Modul Topikal Kbat Matematik Tingkatan 1 (Bi) Latest

MODUL TOPIKAL KEMAHIRAN BERFIKIR ARAS TINGGI

Koleksi Soalan-Soalan Trends in International Mathematics and Science Study (TIMSS) dan Programme for International Students Assessment (PISA) dalam Pengajaran dan Pembelajaran

MATEMATIK TINGKATAN 1 (VERSI BAHASA INGGERIS)

KE ARAH KEMAHIRAN BERFIKIR

MEMBUDAYAKAN ARAS TINGGI

Sektor Pengurusan Akademik Jabatan Pendidikan Negeri Johor

2016

CONTENTS Chapt er

1

2

3

4

Title

Whole Numbers

Number Pattern And Sequence

Fraction

Decimal

Code

Question

Page

1

Memory Stick (Q1)

5

2

MP3 Player (Q2)

6

3

Holiday Apartment (Q1)

7

4

Bicycles (Q1, Q2)

8

5

Cubes

9

6

Staircase

9

7

Climbing Mountain Fuji Q1

10

8

Revolving Door Q3

10

9

Skateboard Q1 , Q3

11

1

Lighthouse Q1, Q3

12

2

Apples Q1

14

3

Step Pattern

15

4

Charts Q3

15

5

Making A Booklet

16

1

Lighthouse Q2

1

Postal Charges (S2)

2

DVD Rental (Q1, Q2)

3

Selling Newspapers (Q1)

4

Exchange Rate Q1 - Q3

5

Reaction Time Q1 - Q2

17

2

18 19 20 21 22

Date / Notes

Chapt er

5

Title

Percentage

Code 1

Coloured Candies (Q1)

2

MP3 Players (Q3)

3

Penguins (Q1)

4

Payable Television (Q1)

5

Coins

6

Drug Concentrations Q1 - Q3

7

8

Basic Measureme nt

Question

Decreasing C

Page 24 25 26 27 28

Level (Q1-

29 31

Q3) 32

8

Which Car? Q3

1

Climbing Mountain Fuji (Q2, Q3)

2

Helen The Cyclist Q1

3

Internet Relay Chats

33 34 35

9

Lines & Angle

1

Revolving Door Q1

10

Polygons

2

Triangles

37

1

Ice Cream Shop

38

2

Oil Spill (Q1)

40

3

Farms Q1

41

4

Continent Area

42

5

Shapes

43

6

Carpenter Q1 (A,C dan D)

44

7

Patio

8

Rock Concert

11

Perimeter And Area

36

45 45

3

Date / Notes

9

12

Solid Geometry

Apartment Purchase

10

Power of the Wind (Q4)

1

Building Blocks Q1 - Q4

46 47 48 50

Answers

CHAPTER 1: WHOLE NUMBER

4

QUESTION 1

MEMORY STICKS

A memory stick is a small, portable computer storage device. Ivan has a memory stick that stores music and photos. The memory stick has a capacity of 1 GB (1000 MB). The graph below shows the current disk status of his memory stick.

Translation Note: Please translate “memory stick” with the commonly used term in your language, for example, “USB key”. Ivan wants to transfer a photo album of 350 MB onto his memory stick, but there is not enough free space on the memory stick. While he does not want to delete any existing photos, he is happy to delete up to two music albums. Ivan’s memory stick has the following size music albums stored on it. Album

Size

Album 1

100 MB

Album 2

75 MB

Album 3

80 MB

Album 4

55 MB

Album 5

60 MB

Album 6

80 MB

Album 7

75 MB

Album 8

125 MB

By deleting at most two music albums is it possible for Ivan to have enough space on his memory stick to add the photo album? Circle “Yes” or “No” and show calculations to support your answer. Answer: Yes / No

QUESTION 2

MP3 PLAYERS

5

Olivia added the prices for the MP3 player, the headphones and the speakers on her calculator. The answer she got was 248.

Olivia’s answer is incorrect. She made one of the following errors. Which error did she make? •

She added one of the prices in twice.

• • •

She forgot to include one of the three prices. She left off the last digit in one of the prices. She subtracted one of the prices instead of adding it.

QUESTION 3

HOLIDAY APARTMENT

Christina finds this holiday apartment for sale on the internet. She is thinking about 6

buying the holiday apartment so that she can rent it out to holiday guests

If the value estimated by the expert is greater than the advertised selling price, the price is considered to be "very good" for Christina as the potential buyer. Show that based on the expert’s criteria, the selling price on offer is "very good" for Christina. ........................................................................................................................................... .......... ........................................................................................................................................... .......... ........................................................................................................................................... .......... ........................................................................................................................................... .......... ........................................................................................................................................... ..........

7

QUESTION 4

BICYCLES

Justin, Samantha and Peter ride bicycles of different sizes. The following table shows the distance their bicycles travel for each complete turn of the wheels.

Question 4A: Peter pushed his bike for three complete turns of his wheel. If Justin did the same with his bike, how much further would Justin’s bike travel than Peter’s? Give your answer in centimetres.

Answer: .................................................. cm. Question 4B : How many turns of the wheel does it take for Samantha’s bike to travel 1280 cm?

Answer: .................................................. turns.

8

QUESTION 5

CUBES

In this photograph you see six dice, labelled (a) to (f). For all dice there is a rule: The total number of dots on two opposite faces of each die is always seven.

Write in each box the number of dots on the bottom face of the dice corresponding to the photograph.

QUESTION 6

STAIRCASE

The diagram below illustrates a staircase with 14 steps and a total height of 252 cm:

What is the height of each of the 14 steps?

Height: ....................................................cm

QUESTION 7

CLIMBING MOUNT FUJI 9

Mount Fuji is a famous dormant volcano in Japan

Translation Note: Please do not change the names of locations or people in this unit: retain “Mount Fuji”, “Gotemba” and “Toshi”. Mount Fuji is only open to the public for climbing from 1 July to 27 August each year. About 200 000 people climb Mount Fuji during this time. On average, about how many people climb Mount Fuji each day? A 340 B 710 C 3400 D 7100 E 7400

QUESTION 8

REVOLVING DOOR

The door makes 4 complete rotations in a minute. There is room for a maximum of two people in each of the three door sectors. What is the maximum number of people that can enter the building through the door in 30 minutes? A 60 B 180 C 240 D 720

QUESTION 9

SKATEBOARD

Eric is a great skateboard fan. He visits a shop named SKATERS to check some prices. At this shop you can buy a complete board. Or you can buy a deck, a set of 4 10

wheels, a set of 2 trucks and a set of hardware, and assemble your own board. The prices for the shop’s products are:

Question 9A Eric wants to assemble his own skateboard. What is the minimum price and the maximum price in this shop for self-assembled skateboards? (a) Minimum zeds price: ................................. . (b) Maximum price: ................................

zeds .

Question 9B Eric has 120 zeds to spend and wants to buy the most expensive skateboard he can afford. How much money can Eric afford to spend on each of the 4 parts? Put your answer in the table below.

