square 4 x 4 = 16 cm2 Area of the shaded part 16 x 10 = 160 cm2
12
4 11
= 143
Number of cards Harry had 143 – 104 = 39 The total number of cards three of them had: 104 + 52 + 39 = 195 cards 400 = 2 x 2 x 2 x 2 x 5 x 5 We have 2 x 5 = 10 2 x 2 x 2 x 5 = 40 Therefore Jane had $10 and her brother had $40
13
Ratio of the cost of 1 pair of shoes and 1 pair of socks is 9 : 1 Ratio of the cost of 3 pairs of shoes and 5 pairs of socks is 27 : 5 Cost of 3 pairs of shoes 192 ÷ (27 + 5) x 27 = 162 Cost of 1 pair of shoes 162 ÷ 3 = 54 A pair of shoes costs $54.
15
Total mass of the two bags 33.25 x 2 = 66.5 kg The mass of the powder bag
66.25 ÷ (2 12 + 1) = 19 kg
Area of the rectangle 15 x 19 = 285 cm2 Area of the triangle 19 x (15 – 7) ÷ 2 = 76 cm2 Area of the shaded part 285 – 76 = 209 cm2 Alice bought 5 more notepads.
16
Number of pens 36 ÷ (7 – 3) x 7 = 63 There were 63 pens at first.
18
6 ÷ 3 x 7 = 14,
14 – 9 = 5,
17
Answers to Semestral Assessment 1: Mock Paper 5 Paper 1 Q1 Q2 4 3
Q3 4
Q4 4
Q5 3
Q6 1
16 18
Eight million six thousand five hundred.
20
Area MQH = area KNP =
1300 5000
=
13 50
=> Area MKPH = Shaded area = 22 24
Q7 1
1 2
1 2
1 4
area MNPQ
Q8 2
Q9 3
1 4
Q11 1
17 19
3
21
( 12 + 14 ) ÷ 2 = 83
area MNPQ
area MKPH =
Q10 4
23 5
Q12 4
Q13 2
Q14 2
Q15 4
= 4 53 It is 4600metres.
Jing Jing had done
3 8
of the homework.
area MNPQ.
40 ÷ 8 = 5 5 carpenters are required. 4 hours 40 minutes – 2 hours 45minutes = 1 hour 55 minutes. The carpenter started at 1.55 pm.
23
A = (100+21)×100 = 5050
25
Feng Xue and Ann each had (181 – 37) ÷ 2 = 72 stamps. Ann later had 72 + 29 = 101 stamps Ann had 101 stamps in the end.
151
26 28
(148.5 + 43.5) ÷ 2 = 96 (148.5 – 43.5) ÷ 2 = 52.5 The two numbers are 96 and 52.5 5 9
of the apples is equal to
5 7
of the pears
27
DH = 30 ÷ (7 + 3) x 7 = 21 cm Area BDH = 21 x 30 ÷ 2 = 315 cm2
29
Fraction of the full water volume taken from the tank 5 6
Ratio of apples to pears is 9 : 7 Number of pears at first 592 ÷ (9 + 7) x 7 = 259 Number of pears sold
Mass of the water taken out 81.74 – 59.8 = 21.94 kg Mass of the full water
259 × = 74 2 7
74 pears were sold.
volume 21.94 ÷ 13
30
Women : adults = 3 : 4 = 9 : 12 Adults : children = 3 : 7 = 12 : 28 Women : children = 9 : 28 Number of children 114 ÷ (28 – 9) x 28 = 168 There were 168 children at the concert. Paper 2 1 3.25 kg = 3250 g 3250 ÷ 250 x 0.65 = 8.45 Mr. Khoo paid $8.45 3 Total mass of 3 packets 903.6 x 3 = 2710.8 g Apple : strawberry : mango = 2 : 1 :
5
6
4 5
(1746 + 54) ÷
6 7
65.82 × 12 = 32.91kg Mass of the tank 59.8 – 32.91 = 26.89 kg
2 4
= 10 : 5 : 4
7
= 2100
Tom’s salary is 2100 ÷
3 4
= 2800
Tom’s salary is $2800 8
1 12 + 16 = 1 23
= 65.82kg
Mass of half of the water volume
Mass of the packet of apple candies 2710.8 ÷ (10 + 5 + 4) x 10 ÷ 1000 = 1.43 kg In every minute, tank X receives 8l more than tank Y 54 – 22 = 32 Time taken so that tank X is 32l more than tank Y 32 ÷ 8 = 4 minutes Rate of water flowing in tank Y 22 ÷ 4 + 56.5 = 62 After 1 hour, the volume of water in tank Y is (62 – 56.5) x 60 = 330l The remainder before Tom bought the computer: (846 + 27) x 2 = 1746 The remainder before Tom paid his bills:
− 12 = 13
9
Area ABC = 22 x 16 ÷ 2 = 176 cm2 Area BCD = 22 x 7 ÷ 2 = 77 cm2 Area ACD = 176 – 77 = 99 cm2 2 boxes of candies and 3 boxes of cookies is 5 x 3.84 = 19.2 kg Therefore 4 boxes of candies and 6 boxes of cookies is 19.2 x 2 = 38.4 kg 3 boxes of candies and 2 boxes of cookies is 5 x 3.7 = 18.5 kg Therefore 9 boxes of candies and 6 boxes of cookies is 18.5 x 3 = 55.5 kg So 5 boxes of candies is 55.5 – 38.4 = 17.1 kg 1 boxes of candies is 17.1 ÷ 5 = 3.42 kg 1 boxes of cookies is (19.2 – 2 x 3.42) ÷ 3 = 4.12 kg The total mass of 2 boxes of candies and 1 box of cookies is 2 x 3.42 + 4.12 = 10.96 kg Number of plastic pieces 64 x 2 = 128 Number of chairs (128 + 64) ÷ 8 x 5 = 120 Number of tables 120 ÷ 5 x 3 = 72 Number of plastic chairs 120 – 32 = 88 Number of plastic tables 128 – 88 = 40 Number of wooden tables 72 – 40 = 32 Ratio of the number of plastic chairs to that of wooden tables 88 : 32 = 11 : 4 Fraction of the magazine: read on Saturday (1- 15 )x
(1 12 + 1 23 ) ÷ 2 = 1 127 ≈ 1.58m
read on Sunday
The average height of the two children is 1.58m.