CHAPTER 2: SEQUENCE AND NUMBER PATTERN 11

QUESTION 1

LIGHT HOUSE

Lighthouses are towers with a light beacon on top. Lighthouses assist sea ships in finding their way at night when they are sailing close to the shore. A lighthouse beacon sends out light flashes with a regular fixed pattern. Every lighthouse has its own pattern.

In the diagram below you see the pattern of a certain lighthouse. The light flashes alternate with dark periods.

It is a regular pattern. After some time the pattern repeats itself. The time taken by one complete cycle of a pattern, before it starts to repeat, is called the period. When you find the period of a pattern, it is easy to extend the above diagram for the next seconds or minutes or even hours.

QUESTION 1A Which of the following could be the period of the pattern of flashes of this lighthouse? A 2 conds B 3 seconds C 5 seconds D 12 seconds QUESTION 1B In the diagram below, make a graph of a possible pattern of light flashes of a lighthouse 12

that sends out light flashes for 30 seconds per minute. The period of this pattern must be equal to 6 seconds.

QUESTION 2

APPLES

A farmer plants apple trees in a square pattern. In order to protect the apple trees against 13

the wind he plants conifer trees all around the orchard. Here you see a diagram of this situation where you can see the pattern of apple trees and conifer trees for any number (n) of rows of apple trees:

1. Complete the table :

QUESTION 3

STEP PATTERN

Rahim builds a step pattern using squares. Here are the stages he follows. 14

Diagram shows, he uses one square for Stage 1, three squares for Stage 2 and six for Stage 3. 1. How many squares should he use for the fourth stage? ………………… squares 2. If the stage are extended, calculate the number of squares in stage 10. …………………. squares

QUESTION 4

CHARTS

In January, the new CDs of the bands 4U2Rock and The Kicking Kangaroos were released. In February, the CDs of the bands No One’s Darling and The Metalfolkies followed. The following graph shows the sales of the bands’ CDs from January to June.

The manager of The Kicking Kangaroos is worried because the number of their CDs that sold decreased from February to June. What is the estimate of their sales volume for July if the same negative trend continues? A 70 CDs B 370 CDs C 670 CDs D 1340 CDs

QUESTIONS 5

MAKING A BOOKLET

15

Figure 1 Figure 1 shows how to make a small booklet. The instructions are given below: • Take a piece of paper and fold it twice. • Staple edge a. • Cut open two edges at b. The result is a small booklet with eight pages.

Figure 2 shows one side of a piece of paper that is used to make such a booklet. The page numbers have been put on the paper in advance. The thick line indicates where the paper will be cut after folding. Write the numbers 1, 4, 5 and 8 in the correct boxes in the following diagram to show which page number is directly behind each of the page numbers 2, 3, 6 and 7.

CHAPTER 3: FRACTION QUESTIONS 1

LIGHTHOUSE 16

Lighthouses are towers with a light beacon on top. Lighthouses assist sea ships in finding their way at night when they are sailing close to the shore. A lighthouse beacon sends out light flashes with a regular fixed pattern. Every lighthouse has its own pattern.

In the diagram below you see the pattern of a certain lighthouse. The light flashes alternate with dark periods.

It is a regular pattern. After some time the pattern repeats itself. The time taken by one complete cycle of a pattern, before it starts to repeat, is called the period. When you find the period of a pattern, it is easy to extend the above diagram for the next seconds or minutes or even hours. For how many seconds does the lighthouse send out light flashes in 1 minute? A B C D

4 seconds 12 seconds 20 seconds 24 seconds

CHAPTER 4: DECIMALS QUESTIONS 1

POSTAL CHARGES 17

The postal charges in Zedland are based on the weight of the items (to the nearest gram), as shown in the table below:

Jan wants to send two items, weighing 40 grams and 80 grams respectively, to a friend. According to the postal charges in Zedland, decide whether it is cheaper to send the two items as one parcel, or send the items as two separate parcels. Show your calculations of the cost in each case.

QUESTION 2

DVD RENTAL

Jenn works at a store that rents DVDs and computer games. At this store the annual membership fee costs 10 zeds. The DVD rental fee for members is lower than the fee for non-members, as shown in the 18

following table:

Translation Note: Change to, instead of . for decimal points, if that is your standard usage, in EACH occurrence. Translation Note: The use of zeds is important to the Unit, so please do not adapt “zed” into an existing currency. Question 2A Troy was a member of the DVD rental store last year. Last year he spent 52.50 zeds in total, which included his membership fee. How much would Troy have spent if he had not been a member but had rented the same number of DVDs? Number of zeds: .....................................

Question 2B What is the minimum number of DVDs a member needs to rent so as to cover the cost of the membership fee? Show your work. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... Number of DVDs: ...................................

QUESTION 3

SELLING NEWSPAPER

In Zedland there are two newspapers that try to recruit sellers. The posters below show how they pay their sellers.

19

Translation Note: Change to , instead of . for decimal points, if that is your standard usage, in EACH occurrence. Translation Note: The use of zeds is important to the unit, so please do not adapt “zed” into an existing currency. QUESTION On average, Frederic sells 350 copies of the Zedland Star every week. How much does he earn each week, on average?

Amount in zeds: .....................................

QUESTION 4

EXCHANGE RATE

Mei-Ling from Singapore was preparing to go to South Africa for 3 months as an exchange student. She needed to change some Singapore dollars (SGD) into South African rand (ZAR). 20

Question 4A: EXCHANGE RATE Mei-Ling found out that the exchange rate between Singapore dollars and South African rand was: 1 SGD = 4.2 ZAR Mei-Ling changed 3000 Singapore dollars into South African rand at this exchange rate. How much money in South African rand did Mei-Ling get?

Answer: ..................................................

QUESTION 4B On returning to Singapore after 3 months, Mei-Ling had 3 900 ZAR left. She changed this back to Singapore dollars, noting that the exchange rate had changed to: 1 SGD = 4.0 ZAR How much money in Singapore dollars did Mei-Ling get?

Answer: ..................................................

QUESTION 4C During these 3 months the exchange rate had changed from 4.2 to 4.0 ZAR per SGD. Was it in Mei-Ling’s favour that the exchange rate now was 4.0 ZAR instead of 4.2 ZAR, when she changed her South African rand back to Singapore dollars? Give an explanation to support your answer.

QUESTION 5

REACTION TIME

In a Sprinting event, the ‘reaction time’ is the time interval between the starter’s gun firing and the athlete leaving the starting block. The ‘final time’ includes both this reaction time, and the running time. 21

The following table gives the reaction time and the final time of 8 runners in a 100 metre sprint race.

Question 5A Identify the Gold, Silver and Bronze medalists from this race. Fill in the table below with the medalists’ lane number, reaction time and final time.

Question 5B To date, no humans have been able to react to a starter’s gun in less than 0.110 second. 22

If the recorded reaction time for a runner is less than 0.110 second, then a false start is considered to have occurred because the runner must have left before hearing the gun. If the Bronze medalist had a faster reaction time, would he have had a chance to win the Silver medal? Give an explanation to support your answer.

CHAPER 5: PERCENTAGE QUESTION 1

COLOURED CANDIES

Robert’s mother lets him pick one candy from a bag. He can’t see the candies. The number of candies of each colour in the bag is shown in the following graph.

23

What is the probability that Robert will pick a red candy? A 10% B 20% C 25% D 50%

QUESTION 2

MP3 PLAYERS

Music City has a sale. When you buy two or more items at the sale, Music City takes 20% off the normal selling prices of these items. Jason has 200 zeds to spend. At the sale, what can he afford to buy? 24

Circle “Yes” or “No” for each of the following options.

QUESTION 3

PENGUINS The animal photographer Jean Baptiste went on a year-long expedition and took numerous photos of penguins and their chicks. He was particularly interested in the growth in the size of different penguin colonies.

25

Translation Note: In French, “penguin” is “manchot”. Normally, a penguin couple produces two eggs every year. Usually the chick from the larger of the two eggs is the only one that survives. With rock hopper penguins, the first egg weighs approximately 78 g and the second egg weighs approximately 110 g.

By approximately how many percent is the second egg heavier than the first egg? A B C D

29% 32% 41% 71%

Translation Note: Rock hopper - Eudyptes chrysocome

QUESTION 4

CABLE TELEVISION

The table below shows data about household ownership of televisions (TVs) for five countries. It also shows the percentage of those households that own TVs and also subscribe to cable TV.

Translation Note: Please do not change the countries in this unit.

26

Translation Note: Change to , instead of . for decimal points, if that is your standard usage, in EACH occurrence. Translation Note: You may change the term “cable TV” to a relevant local terminology, for example, “subscription TV” or “pay per view TV”. Translation Note: There may be no word for “million” in some languages; translate one million appropriately (e.g. ten hundred thousand); if absolutely necessary, the numeral 1 000 000 could be used throughout. The table shows that in Switzerland 85.8% of all households own TVs. Based on the information in the table, what is the closest estimate of the total number of households in Switzerland? A B C D

2.4 2.9 3.3 3.8

million million million million

QUESTION 5

COINS

You are asked to design a new set of coins. All coins will be circular and coloured silver, but of different diameters.

27

Researchers have found out that an ideal coin system meets the following requirements: •

diameters of coins should not be smaller than 15 mm and not be larger than 45 mm.

•

given a coin, the diameter of the next coin must be at least 30% larger.

•

the minting machinery can only produce coins with diameters of a whole number of millimetres (e.g. 17 mm is allowed, 17.3 mm is not).

You are asked to design a set of coins that satisfy the above requirements. You should start with a 15 mm coin and your set should contain as many coins as possible. What would be the diameters of the coins in your set?

QUESTION 6

DRUG CONCENTRATIONS

Question 6A: A woman in hospital receives an injection of penicillin. Her body gradually breaks the penicillin down so that one hour after the injection only 60% of the penicillin will remain active. This pattern continues: at the end of each hour only 60% of the penicillin that was present at the end of the previous hour remains active. Suppose the woman is given a dose of 300 milligrams of penicillin at 8 o’clock in the 28

morning. Complete this table showing the amount of penicillin that will remain active in the woman’s blood at intervals of one hour from 0800 until 1100 hours.

Question 6B: Peter has to take 80 mg of a drug to control his blood pressure. The following graph shows the initial amount of the drug, and the amount that remains active in Peter’s blood after one, two, three and four days.

How much of the drug remains active at the end of the first day? A 6 mg. B 12 mg. C 26 mg. 29

D 32 mg.

Question 6C: From the graph for the previous question it can be seen that each day, about the same proportion of the previous day’s drug remains active in Peter’s blood. At the end of each day which of the following is the approximate percentage of the previous days drug that remains active? A 20%. B 30%. C 40%. D 80%.

QUESTION 7

DECREASING CO2 LEVELS

Many scientists fear that the increasing level of CO2 gas in our atmosphere is causing climate change. The diagram below shows the CO2 emission levels in 1990 (the light bars) for several countries (or regions), the emission levels in 1998 (the dark bars), and the percentage change in emission levels between 1990 and 1998 (the arrows with percentages).

30

Question 7A: In the diagram you can read that in the USA, the increase in CO 2 emission level from 1990 to 1998 was 11%. Show the calculation to demonstrate how the 11% is obtained.

Question 7B: Mandy and Niels discussed which country (or region) had the largest increase of CO2 emissions. Each came up with a different conclusion based on the diagram. Give two possible ‘correct’ answers to this question, and explain how you can obtain each of these answers

QUESTION 8

WHICH CAR?

Question 8: Chris has just received her car driving licence and wants to buy her first car. This table below shows the details of four cars she finds at a local 31

car dealer.

Translation Note: Change the car’s names to other more suitable fictional names if necessary – but keep the other numbers and values the same. Translation Note: The use of zeds is important to the Unit, so please do not adapt “zed” into an existing currency. Translation Note: Change to , instead of . for decimal points, if that is your standard usage, in EACH occurrence. Question 8: Chris will have to pay an extra 2.5% of the advertised cost of the car as taxes. How much are the extra taxes for the Alpha? Extra taxes in zeds: ................................

CHAPTER 8: BASIC MEASUREMENT QUESTION 1

CLIMBING MOUNT FUJI

Mount Fuji is a famous dormant volcano in Japan.

32

Translation Note: Please do not change the names of locations or people in this unit: retain “Mount Fuji”, “Gotemba” and “Toshi”. Question 1A: The Gotemba walking trail up Mount Fuji is about 9 kilometres (km) long. Walkers need to return from the 18 km walk by 8 pm. Toshi estimates that he can walk up the mountain at 1.5 kilometres per hour on average, and down at twice that speed. These speeds take into account meal breaks and rest times. Using Toshi’s estimated speeds, what is the latest time he can begin his walk so that he can return by 8 pm? ................................................................................................................................... Translation Note: Please use local convention for stating times of the day, and for writing decimal values with , instead of . . Translation Note: In this unit please retain metric units throughout. Question 1B: Toshi wore a pedometer to count his steps on his walk along the Gotemba trail. His pedometer showed that he walked 22 500 steps on the way up. Estimate Toshi’s average step length for his walk up the 9 km Gotemba trail. Give your answer in centimetres (cm). Answer: .................................................. cm

QUESTION 2

HELEN THE CYCLIST

33

Helen has just got a new bike. It has a speedometer which sits on the handlebar. The speedometer can tell Helen the distance she travels and her average speed for a trip.