1 5
x2=
1 4
= 15
2 5
Fraction of the magazine that was not read 1- 15 - 15 10
Cost of the LCD 900 ÷ (9/4) = 400 Average cost (400 + 900) ÷ 2 = 650 The average cost of the two devices is $650.
11
12
Indian : Chinese = 2 : 7 = 8 : 28 Malay : Chinese = 3 : 4 = 21 : 28 Indian : Malay : Chinese = 8 : 21 : 28
13
152
2 5
= 15
A pair of jeans cost $5 more than a pair of shirts. Therefore, if Ken bought 2 pairs of jeans instead of 2 shirts, he would have to pay 5 x 2 = 10 more The cost of 1 pairs of jeans (90 + 10) ÷ 5 = 20 A pair of jeans costs $20. 172000 x 0.68% = 1169.6 Interest that Bill would earn after a year is $1169.60
14
16 17 18
After giving money, the total would not change. Amount that Margaret had in the end 630 ÷ (8 + 1) = 70 Amount that Margaret had at first 70 + 52.70 = 122.70 Amount that Soo Hui had at first 630 – 122.70 = 507.30 507.30 – 122.70 = 384.60 The difference is $384.60 3290 x 80% = 2632 2632 x 107% = 2816.24 Mr. Tay paid $2816.24 for the furniture. 263790
15
Value of one equal part (400 + 30) ÷ 8 = 53.75l The initial volume of water in tank B was 53.75l
128 ÷ 2 = 64, 64 ÷ 2 = 32, 32 ÷ 2 = 16, 16 ÷ 2 = 8, 8 ÷ 2 = 4, 4 ÷ 2 = 2, 2 ÷ 2 = 1, 1 ÷ 2 = 0.5 It took 8 times 12 minutes for the bacteria to reach 128 mg. Time taken is 12 x 8 = 96 minutes. So the starting time was 5 hours – 96 minutes = 3 hours 24 minutes. The starting time was 3:24 pm. Answers to Semestral Assessment 2: Mock Paper 1
Paper 1 Q1 Q2 3 2
Q3 1
Q4 1
Q5 4
Q6 1
Q7 2
Q8 3
Q9 2
Q10 4
Q11 1
Q12 1
Q13 1
Q14 4
16
3256 = 19 x 191 + 7 The remainder is 7
17
680 795
18
23 3 16 − 52 = 2 30
19
261
20 22
1l 25 ml = 1025 cm3
23
63.08l = 63 080 ml
25
5 : 9 = 35 : 63 => Y = 35 7 : 35 = 1 : 5 => X = 1 100% - 75% = 25% , 25% x 40% = 10%
21
5 6
× (1 − 13 ) = 59
The volume of milk left in the bottle is 24 26
5 9
l
2 x 3.65 + 3 x 5.99 = 25.27 Uncle Tiong spent $25.27 If each pupil gets 7 pens, there will be 3 pens extra. To give each pupil 8 pens, the 3 extra pens can be given to 3 pupils. There are 4 pens short. So the number of pupil is 4 + 3 = 7 Number of pens 7 x 7 + 3 = 52 a) There are 7 pupils b) There are 52 pens.
27
Q15 4
x = 5 ÷ 23 × 4 = 30
100% - 75% - 10% = 15% , 15%=
3 20
Total number of candies 20 ÷ 10% = 200 Number of chocolate candies: 200 x 75% = 150 Number of strawberry candies: 200 x 15% = 30 a) The number of strawberry flavored candies is
28
Percentage of the breadth to half-perimeter 15% x 2 = 30% Percentage of the length to half-perimeter 100% - 30% = 70% Ratio of breadth to length is 3 : 7 The breadth is 760 ÷ (7 – 3) x 3 = 570 cm = 5.7m The length is 760 + 570 = 1330 cm = 13.3m Area = 5.70 x 13.30 = 75.81 m2 570 ÷ 30 = 19 1330 ÷ 30 =44.33 The maximum number of cartons that can be stored is 19 x 44 = 836 cartons
30
Number of Peter’s books:
29
32 ÷ 23 = 48
Number of Fahan’s books: 48 ÷ 2 = 24 Total number of books: 48 + 24 + 32 = 104.
153
of the total. b) 150 – 30 = 120 There are 120 more chocolate candies than strawberry candies. In January Charges for first 40 units: 1.17 x 40 = 46.80 Charges for the remaining units 1.40 x (56 – 40) = 22.40 Total bill: 46.80 + 22.40 = 69.20 In February Charges for the units above the first 40 units: 135 – 46.80 = 88.20 Number of units above the first 40 units: 88.20 ÷ 1.40 = 63 Total consumption in February 40 + 63 = 103 Average consumption: (56 + 40 + 63) ÷ 2 = 79.5 Average bill (69.20 + 135) ÷ 2 = 102.1 a) 103 units b) 79.5 units c) $102.10
3 20
Paper 2 1 Four other pupils each can have a maximum score of 50 marks. Highest possible average is (50 + 50 + 50 + 50 + 15) ÷ 5 = 43 marks. 3 Mary : Andy = 0.4 : 1 , Mary : Bob = 1 : 2 Mary : Andy : Bob = 2 : 5 : 4 660 ÷ (2 + 5 + 4) x 5 = 300, Andy donated $300. 5 12 ÷ 30% = 40 He had 40 stamps at first. 7 Number of males: 2500 – 1100 = 1400 1400 ÷ 1100 x 100% = 127.27% There are 27.27% more males than females. 9 The largest possible difference is when the number of adults is largest and the number of children is smallest. The largest possible number of adults is 3349. The smallest possible number of children is 1651. The largest difference is 3349 – 1651 = 1698 11
2
4 6 8 10
Height of triangle D is the width of the rectangle, so it is 6 cm. The base of triangle D is 30 x 2 ÷ 6 = 10 cm Triangles A and D have the same height. Therefore the base of triangle A is 10 x 3 ÷ 5 = 6 cm Triangles A and B also have the same height. So the base of triangle B is 6 x 3 = 18 cm The length of the rectangle is 18 + 10 = 28 cm The perimeter of the rectangle is (28 + 6) x 2 = 68 cm
Number of students remained 36 – 9 = 27 Number of extra lollipops 27 x 3 = 81 Ratio of the number of student left to the total number of students 9 : 36 = 1 : 4 Number of lollipops 81 x 4 = 324 Miss Chua bought 324 lollipops.
13
AC = 9 cm BC = 12 cm Side of the small square inside: 12 – 9 = 3 cm Area of triangle ABC 9 x 12 ÷ 2 = 54 cm2 Area of the small square 3 x 3 = 9 cm2 Area of the square MNPQ 54 x 4 + 9 = 225 cm2
15
Ratio of story books to comic books is 1.5 : 1 = 3 : 2 Ratio of story books sold to comic books sold
16
(3 x
2 3
) : (2 x 1) = 2 : 2 = 1 : 1
Ratio of money received from selling story books to comic books (1 x 12) : (1 x 8) = 12 : 8 = 3 : 2 Money received from selling story books 6400 ÷ (3 + 2) x 3 = 3840 Money the shop would received from selling the remaining
From the figure,
3 5
of Joey’s marbles is
1 3
of the story books
3840 ÷ 2 = 1920 Money the shop would receive at the end 6400 + 1920 = 8320 When all the books were sold, the shop would receive $8320.
(45 + 6 + 3) ÷ 2 = 27 Lucy had $27 at first. 17
7 + 16 + 5 = 28 , 5 + 9 + 28 = 42 28 ÷ 42 x100% = 66.67% 2 : 4 : 5 = 6 : 12 : 15 Total number of questions done is 6 + 12 + 15 = 33 Triangle SQR and triangle PQR have the same base QR and their heights are in the ratio of 1 : 4. Therefore there areas are also in the ratio of 1 : 4. Therefore the ratio of the shaded area to that of triangle PQR is 3 : 4 Area of triangle PQR is 54 ÷ 3 x 4 = 72 cm2
12
From the figure, the unshaded area of Square B is 27 x 2 ÷ (5 – 3) = 27 cm2+ Area of the square is 27 + 27 = 54 cm2 The area of the square is 54 cm2 14
George folded 100% - 35% = 65% of the birds. The difference between them is 65% -35% = 30% of the birds. Total number of birds: 90 ÷ 30% = 300. George folded 300 x 65% = 195 birds. ABD = (180° - 116°) ÷ 2 = 32° ABE = 180° - 32° = 148°
2 7
that of Thomas.