Question 2: On one trip, Helen rode 4 km in the first 10 minutes and then 2 km in the next 5 minutes. Which one of the following statements is correct? A Helen’s average speed was greater in the first 10 minutes than in the next 5 minutes. B Helen’s average speed was the same in the first 10 minutes and in the next 5 minutes. C Helen’s average speed was less in the first 10 minutes than in the next 5 minutes. D It is not possible to tell anything about Helen’s average speed from the information given. Translation Note: Throughout this Unit please retain metric units. 34

QUESTION 3

INTERNET RELAY CHATS

Internet Relay Chat Mark (from Sydney, Australia) and Hans (from Berlin, Germany) often communicate with each other using “chat” on the Internet. They have to log on to the Internet at the same time to be able to chat. To find a suitable time to chat, Mark looked up a chart of world times and found the following:

Question 3A: At 7:00 PM in Sydney, what time is it in Berlin? Answer: ..................................................

Question 3B: Mark and Hans are not able to chat between 9:00 AM and 4:30 PM their local time, as they have to go to school. Also, from 11:00 PM till 7:00 AM their local time they won’t be able to chat because they will be sleeping. When would be a good time for Mark and Hans to chat? Write the local times in the table.

35

CHAPTER 9: LINES AND ANGELS QUESTION 1

REVOLVING DOOR

A revolving door includes three wings which rotate within a circular-shaped space. The inside diameter of this space is 2 metres (200 centimetres). The three door wings divide the space into three equal sectors. The plan below shows the door wings in three different positions viewed from the top.

Translation Note: If the term for “wings” in the context of a revolving door is not familiar to 15-year olds in your country, you may wish to introduce the term as for example in the FRE source version: “Une porte à tambour est composée de trois « ailes », appelées vantaux, qui tournent au sein d’un espace circulaire.” Question 1: What is the size in degrees of the angle formed by two door wings?

Size of the angle: ................................... º

36

CHAPTER 10: POLIGON QUESTION 1

TRIANGLES

Question 1: Circle the one figure below that fits the following description. Triangle PQR is a right triangle with right angle at R. The line RQ is less than the line PR. M is the midpoint of the line PQ and N is the midpoint of the line QR. S is a point inside the triangle. The line MN is greater than the line MS.

CHAPTER 11: PERIMETER AND AREA 37

QUESTION 1

ICE CREAM SHOP

This is the floor plan for Mari’s Ice-cream Shop. She is renovating the shop. The service area is surrounded by the serving counter.

Note: Each square on the grid represents 0.5 metres X 0.5 metres.

Question 1A: ICE-CREAM SHOP Mari is also going to put new flooring in the shop. What is the total floor space area of the shop, excluding the service area and counter? Show your work. ................................................................................................................................... ................................................................................................................................... ...................................................................................................................................

Translation Note: “The total floor space area”: In some languages the term 38

used for “area” varies according to the context. You may choose to use both terms in the first occurrence, with one between parentheses as in the FRE source version: “La superficie (l’aire) totale”. Question 1B:

Mari wants to have sets of tables and four chairs like the one shown above in her shop. The circle represents the floor space area needed for each set. For customers to have enough room when they are seated, each set (as represented by the circle) should be placed according to the following constraints: •

Each set should be placed at least at 0.5 metres away from walls.

•

Each set should be placed at least at 0.5 metres from other sets.

What is the maximum number of sets that Mari can fit into the shaded seating area in her shop? Number of sets: ......................................

QUESTION 2

OIL SPILL

OIL SPILL An oil tanker at sea struck a rock, making a hole in the oil storage tanks. The tanker was about 65 km from land. After a number of days the oil had spread, as shown on the map 39

below.

Translation Note: Please do not change the size of the image relative to the map scale. When printed, the scale length shown on the legend should equal 1.0 cm. Translation Note: In this unit please retain metric units throughout. Question 2A: Using the map scale, estimate the area of the oil spill in square kilometres (km2). Answer: .................................................. km2 Translation Note: In some languages the term used for “area” varies according to the context. As this unit focuses on the area of the oil spill, you may choose to use in the first instance here both terms with one between parentheses as in the FRE source version: “La superficie (l’aire) de la nappe de pétrole”.

QUESTION 3

FARMS

Here you see a photograph of a farmhouse with a roof in the shape of a pyramid. 40

Below is a student’s mathematical model of the farmhouse roof with measurements added.

The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a block (rectangular prism) EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT and H is the middle of DT. All the edges of the pyramid in the model have length 12 m. Question 3: Calculate the area of the attic floor ABCD. The area of the attic floor ABCD =______________

QUESTION 4

m²

CONTINENT AREA 41

Question 4: Estimate the area of Antarctica using the map scale. Show your working out and explain how you made your estimate. (You can draw over the map if it helps you with your estimation)

QUESTION 5

SHAPES

42

Question 5A: Which of the figures has the largest area? Explain your reasoning.

Question 5B: Describe a method for estimating the area of figure C.

Question 5C: Describe a method for estimating the perimeter of figure C.

QUESTION 6

CARPENTER

Question 6: A carpenter has 32 metres of timber and wants to make a border around a garden 43

bed. He is considering the following designs for the garden bed.

Circle either “Yes” or “No” for each design to indicate whether the garden bed can be made with 32 metres of timber.

QUESTION 7

PATIO

Question 7: Nick wants to pave the rectangular patio of his new house. The patio has length 5.25 metres and width 3.00 metres. He needs 81 bricks per square metre. 44

Calculate how many bricks Nick needs for the whole patio.

QUESTION 8

ROCK CONCERT

Question 8: For a rock concert a rectangular field of size 100 m by 50 m was reserved for the audience. The concert was completely sold out and the field was full with all the fans standing. Which one of the following is likely to be the best estimate of the total number of people attending the concert? A 2 000 B 5 000 C 20 000 D 50 000 E

100 000

QUESTION 9

APARTMENT PURCHASE

APARTMENT PURCHASE This is the plan of the apartment that George’s parents want to purchase from a real estate agency.

45

Translation Note: In this unit please retain metric units throughout. Translation Note: Translate the term “real estate agency” into local terminology for businesses that sell houses. Question 1: APARTMENT PURCHASE To estimate the total floor area of the apartment (including the terrace and the walls), you can measure the size of each room, calculate the area of each one and add all the areas together. However, there is a more efficient method to estimate the total floor area where you only need to measure 4 lengths. Mark on the plan above the four lengths that are needed to estimate the total floor area of the apartment. Translation Note: In some languages the term used for “area” varies according to the context. As this unit focuses on the areas of rooms, you may choose to use in the first instance here both terms with one between parentheses as in the FRE source version: “La superficie (l’aire) totale de l’appartement”.

QUESTION 10

POWER OF THE WIND

Zedtown is considering building some wind power stations to produce electricity. 46

The Zedtown Council gathered information about the following model.