Ratio between Joey’s marbles and Thomas’s marbles is 10 : 21 Ratio between Joey’s marbles to the difference between them is 10 : 11 Ratio between Joey’s marbles to Ben’s marbles is 10 : 22 = 5 : 11 Joey’s marbles is 48 ÷ (11 – 5) x 5 = 40 Thomas’s marbles is 40 / 10 x 21 = 84 Ben’s marbles is 40 ÷ 5 x 11 = 88 , 84 + 40 + 88 = 212. They have 212 marbles altogether. 18
Volume of tank A 4 x 6 x 1 = 24 m3 , Volume of tank B 5 x 3 x 2 = 30 m3 The volume of water in each tank is 4 x 6 x 0.5 = 12 m3. The height of water in tank B is 12 ÷ (5 x 3) = 0.8 m
154
Answers to Semestral Assessment 2: Mock Paper 2 Paper 1 Q1 Q2 2 1 16 18
Q3 4
Q4 1
1 2
1 2
26 28
Q7 2
Q8 2
Q9 2 17
of a square, so each triangle is
× 19 = 181 of the figure
So the fraction shaded is
24
Q6 1
9 : (5 + 9) = 9 : 14 The ratio is 9 : 14 Number of squares: 3 x 3 = 9 Each triangle is
22
Q5 3
19 20 21
1 18
×4 =
2 9
2100 x 107% = 2247 The price is $2247 1053 ÷ (5 + 8) x 5 = 405 Kavitha’s saving is $405
Q11 1
Q12 2
Q13 4
Q14 2
Q15 4
12.42 + 2.07 = 14.49 The volume of juice drink is 14.49 l 0.064 1 12
3 years ago Mohammed was 15 – 3 = 12 years old. His brother’s age was
of the figure.
i.e. 22.22% of the figure is shaded 2009 is a normal year so there are 365 days. There are 30 days in September. 30 ÷ 365 x 100% = 8.22% 26
Q10 1
12 ÷ 23 = 18
His brother’s age now is 18 + 3 = 21 years old. 23
105 51 0.051, 1000 ,0.501, 100
25
16 25
27 29
1.25 + 2.125 + 0.786 = 4.161 ≈ 4.16 The total volume is 4.16 Volume of the pool 20 x 10 x 1.5 = 300 m2 Volume of water to be filled 300 ÷ 2 = 150 m2 Total volume of water that can be filled in a minute 0.375 x 4 = 1.5 m3 Total time required 150 ÷ 1.5 = 100 minutes
30
8.5 – 5 = 3.5 An adult ticket cost 3.5 more than a child ticket. 126 ÷ 2 = 63 If there were 126 more child tickets sold, the cinema would received 2907 + 126 x 5 = 3537 By then there would be an equal amount of adult and child ticket. Ratio of the money received from selling adult tickets to child tickets would be 8.5 : 5 Amount received from selling adult tickets 3537 ÷ (8.5 + 5) x 8.5 = 2227 Number of adult tickets 2227 ÷ 8.5 = 262. There were 262 adults. Paper 2 1 Total money saved by all children: 604 x 10 = 6040 2 Number of Indian pupils 1200 x 20% = 240 Total money saved by the boys 592 x 2 = 1184 Percentage of Chinese pupils (100% - 20%) x 65% = Total money saved by the girls 6040 – 1184 = 4856 52% Average of savings of the girls 4856 ÷ 8 = 607 Number of Chinese pupils 1200 x 52% = 624 On average, each girl saved $607. Percentage of Malay pupils 100% - 20% - 52% = 28% a) 624 Chinese pupils b) 28% of the pupils are Malay. 4 3 Fraction of the balloons sold on the last two days:
1 − 15 =
4 5
Fraction of the balloons sold on the last day 4 5
÷ 5× 3 =
12 25
Fraction of the balloons sold on the second day 4 5
÷ 5× 2 =
2u + 2v = 858 => 6u + 6v = 2574 5v – 3u = 225 => 10v – 6u = 450 => 16v = 3024 => v = 189 Number of tulips 189 x 5 = 945 Number of roses 945 – 225 = 720 945 + 720 = 1665 There were 1665 flowers at first.
8 25
Ratio of the number of balloons sold on the first day to the second day to the last day 5 : 8 : 12 Number of balloons sold on the last day 92 ÷ (12 – 8) x 12 = 276 Number of balloons sold on the second day 276 – 92 = 184 Number of balloons sold on the first day 184 ÷ 8 x 5 = 115 Total number of balloons 115 + 184 + 276 = 575 Money received 575 x 1.2 = 690 Mr Chan earned $690 in total.
155
5
7
AFD = FGD = 80° ADE = (180° - AFD) ÷ 2 = 50° EDC = 90° - 50° = 40° DAE = ADE = 50°
6
There are 4 spaces between the third tree and the seventh tree. Distance between any two trees 7920 ÷ 4 = 1980 cm = 19.8 m Distance from the 15th tree to the first tree: 19.8 x 14 = 277.2 m
8
3 8
x4500g=1687.5g=1.6875 kg
48%x18 kg=8.64 kg Total mass 1.6875 + 8.64 = 10.3275 ≈10.33 kg Distance travelled when the ball hit the ground the first time: 15m Distance bounced up 15x 45 =12 m
9
10
11
Distance travelled to hit the ground the second time: 12 m Total distance: 15 + 12 + 12 = 39 m If all trucks were small trucks, the number of wheels would be 10 x 32 = 320 Number of wheels extra 408 – 320 = 88 Number of large trucks 88 ÷ (14 – 10) = 22 There are 22 large trucks. Francis’s money before he gave to his sister (443+53)
Age of the last child (193 – 3 – 3 x 2 – 3 x 3) ÷ 7 = 25 Age of the first child 25 + 9 = 34 The first child is 34 years old. 12
The ratio of the mass of an elephant to that of a zebra is 5.5 : 1 The ratio of the mass of 2 elephants to that of 3 zebras is 5.5 x 2 : 1 x 3 = 11 : 3 Mass of 2 elephants 1260 ÷ (11 + 3) x 11 = 990 Mass of an elephant 990 ÷ 2 = 495 Mass of a zebra 495 ÷ 5.5 = 90 Mass of an elephant and 4 zebras 495 + 4 x 90 = 855 The total mass of one elephant and 4 zebras is 855 kg.
14
13
15
16 (1459 + 296) ÷ (4 + 4 + 1) = 195 Kathy raised $195 17
Perimeter of the rectangle (75 + 33) x 2 = 216 cm That is also the total perimeter of the two triangles. The base of each triangle is (216 – 39 x 4) ÷ 2 = 30 cm The area of one triangle is 36 x 30 ÷ 2 = 540 cm2
18
÷ 52 =1240
Francis’s money before he bought the book 1240 + 61 = 1301 Francis’s money before he bought the furniture (1301 + 49) ÷ 75% = 1800 Francis’s salary (1800 + 100) x 2 = 3800 Francis’s salary is $3800. Total money earned from January to August 2 340 x 8 = 18 720 Total money earned for the year 3 290 x 12 = 39 480 Total money earned from September to December 39 480 – 18 720 = 20 760 Average earning during that period 20 760 ÷ 4 = 5 190 Number of roses 954 ÷ (9 – 3) x 3 = 477 Number of lilies 477 ÷ 3 x 5 = 795 795 – 477 = 318 There were 318 more lilies than roses. The total number of pages in 1 book of each type 10 000 ÷ 20 = 500 pages The number of pages in a Physics book (500 – 20 – (20 + 70)) ÷ 3 = 130 There are 130 pages in a Physics book Derek’s money after buying stationeries 150 + 246 = 396 Fraction of Derek’s money that he spent on toys on stationary The amount of money that Derek had: The amount of money that Josh had 720 ÷ 5 x 3 = 432. Josh had $432.
156
Answers to Semestral Assessment 2: Mock Paper 3 Paper 1 Q1 Q2 1 1 16 18
Q3 2
Q4 2
Q5 2
Q6 2
Q7 1
Q8 1
48% 6 ÷ 4 x 24 = 36 Two dozen cans cost $36
20
M
A
B
H
I
D
N
21
390 ÷ 12 = 32.5 33 pencil cases are needed.
22
1 − 157 = 158 ,
1 2
23
C
24 25
MBJH =
26 1 2
IHND =
1 4
AMND
1 4
29
30
72 ÷ 36% = 200 ml The bottle is 200 ml 4750 g = 4.75 kg 42.5 + 4.75 = 47.25 The scale indicates 47.25 kg 1
2 5
km = 1.4 km = 1400 m,
28
3 4
km = 0.75 km = 750 m,
2
3
Price at which Mrs. Choo bought the grapes 3.20 – 0.70 = 2.50 per 100 g Amount that Mrs. Ong paid 2000 ÷ 100 x 3.20 = 64 Amount of grapes that Mrs. Choo bought 64 x 100 ÷ 2.50 ÷ 1000 = 2.56, 2.56 – 2 = 0.56 Mrs. Choo bought 0.56 kg more than Mrs. Ong. Total distance of the first 3 attempts 155 x 3 = 465 cm Total distance of all attempts 145 x 5 = 725 cm Total distance of the last 2 attempts 725 – 465 = 260 cm Average distance of the last 2 attempts = 130 cm Fraction of the milk that Guo Qi drank on the next 2 days
4
(1- 15 )x75%= 35
9
7
3 5
Q14 1
Q15 3
: 157 = 8 : 7
At some times later, the difference in ages will still remain the same Raphael’s age then 38 ÷ (3 – 1) = 19 The number of years is 19 – 10 = 9 After 10 years, Raphael’s father‘s age will be three times his age. 500 ÷ 40 = 12.5 600 ÷ 40 = 15 300 ÷ 40 = 7.5 The maximum number of boxes that can be stored is 12 x 15 x 7 = 1260 boxes Antoine had walked 650 m
Area IBK = (25 – 18) x (25 – 2) ÷ 2 = 80.5 cm2 Remaining area = 25 x 25 – 2 x 80.5 = 464 cm2 1=1x1 4=2x2 9=3x3 25 = 5 x 5 So the missing value is 16, since 16 = 4 x 4
6
NMQ = 180° - 29° x 2 = 122° QNP = MNQ = 29° ONP = 180° - 29° = 151° NOP = (180° - 151°) ÷ 2 = 14.5°
8
1.4 ÷ (2 + 5) x 2 = 0.4 l = 400 ml The volume of syrup needed is 400 ml Number of toothpicks needed to make n shapes is 6 + 4(n – 1) To make 5 shapes, the number of toothpicks needed is 6 + 4(5 – 1) = 22 Using 258 toothpicks 6 + 4 (n – 1) = 258 n = 64 64 shapes can be made.