Note: A kilowatt hour (kWh) is a measure of electrical energy. Translation Note: In this unit please retain metric units throughout. Translation Note: Change to , instead of . for decimal points, if that is your standard usage. Question 10: POWER OF THE WIND What is the maximum speed that the ends of the rotor blades for the wind power station move? Describe your solution process and give the result in kilometres per hour (km/h). Refer back to the information about the E-82 model. .............................................................................................................................................. .................. .............................................................................................................................................. ................. .............................................................................................................................................. ................. .............................................................................................................................................. ................. .............................................................................................................................................. ................. Maximum speed: .................................... km/h

47

CHAPTER 12: PEPEJAL GEOMETRI QUESTION 1

BUILDING BLOCKS

Susan likes to build blocks from small cubes like the one shown in the following diagram:

Susan has lots of small cubes like this one. She uses glue to join cubes together to make other blocks. First, Susan glues eight of the cubes together to make the block shown in Diagram A:

Then Susan makes the solid blocks shown in Diagram B and Diagram C below:

Question 1A: BUILDING BLOCKS How many small cubes will Susan need to make the block shown in Diagram B? Answer: ..................................................cubes. 48

Question 1B: How many small cubes will Susan need to make the solid block shown in Diagram C?

Answer: ..................................................cubes.

Question 1C : Susan realises that she used more small cubes than she really needed to make a block like the one shown in Diagram C. She realises that she could have glued small cubes together to look like Diagram C, but the block could have been hollow on the inside. What is the minimum number of cubes she needs to make a block that looks like the one shown in Diagram C, but is hollow?

Answer: ..................................................cubes.

Question 1D: Now Susan wants to make a block that looks like a solid block that is 6 small cubes long, 5 small cubes wide and 4 small cubes high. She wants to use the smallest number of cubes possible, by leaving the largest possible hollow space inside the block. What is the minimum number of cubes Susan will need to make this block?

Answer: ..................................................cubes.

ANSWER SCHEME 49

CHAPTER 1: WHOLE NUMBER QUESTION 1 : YES YES, explicitly or implicitly, AND give any example of a combination of two albums that use 198 MB of space or more. • He needs to delete 198 MB (350-152) so he could erase any two music albums that added up to more than 198 MB, for example albums 1 and 8. • Yes, he could delete Albums 7 and 8 which gives available space of 152 + 75 + 125 = 352 MB. QUESTION 2 C. She left off the last digit in one of the prices. QUESTION 3 A response that shows that the estimated value according to the expert’s criteria is 210 000 zeds which is more than 200 000 zeds hence making it a “very good” price. [The expert’s value of 210 000 zeds must be explicitly stated, but the advertised price can be referred to implicitly or explicitly]. • The expert’s total is 210 000 zeds which is greater than the advertised price of 200 000 which means it is a very good price. • The total of 210 000 zeds is greater than the advertised price. QUESTION 4 4A : 282 cm 4B: 8 QUESTION 5

QUESTION 6 18 QUESTION 7 50

C. 3400 QUESTION INTENT: Description: Identify an average daily rate given a total number and a specific time period (dates provided) Mathematical content area: Quantity Context: Societal Process: Formulate QUESTION 8 D. 720 QUESTION INTENT: Description: Identify information and construct an (implicit) quantitative model to solve the problem Mathematical content area: Quantity Context: Scientific Process: Formulate QUESTION 9 9A Only the minimum (80) correct. Only the maximum (137) correct. 9B 65 zeds on a deck, 14 on wheels, 16 on trucks and 20 on hardware.

CHAPTER 2 : SEQUENCE AND NUMBER PATTERN QUESTION 1A 5 seconds. 51

QUESTION 1B Graf menunjukkan suatu pola keadaan bercahaya dan bergelap pada kelipan 3 saat dalam tempoh 6 saat. Ini dapat ditunjukkan dalam beberapa cara:  3 satu-saat bercahaya, bergantian dengan 3 satu-saat bergelap, ATAU  1 satu-saat bercahaya dan 1 dua-saat bercahaya (ini dapat ditunjukkan dalam beberapa cara), ATAU  1 tiga-saat bercahaya (ini dapat ditunjukkan dalam beberapa cara) Sekiranya 2 pola diberikan, pola tersebut mestilah sama untuk setiap kitaran.

Jawapan kredit sebahagian: Graf menunjukkan pola suatu keadaan bercahaya dan bergelap dalam kelipan 3 saat dalam tempoh 6 saat, tetapi tempohnya tidak menunjukkan 6 saat. Jika 2 kitaran ditunjukkan, polanya mestilah sama untuk setiap kitaran.

QUESTION 2:

52

All 7 entries correct. Partial credit [These codes are for ONE error/missing in the table. Code 11 is for ONE error for n = 5, and Code 12 is for ONE error for n = 2 or 3 or 4] * Correct entries for n = 2, 3, 4, but ONE cell for n = 5 incorrect or missing  The last entry ‘40’ is incorrect; everything else is correct.  ‘25’ incorrect; everything else is correct. *The numbers for n = 5 are correct, but there is ONE error /missing for n = 2 or 3 or 4. QUESTION 3 QUESTION 3A 10 SQUARES QUESTION 3B 55 SQUARES

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3C

QUESTION 4 B. 370 CDs QUESTION INTENT: Description: Interpret a bar chart and estimate the number of CDs sold in the future assuming that the linear trend continues Mathematical content area: Uncertainty and data Context: Societal Process: Employ

QUESTION 5

Page numbers placed correctly in the following positions (ignore the orientation of the numbers):

CHAPTER 3: FRACTION QUESTION 1 D 54

CHAPTER 4 : DECIMALS QUESTION 1 Full credit Code 1: It will be cheaper to send the items as two separate parcels. The cost will be 1.71 zeds for two separate parcels, and 1.75 zeds for one single parcel containing both items.

No credit Code 0: Other responses. Code 9:

Missing.

QUESTION 2A No Credit

QUESTION INTENT: Description: Calculate and compare numbers in an everyday situation Mathematical content area: Quantity Context: Personal Process: Employ

Full Credit

Code 1: 54.40. 55

Code 0: Other responses. Code 9: Missing.

QUESTION 2B QUESTION INTENT: Description: Calculate and compare numbers in an everyday situation Mathematical content area: Quantity Context: Personal Process: Formulate Full Credit Code 21: 15. [Algebraic solution with correct reasoning]. • 3.20x = 2.50x + 10 0.70x =10 x =10 / 0.70 = 14.2 approximately but whole number solution is required: 15 DVDs • 3.20x > 2.50x + 10 [Same steps as previous solution but worked as an inequality]. Code 22: 15. [Arithmetical solution with correct reasoning]. • For a single DVD, a member saves 0.70 zeds. Because a member has already paid 10 zeds at the beginning, they should at least save this amount for the membership to be worthwhile. 10 / 0.70 = 14.2... So 15 DVDs. Code 23: 15. [Solve correctly using systematic trial and error, where student chooses a number and finds the fee for members and non-members, and uses this to locate the correct number (15) for which a member pays less than a non-member]. • 10 DVDs = 32 zeds non-members and 25 zeds + 10 zeds = 35 zeds for members.

Therefore try a higher number than 10. 15 DVDs is 54 zeds for non-members and 37.50 + 10 = 47.50 zeds for members. Therefore try a smaller value: 14 DVDs = 44.80 zeds for non-members and 35 +10 = 45 zeds for members. Therefore 15 DVDs is the answer.