Fraction of the remaining milk 1- 15 -
8 15
Q13 2
Number of $5 notes 45 ÷ (1 + 1.5) = 18 Number of $2 notes 18 x 1.5 = 27 Total amount of money 27 x 2 + 18 x 5 = 144 Brian has $144 18 = 2 x 3 x 3 45 = 3 x 3 x 5 The common factors are 3, 9 55 x 18 = 990 Kiara’s school is 990m from her home.
1400 – 750 = 650,
Paper 2 1 60 x 25 x 30 = 45000, 45000 cm3 = 45 l 45 ÷ 3 = 15, Uncle Tiong has to fill 15 times.
5
Q12 3
480 cm2 x = 162° ÷ 2 = 81°
Ratio of the total shaded area to the area of ABCD is
27
Q11 3
17 19
J
MBCN
The shaded area on the left =
Q10 1
The ratio is 8 : 7
The shaded area on the right = 1 4
Q9 4
= 15
Volume of the carton
750 ÷ 15 = 3750ml = 3.75l
157
10
952 ÷ (0.4 + 1) = 680 The number of stickers that Zoe had is 680
11 13
12
Number of black pepper chickens 90 ÷ 5 x 2 = 36 Number of honey roasted chickens 36 x 3 = 108 a) 108 honey roasted chickens were sold. b) 36 black pepper chickens were sold. 14
16
Area of 2, 3, 4 and 5 is 1 unit Area of 1 is 4 x 4 = 16 units Area of 1 and 2 is 16 + 1 = 17 units The ratio is 17 : (16 + 4) = 17 : 20 Fraction of the pupils who like chess 1 3
(1- )x
1 4
=
15
17
1 6
Total number of pupils
10 ÷ 16 = 60
Number of pupils who like basketball 60x 13 =20 Number of pupils who like either chess or basketball 20 + 10 = 30 pupils 18
Total mass 44 x 3 = 132 kg Chek Khoon’s mass is (132 + 4) ÷ (5 + 6 + 6) x 6 = 48 kg If Andy only bought 3 comic books and 3 story books, he would save 18 x 2 = 36 Amount left after buying 3 comic books and 3 story books 36 + 24 = 60 With this $60, if he buys 2 more story books, he will need $16 more. Therefore, cost of a comic book is (60 – 16) ÷ 2 = 38 Amount of money that Andy had 3 x 38 + 5 x 18 + 24 = 228 Andy has $228 Amount received from selling plastic tables 75 x 150 = 11250 Number of wooden tables (12850 – 11250) ÷ 80 = 20 20 wooden tables were sold. Ratio of the amount paid for safe delivery to amount received for broken products 9 x 16.5 : 1 x 66 = 9 : 4 Amount received for broken products 15015 ÷ (9 – 4) x 4 = 12012 Number of broken products 12012 ÷ 66 = 182 There were 182 products broken on the way.
149 – 53 = 96 Each day Ryan ate 8 more cookies than Mindy. Number of days taken to eat 96 more cookies: 96 ÷ 8 = 12 Number of cookies each of them had at first 149 + 23 x 12 = 425 a) 12 days b) 425 cookies. Answers to Semestral Assessment 2: Mock Paper 4
Paper 1 Q1 Q2 4 3
Q3 4
Q4 3
Q5 2
Q6 2
Q7 3
Q8 2
Q9 1
Q10 3
Q11 2
Q12 1
16
Goldfish : clownfish = 2 : 7 = 10 : 35 Clownfish : angelfish = 5 : 2 = 35 : 14 Goldfish : angelfish = 10 : 14 = 5 : 7
17
18
1 12 + 1 56 = 3 13
19
11 ÷ 1.20 = 9.17 At most, 9 pens can be bought
There was 3 13 l of milk in the fridge at first
Q13 2
Q14 2
Q15 1
1 6
20 22
i = 154° - 87° = 67° A=9–1–1–1=6
21
A + B = 80 x 2 = 160 , A + B + C = 85 x 3 = 255 C = 255 – 160 = 35
23
24
25
(72 + 83 + 67) ÷ 3 = 74 Benjamin’s average mark is 7 5 839 x 7 = 40 873
27
12.8 – 0.91 x 5 – 1.32 x 3 = 4.29 km
28
24 = 2 x 2 x 2 x 3, 36 = 2 x 2 x 3 x 3 The common factors are 2, 4, 6, 12 Area of one face 54 ÷ 6 = 9 cm2 Since 9 = 3 x 3, the sides of the cube are 3 cm. Volume of the cube 3 x 3 x 3 = 27 cm3 ABC = 180° - 93° - 43° = 44° ABD = 44° - 37° = 7°
Percentage of adults 100% - 30% = 70% 29 Number of adults 10 200 x 70% = 7140 Number of adults working outside 7140 x 40% = 2856 There are 2856 adults working outside the village. The price of 2 shirts is equal to the price of 3 skirts. Therefore the price of 4 shirts is equal to the price of 6 shirts. The price of 4 shirts 162 ÷ 2 = 81. The price of a shirt 81 ÷ 4 = 20.25. A shirt costs $20.25
30
26
158
Paper 2 1
4
6
8
10
2
Amount left after spending 1144 ÷ 2 x 3 = 1716 Amount withdrawn 1716 x 2 = 3432 Area of unshaded triangle at the bottom left 20 x (20 + 36) ÷ 2 = 560 cm2 Area of the unshaded triangle at the top right 36 x 36 ÷ 2 = 648 cm2 Total area 20 x 20 + 36 x 36 = 1696 cm2 Area of the shaded part 1696 – 560 – 648 = 488 cm2 Number of red roses 24 ÷ 3 x 5 = 40 Number of white roses 24 ÷ 3 x 2 = 16 Total number of flowers (40 + 16) ÷ (1 – 0.2) = 70 Number of daisies 70 x 0.2 = 14 Cost of the fish 3300 ÷ 100 x 1.59 = 52.47 Cost of the beef 2800 ÷ 500 x 4.89 = 27.38 Cost of the vegetable 0.86 x 7 = 6.02 Total cost 52.47 + 27.38 + 6.02 = 85.87 Mrs. Foo paid $85.87 The number of pens at first was 280 x 70% = 196 Number of other pens 280 – 196 = 84 After selling some blue pens, the number of other pens was 40% total. Total number of pens in the end 84 ÷ 40% = 210 Number of blue pens sold 280 – 210 = 70
3 5
7
9
11
14
12
5 bags weigh 86.25 Kg. 1 bag weighs 17.25 Kg. Each porter can lift Maximum of 60/17.25 =3.47 that is 3 bags. For lifting 20 bags we need 20/3=6.666 That is 7 porters. 3.115 ÷ 14 x 100% = 22.25% Total number of stamps 168 ÷ 7 x (3 + 7 + 9) = 456 Number of Charlie’s stamp 168 ÷ 7 x 3 = 72 Number of stamps that Mark gave Charlie (168 – 72) ÷ 2 = 48 CED = 42° - 31° = 11° FCB = 180° - 42°= 138° ACF = 138° - 60° = 78° Ratio of the amount the shop received from selling curry puffs to that from selling cakes 1 x 2 : 4 x 5 = 1 : 10 Amount from selling cakes 1892 ÷ (10 + 1) x 10 = 1720 Number of cakes 1720 ÷ 5 = 344 There are 344 cakes. A textbook and a bag cost $30. A textbook and a comic book cost $22.5. 2 textbooks and a bag and a comic book cost 30 + 22.5 = 52.5 4 textbooks, 2 bags and 1 comic book for $100 2 textbooks and 1 bag cost 100 – 52.5 = 47.5 Cost of 1 text book 47.5 – 30 = 17.5 Cost of 1 comic book 22.5 – 17.5 = 5 A comic book cost $5 Fraction of apples: 2/5 Fraction of oranges: (1- 52 )x
4 5
= 12 25
Fraction of mangoes:
13 15
16
18
Ratio of the number of apples to that of oranges to that of mangoes 10 : 12 : 3 Total number of fruits 648 ÷ (12 – 10) x (10 + 12 + 3) = 8100 Number of apples
Earning from sales 72 000 ÷ 5 x 1.2 = 17280 Average earning from sale a month 17 280 ÷ 8 = 2160 Average earning a month 2160 + 1575 = 3735 Initial water volume 60 x 43 x 24 x
17
3 1 − 25 − 12 25 = 25
24 ÷ 12 x 5 = 60 Marion had 60 beads at first. 350 ÷ 4000 x 100% = 8.75%
1 3
= 20 640 cm3 = 20.64 l
After 20 minutes, volume of water flowed into the tank is 1.8 x 20 = 36 l Total volume of water in the tank 20.64 + 36 = 56.64 l Total area: 21 squares Shaded area: 6 squares Ratio: 6 : 21 = 2 : 7 3N -
2 3
8100 x
2 5
= 3240
8100 x
3 25
= 972
Total of oranges and mangoes 8100 – 3240 = 4860 After some apples have been sold, the total of oranges and mangoes is 90% of the total fruits. Number of fruits at the end 4860 ÷ 90% = 5400 Number of apples sold 8100 – 5400 = 2700 2700 apples have been sold.
N = N + 36
N = 27 The number is 27.