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Code 24: 15. With other correct reasoning.

Partial Credit Code 11: 15. No reasoning or working. Code 12: Correct calculation but with incorrect rounding or no rounding to take into account context. • 14 • 14.2 • 14.3 • 14.28 … No Credit Code 00: Other responses. Code 99: Missing.

QUESTION 3: SELLING NEWSPAPERS QUESTION INTENT: Description: Identify relevant information for a simple mathematical model to calculate a number Mathematical content area: Change and relationships Context: Occupational Process: Formulate Full Credit Code 1: 92 or 92.00. No Credit Code 0: Other responses. Code 9: Missing. QUESTION 4A Full credit Code 1: 12 600 ZAR (unit not required). 57

No credit Code 0: Other responses. Code 9: Missing QUESTION 4B: EXCHANGE RATE SCORING 2 Full credit Code 1: 975 SGD (unit not required). No credit Code 0: Other responses. Code 9: Missing. QUESTION 4C: EXCHANGE RATE SCORING 3 Full credit Code 11: ‘Yes’, with adequate explanation. • Yes, by the lower exchange rate (for 1 SGD) Mei-Ling will get more Singapore dollars for her South African rand. • Yes, 4.2 ZAR for one dollar would have resulted in 929 ZAR. [Note: student wrote ZAR instead of SGD, but clearly the correct calculation and comparison have been carried out and this error can be ignored] • Yes, because she received 4.2 ZAR for 1 SGD, and now she has to pay only 4.0 ZAR to get 1 SGD. • Yes, because it is 0.2 ZAR cheaper for every SGD. • Yes, because when you divide by 4.2 the outcome is smaller than when you divide by 4. • Yes, it was in her favour because if it didn’t go down she would have got about $50 less. No credit Code 01: ‘Yes’, with no explanation or with inadequate explanation. • Yes, a lower exchange rate is better. • Yes it was in Mei-Ling’s favour, because if the ZAR goes down, then she will have more money to exchange into SGD. • Yes it was in Mei-Ling’s favour. 58

Code 02: Other responses. Code 99: Missing. QUESTION 5 QUESTION 5A

QUESTION 5B Full credit Code 1: Yes, with adequate explanation. • Yes. If he had a reaction time of 0.05 sec faster, he would have equalled second place. • Yes, he would have a chance to win the Silver medal if his reaction time was less than or equal to 0.166 sec. • Yes, with the fastest possible reaction time he would have done a 9.93 which is good enough for silver medal. No credit Code 0: Other responses, including yes without adequate explanation. Code 9: Missing.

CHAPTER 5 : PERCENTAGE 59

QUESTION 1 : COLOURED CANDIES Full credit Code 1: B. 20%. No credit Code 0: Other responses. Code 9: Missing.

QUESTION 2: MP3 PLAYERS QUESTION INTENT: Description: Decide whether a known monetary amount will be sufficient to purchase a selection of items at a given percentage discount Mathematical content area: Quantity Context: Personal Process: Interpret Full Credit Code 1: Three correct responses: Yes, Yes, No, in that order. No Credit Code 0: Other responses. Code 9: Missing. QEUSTION 3: PENGUINS QUESTION INTENT: Description: Calculate with percentage within a real context Mathematical content area: Quantity Context: Scientific Process: Employ Full Credit Code 1: C. 41% No Credit Code 0: Other responses. Code 9: Missing. QUESTION 4 : CABLE TELEVISION QUESTION INTENT: Description: Apply proportionality based on a set of data 60

Mathematical content area: Uncertainty and data Context: Societal Process: Interpret Full Credit Code 1: C. 3.3 million. No Credit Code 0: Other responses. Code 9: Missing.

QUESTION 5 : COINS QUESTION INTENT: Understanding and use of complicated information to do calculations. Code 1: 15 – 20 – 26 – 34 – 45. It is possible that the response could be presented as actual drawings of the coins of the correct diameters. This should be coded as 1 as well. Code 8: Gives a set of coins that satisfy the three criteria, but not the set that contains as many coins as possible, eg., 15 – 21 – 29 – 39, or 15 – 30 – 45 OR The first three diameters correct, the last two incorrect (15 – 20 – 26 - ) OR The first four diameters correct, the last one incorrect (15 – 20 – 26 – 34 - ) Code 0: Other responses. Code 9 : Missing

QUESTION 6 : QUESTION 6A: DRUG CONCENTRATIONS SCORING 1 Full credit Code 2: All three table entries correct. Time

Penicillin (mg)

0800

300

0900

180

Partial credit Code 1: One or two table entries correct. 61

1000

1100

108

64.8 or 65

No credit Code 0: Other responses. Code 9: Missing. QUESTION 6B Full credit Code 1: D. 32mg. No credit Code 0: Other responses. Code 9: Missing. QUESTIONS 6B: Full credit Code 1: C. 40%. No credit Code 0: Other responses. Code 9: Missing

QUESTION 6C: Full credit Code 1: C. 40%. No credit Code 0: Other responses. Code 9: Missing QUESTION 7 : QUESTION 7A: DECREASING CO2 LEVELS SCORING 1 Full credit

Code 2: 62

Partial credit Code 1:

No credit Code 0: Other responses, including just ‘Yes’ or ‘No’. • Yes, it is 11%. Code 9: Missing.

QUESTION 7B: Full credit Code 2: Response identifies both mathematical approaches (the largest absolute increase and the largest relative increase), and names the USA and Australia. • USA has the largest increase in millions of tons, and Australia has the largest increase in percentage. Partial credit Code 1: Response identifies or refers to both the largest absolute increase and the largest relative increase, but the countries are not identified, or the wrong countries are named. • Russia had the biggest increase in the amount of CO 2 (1078 tons), but Australia had the biggest percentage increase (15%). No credit Code 0: Other responses. Code 9: Missing. QUESTION 8: 63

QUESTION INTENT: Description: Calculate 2.5% of a value in the thousands within a financial context Mathematical content area: Quantity Context: Personal Process: Employ Full Credit Code 1: 120. No Credit Code 0: Other responses. • 2.5% of 4800 zeds [Needs to be evaluated.] Code 9: Missing.