159
Answers to Semestral Assessment 2: Mock Paper 5 Paper 1 Q1 Q2 3 2 16
1- 13 =
Q3 1
2 3
,
2 3
22 23 24 25
Q5 1
Q6 1
Q7 3
Q8 4
÷ 6 = 19
Each friend got 20
Q4 1
1 9
Q9 2 17
of the chocolates.
Volume of container 1: 20 x 15 x 10 = 3000 cm3 Volume of container 2: 15 x 7 x 5 = 525 cm3 Total volume 3000 + 525 = 3525 cm3 95
Q10 1
Q14 1
18 19
20.08 l = 20 l 80 ml
21
Q15 2
A
1 13 x 60 x 60 = 4800
C
18 : 22 = 63 : 77 28 : 63 = 8 : 18 Therefore 8 : 18 : 22 = 28 : 63 : 77
28
0.1N =
2 5
N– 33
N = 110 The number is 110
27
Ticket price for the 9-year-old daughter: $600. Ticket price for each of other family members: $1200 Total ticket cost 600 + 1200 x 3 = 4200 The family paid $4200 altogether. 29 144 = 12 x 12 The side of each square is 12 cm The perimeter of the large rectangle is (12 x 3 + 12) x 2 = 96 cm Therefore 1 hour and 15 minutes have passed. The time then will be 10.15 am.
30 450° = 360° + 90° Paper 2 1 30 000 x 3.75% = 1125 Swee Swee will receive $1125 of interest after a year
5
Q13 2
36 = 2 x 2 x 3 x 3, 48 = 2 x 2 x 2 x 2 x 3 The smallest common factor is 2 x 2 x 2 x 2 x 3 x 3 = 144 246.11
26
4
Q12 3
150 x (1 + 0.07 + 0.1) = 175.5 Mr. Smith had to pay $175.50 99 + 108 + 117 + 126 + 135 + 144 + 153 = 882
There are 4800 seconds.
3
Q11 1
2
M
There are 3 options for the appetizer, 3 options for main course, and 3 options for dessert. Total number of options is 3 x 3 x 3 = 27 9×0+9×1+...+9×6+9×7 8
4 5
=
. B
( 9×72×8 ) = 31.5 8
− 107 = 101
A
0.1 kg of meat has not been cooked. 6
9 10
Total volume: 6 + 9 = 15 l Volume of a container 12 x 7 x 5 = 420 cm3 = 0.42 l 15 ÷ 0.42 = 35.71 35 containers could be filled completely. Volume of drink left over: 15 – 35 x 0.42 = 0.3 l Total time 3.2 x 8 = 25.6 minutes = 25 minutes 36 seconds. Number of roses 400 x
5 8
7 8
x = 180° - 78° - 33° = 69° Length of the rectangle 6.5 + 17.5 = 24 cm Breadth of the rectangle 24 x
3 4
= 18 cm
Area of the shaded part (17.5 x 18) ÷ 2 = 157.5 cm2 11
= 250
Number of other flowers 400 – 250 = 150 Total number of flowers after selling
150 ÷ (1 − 53 ) = 375 Number of roses sold 400 – 375 = 25 25 roses were sold
160
16 = 4 x 4, 49 = 7 x 7 The side of the smaller square is 4 cm and that of the larger square is 7 cm. Total area 16 + 49 = 65 cm2 Area of the large triangle at the bottom (4 + 7) x 7 ÷ 2 = 38.5 cm2 Area of the triangle on top of the smaller square 4 x 4 ÷ 2 = 8 cm2 Area of the triangle on top of the larger square (7 – 4) x 7 ÷ 2 = 10.5 cm2 Area of the shaded part 65 – 38.5 – 8 – 10.5 = 8 cm2
12 14
13
x + y + z = 142° z = (142° - 12°) ÷ 2 = 65° a) Number of goals scored on the last match 7 + 2 x 6 = 19 Total number of goals 7 + 9 + … + 17 + 19 =
(19+7 ) x 7 2
138 x 3 = 414 minutes =
6 109 − 2 12 = 4 52 hours
= 91
Time spent on Wednesday
Nelson’s sister’s height 1.52 – 0.2 = 1.32 m 1.32 ÷ 1.52 =
6 109 hours
Total time spent on Tuesday and Wednesday
b) Average number of goals per match 91 ÷ 7 = 13 15
Total time spent
16
33 38
17
The price of the table 300 ÷ 4 x 2 = 150 The price of the table is $150
18
Number of digits to write from 1 to 9: 9 x 1 = 9 Number of digits to write from 10 to 99: 90 x 2 = 180 Number of digits to write 100: 3 Total number of digits: 9 + 180 + 3 = 192 Peter wrote 192 digits.
161
4 52 ÷ 3 × 2 = 2 14 15 hours
The first team has to play 9 matches again 9 other teams. The second team already played one match with the first team, so it has to play 8 matches more with 8 remaining teams. Similar reasoning can be applied for the other teams. Total number of matches : 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 +1 =45 There are 45 matches altogether.