CHAPTER 8 : BASIC MEASUREMENT QUESTION 1A: CLIMBING MOUNT FUJI

QUESTION INTENT: Description: Calculate the start time for a trip given two different speeds, a total distance to travel and a finish time Mathematical content: Change and relationships Context: Societal Process: Formulate Full Credit Code 1: 11 (am) [with or without am, or an equivalent way of writing time, for example, 11:00] No Credit Code 0: Other responses. Code 9: Missing. QUESTION 1B: QUESTION INTENT: Description: Divide a length given in km by a specific number and express 64

the quotient in cm Mathematical content: Quantity Context: Societal Process: Employ Full Credit Code 2: 40 Partial Credit Code 1: Responses with the digit 4 based on incorrect conversion to centimetres. • 0.4 [answer given in metres] • 4000 [incorrect conversion] No Credit Code 0: Other responses. Code 9: Missing. QUESTION 2 : HELEN THE CYCLIST QUESTION INTENT: Description: Compare average speeds given distances travelled and times taken Mathematical content area: Change and relationships Context: Personal Process: Employ Question 3A: INTERNET RELAY CHAT Full credit Code 1: 10 AM or 10:00. No credit Code 0: Other responses. Code 9: Missing. QUESTION 3B: Full credit Code 1: Any time or interval of time satisfying the 9 hours time difference and taken from one of these intervals: Sydney: 4:30 PM – 6:00 PM; Berlin: 7:30 AM – 9:00 AM OR Sydney: 7:00 AM – 8:00 AM; Berlin: 10:00 PM – 11:00 PM • Sydney 17:00, Berlin 8:00. NOTE: If an interval is given, the entire interval must satisfy the constraints. Also, if morning (AM) or evening (PM) is not specified, but the times could otherwise be 65

regarded as correct, the response should be given the benefit of the doubt, and coded as correct. No credit Code 0: Other responses, including one time correct, but corresponding time incorrect. • Sydney 8 am, Berlin 10 pm. Code 9: Missing.

CHAPTER 9: LINES & ANGEL REVOLVING DOOR SCORING 1 QUESTION INTENT: Description: Compute the central angle of a sector of a circle Mathematical content area: Space and shape Context: Scientific Process: Employ Full Credit Code 1: 120 [accept the equivalent reflex angle: 240]. No Credit Code 0: Other responses. Code 9: Missing.

CHAPTER 10 : TRIANGLES QUESTION 1 Full credit Code 1: Answer D. No credit Code 0: Other responses. Code 9: Missing.

CHAPTER 11 : PERIMETER AND AREA QUESTION 1A: ICE CREAM SHOP QUESTION INTENT: Description: Calculate area for polygonal shapes Mathematical content area: Space and shape Context: Occupational Process: Employ 66

Full Credit Code 2: 31.5. [With or without units.] Partial Credit Code 1: Working that clearly shows some correct use of the grid to calculate the area but with incorrect use of the scale or an arithmetical error. • 126. [Response which indicates correct calculation of the area but did not use the scale to get the real value.] • 7.5 x 5 (=37.5) – 3 x 2.5 (=7.5) – ½ x 2 x 1.5 (=1.5) = 28.5 m2. [Subtracted instead of adding the triangular area when breaking total area down into sub areas.] No Credit Code 0: Other responses. Code 9: Missing. QUESTION 1B: QUESTION INTENT: Description: Use scale to and follow constraints to find the number of circlesthat will fit into a polygonal shape Mathematical content area: Space and shape Context: Occupational Process: Employ Full Credit Code 1: 4. No Credit Code 0: Other responses. Code 9: Missing. QUESTION 2: OIL SPILL QUESTION INTENT: Description: Estimation of an irregular area on a map, using a given scale Mathematical content area: Space and shape Context: Scientific Process: Employ Full Credit Code 1: Answers in the range from 2200 to 3300. No Credit Code 0: Other responses. Code 9: Missing. 67

QUESTION 3 : FARMS Full credit Code 1: 144 (unit already given) No credit Code 0: Other responses. Code 9: Missing. QUESTION 4 : CONTINENT AREA Full credit [These codes are for responses using the correct method AND getting the correct answer. The second digit indicates the different approaches] Code 21: Estimated by drawing a square or rectangle - between 12 000 000 sq kms and 18 000 000 sq kms (units not required) Code 22: Estimated by drawing a circle - between 12 000 000 sq kms and 18 000 000 sq kms Code 23: Estimated by adding areas of several regular geometric figures - between 12 000 000 and 18 000 000 sq kms Code 24: Estimated by other correct method – between 12 000 000 sq kms and 18 000 000 sq kms Code 25: Correct answer (between 12 000 000 sq kms and 18 000 000 sq kms ) but no working out is shown. Partial credit [These codes are for responses using the correct method BUT getting incorrect or incomplete answer. The second digit indicates the different approaches, matching the second digit of the Full credit codes.] Code 11: Estimated by drawing a square or rectangle – correct method but incorrect answer or incomplete answer • Draws a rectangle and multiplies width by length, but the answer is an over estimation or an under estimation (e.g., 18 200 000) • Draws a rectangle and multiplies width by length, but the number of zeros are incorrect (e.g., 4000 × 3500 = 140 000) • Draws a rectangle and multiplies width by length, but forgets to use the scale to convert to square kilometres (e.g., 12cm × 15cm = 180) • Draws a rectangle and states the area is 4000km × 3500km. No further 68

working out. Code 12: Estimated by drawing a circle – correct method but incorrect answer or incomplete answer Code 13: Estimated by adding areas of several regular geometric figures – correct method but incorrect answer or incomplete answer Code 14: Estimated by other correct method –but incorrect answer or incomplete answer No credit Code 01: Calculated the perimeter instead of area. • E.g., 16 000 km as the scale of 1000km would go around the map 16 times. Code 02: Other responses. • E.g., 16 000 km (no working out is shown, and the answer is incorrect) Code 99: Missing Summary table A summary table below shows the relationship between the codes:

NOTE: While coding this question, apart from reading what the student wrote in words in the space provided, make sure that you also look at the actual map to see what drawings/markings that the student has made on the map. Very often, the student does not explain very well in words exactly what he/she did, but you can get more clues from looking at the markings on the map itself. The aim is not to see if students 69

can express well in words. The aim is to try to work out how the student arrived at his/her answer. Therefore, even if no explanation is given, but you can tell from the sketches on the map itself what the student did, or from the formulae the student used, please regard it as explanations given. QUESTION 5 : SHAPES QUESTION 5A: QUESTION INTENT: Comparison of areas of irregular shapes Code 1: Shape B, supported with plausible reasoning. • It’s the largest area because the others will fit inside it. Code 8: Shape B, without plausible support. Code 0: Other responses. Code 9: Missing. Example responses Code 1: A B. It doesn’t have indents in it which decreases the area. A and C have gaps. B B, because it’s a full circle, and the others are like circles with bits taken out. C B, because it has no open areas:

Code 8: • B. because it has the largest surface area • The circle. It’s pretty obvious. • B, because it is bigger. Code 0: • They are all the same. QUESTION 5B: SHAPES SCORING 2 QUESTION INTENT: To assess students’ strategies for measuring areas of irregular shapes. Code 1: Reasonable method: • Draw a grid of squares over the shape and count the squares that are more than half filled by the shape. • Cut the arms off the shape and rearrange the pieces so that they fill a square then measure the side of the square. • Build a 3D model based on the shape and fill it with water. Measure the 70

amount of water used and the depth of the water in the model. Derive the area from the information. Code 8: Partial answers: • The student suggests finding the area of the circle and subtracting the area

of the cut out pieces. However, the student does not mention about how to find out the area of the cut out pieces. • Add up the area of each individual arm of the shape Code 0: Other responses. Code 9: Missing. NOTE: The key point for this question is whether the student offers a METHOD for determining the area. The coding schemes (1, 8, 0) is a hierarchy of the extent to which the student describes a METHOD. Example responses Code 1: • You could fill the shape with lots of circles, squares and other basic shapes so there is not a gap. Work out the area of all of the shapes and add together. • Redraw the shape onto graph paper and count all of the squares it takes up. • Drawing and counting equal size boxes. Smaller boxes = better accuracy (Here the student’s description is brief, but we will be lenient about student’s writing skills and regard the method offered by the student as correct) • Make it into a 3D model and filling it with exactly 1cm of water and then measure the volume of water required to fill it up. Code 8: • Find the areas of B then find the areas of the cut out pieces and subtract them from the main area. • Minus the shape from the circle • Add up the area of each individual piece e.g., • Use a shape like that and pour a liquid into it. • Use graph • Half of the area of shape B • Figure out how many mm2 are in one little leg things and times it by 8. 71

Code 0: • Use a string and measure the perimeter of the shape. Stretch the string out

to a circle and measure the area of the circle using πr2. (Here the method described by the student is wrong) QUESTION 5C : QUESTION INTENT: To assess students’ strategies for measuring perimeters of irregular shapes Code 1: Reasonable method:

• Lay a piece of string over the outline of the shape then measure the length

of string used. • Cut the shape up into short, nearly straight pieces and join them together in a line, then measure the length of the line. • Measure the length of some of the arms to find an average arm length then multiply by 8 (number of arms) × 2. Code 0: Other responses. Code 9: Missing. Example responses Code 1: • Wool or string!!! (Here although the answer is brief, the student did offer a METHOD for measuring the perimeter) • Cut the side of the shape into sections. Measure each then add them together. (Here the student did not explicitly say that each section needs to be approximately straight, but we will give the benefit of the doubt, that is, by offering the METHOD of cutting the shape into pieces, each piece is assumed to be easily measurable) Code 0: • Measure around the outside. (Here the student did not suggest any METHOD of measuring. Simply saying “measure it” is not offering any method of how to go about measuring it) • Stretch out the shape to make it a circle. (Here although a method is offered by the student, the method is wrong) QUESTION 6: CARPENTER 72

Full credit Code 2: Exactly four correct Design A Yes Design B No Design C Yes Design D Yes Partial credit Code 1: Exactly three correct. No credit Code 0: Two or fewer correct. Code 9: Missing. QUESTION 7 : PATIO Full credit Code 2: 1275, 1276 or 1275.75 (unit not required). Partial credit Code 1: 15.75 (units not required) OR 1215 bricks for 5m X 3m (This score is used for students who are able to calculate the number of bricks for an integer number of square metres, but not for fractions of square metres. See example response.) OR Error in calculating the area, but multiplied by 81 correctly OR Rounded off the area and then multiplied by 81 correctly No credit Code 0: Other responses. Code 9: Missing. Example responses Code 2: • 5.25 X 3 = 15.75 X 81 = 1276 Code 1: • 5.25 X 3 = 15.75 • 15.75 X 81 = 9000 • 81 X 15 = 1215; 1215 + 21 = 1236 • 5.25 X 3.0 = 15.75 m2; so 15.75 X 1275.75 = 1376 bricks. (Here the student got the first part right, but the second part wrong. Give credit for the first part and ignore the second part. So score as 1)

73

QUESTION 8 : ROCK CONCERT Full credit Code 1: C. 20 000. No credit Code 0: Other responses. Code 9: Missing. QUESTION 9 : APARTMENT PURCHASE QUESTION INTENT: Description: Use spatial reasoning to show on a plan (or by some other method) the minimum number of side lengths needed to determine floor area Mathematical content area: Space and shape Context: Personal Process: Formulate Full Credit Code 1: Has indicated the four dimensions needed to estimate the floor area of the apartment on the plan. There are 9 possible solutions as shown in the diagrams below.

• A = (9.7m x 8.8m) – (2m x 4.4m), A = 76.56m 2 [Clearly used only 4 lengths to measure and calculate required area.] No Credit 74

Code 0: Other responses. Code 9: Missing. QUESTION 10 : POWER OF THE WIND QUESTION INTENT: Description: Use multistep modelling to solve a problem within a kinetic context Mathematical content area: Change and relationships Context: Scientific Process: Employ Full Credit Code 2: The correct result is deduced from a correct, complete, and comprehensible solution process. The result has to be provided in km/h. A sketch is not imperative, just as a separate sentence containing the answer is not. • Maximum rotational speed is 20 rotations per minute; the distance per rotation is 2 π 40 m ≈ 250m; i.e. 20 250 m/min ≈ 5000 m/min ≈ 83 m/s ≈ 300 km/h. Partial Credit Code 1: The correct result is deduced from a correct, complete, and comprehensible solution process. However, the result is not provided in km/h. Here again, a sketch is not imperative, just as a separate sentence containing the answer is not. • Maximum rotational speed is 20 rotations per minute; the distance per rotation is 2 π 40 m ≈ 250 m; i.e. 20 250 m/min ≈ 5000 m/min ≈ 83 m/s. No Credit Code 0: Other responses. Code 9: Missing.

QUESTION 1A: Full credit Code 1: 12 cubes.

CHAPTER 12 : BUILDING BLOCKS

No credit Code 0: Other responses. Code 9: Missing. QUESTION 1B: Full credit Code 1: 27 cubes. 75

No credit Code 0: Other responses. Code 9: Missing. QUESTION 1C: Full credit Code 1: 26 cubes. No credit Code 0: Other responses. Code 9: Missing. QUESTION 1D: Full credit Code 1: 96 cubes. No credit Code 0: Other responses. Code 9: Missing. ---END OF ANSWER SCHEME---

PANEL PENYUMBANG

PENASIHAT:

Pn. Sallina binti Hussain

Ketua Sektor, Sektor Pengurusan Akademik, JPN Johor

Tn. Hj. Shahilon bin Abd. Halim

Ketua Penolong Pengarah Matematik, SPA

En. Junit bin Yasir

Sektor Pengurusan Akademik

Pn. Aerma Nurazalina binti Musa

Sektor Pengurusan Akademik

Hjh. Zunairah binti Ahmad

Sektor Pengurusan Akademik

76

PANEL:

Muslimah binti Shawan

SM Sains Batu Pahat, Batu Pahat, Johor

Azianti binti Nozlan

SMK Taman Nusa Damai, Pasir Gudang, Johor

Zalita binti Katmin

SMK Dato’ Syed Esa, Batu Pahat, Johor

Lee Hui Lian

SMK Seri Perling, Johor Bahru, Johor

Nurul Fasehah binti Zulkifli

SM Sains Batu Pahat, Batu Pahat, Johor

Mohd Ariff bin Yasman

SMK Penghulu Saat, Batu Pahat, Johor

Azlinahani binti Ithnin

SMK Datin Onn Jaafar, Batu Pahat, Johor

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