276563235-Pearson-International-Mathematics-for-the-MYP-Year-2

Foundation Worksheet Class:

11:05 Surface Area

Name:

Examples

Calculate the surface area of each prism. Measurements are in centimetres.

1 12 Area of ends = 2 × (5 × 9) cm2 2 10 Area of ends = 2 × ( -1- × 8 × 6) cm2
= 90 cm2
2
= 48 cm2

5 Area of sides = 2 × (5 × 12) cm2 6 15 Area of base = 8 × 15 cm2

9 = 120 cm2 8 = 120 cm2

Area of top and bottom = 2 × (9 × 12) cm2 Area of slope = 10 × 15 cm2
= 216 cm2 = 150 cm2

∴ Surface area = 90 + 120 + 216 cm2 Area of side = 6 × 15 cm2
= 426 cm2 = 90 cm2

∴ Surface area = 48 + 120 + 150 + 90 cm2

= 408 cm2

• The surface area of a prism is the total area of all its faces.
• Check if any of the faces are the same. If they are, calculate as 2 × ….

Exercise

Find the surface area of each prism. Lengths are in centimetres.

12 5 10 2 6 3 10 4 15
15
10 2 10
5 6
10
6 5
20
15
6

5 6 20 13 7 88 15

7 5 7 10
85 12
11 17
2
12
9 10 11
20

20 30 9 6·5 16
10 14 10 6·5 6·5
25
12

Fun Spot 11:05 | Where do you find baby soldiers?

Calculate each of the following and match the letters to the answers.

A 2×6×7+3×8 E 2 × 7 × 4 + 2 × 8 × 10 F 2 × 10 × 5 + 3 × 7 + 5 × 8

H 6 × 8 × 12 I 0·5 × 8 × 6 × 2 + 8 × 9 N 3 × 8 × 4 + 2 × 9 × 4

R 2 × 3 × 10 + 2 × 9 × 3 + 2 × 9 × 10 T 2 × 0·5 × 10 × 15 Y 0·5 × 20 × 8 × 2

120 168 150 576 216 120 168 161 108 168 150 294 160

Answers can be found in the Interactive Student CD. 36 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

12:03 Solving Circle Problems

Name: Class:

Examples

• π 7 3·142 and has its own calculator button.
• c = πd or c = 2πr gives the circumference (perimeter) of a circle

where d is diameter and r is radius.

1 A roll of sticky tape has a radius of 2 Find the circumference of a CD if its diameter
3·5 cm. Find its circumference. is 10 cm. Answer correct to one decimal place.
c = 2 × π × 3·5 c = π × 10
7 22 cm 7 31·4 cm

Exercise

1 A 20 cent coin has a diameter of 2·8 cm. Find the length of the circumference, correct to the
nearest centimetre.

2 The lid of a jam jar has a 4 cm radius. Find the circumference of the lid, correct to the nearest
centimetre.

3 A roundabout at an intersection has a diameter of 5 m. What length of reflective tape is needed
to go right around its edge (to 2 decimal places)?

4 What length of paper is needed to make a label around a baked bean can with radius 37 mm
(to the nearest millimetre)?

5 A circular bike track has a diameter of 80 metres.
a What is the distance of one lap of the track?
b How many laps are ridden for a 10 000 metre race?

6 A ferris wheel has a radius of 15·3 m.
a How far does it spin in one turn (to the nearest metre)?
b How far does it spin in the 16 turns for one ride?

7 A wall clock has a decorative border around its edge. How long is the border if the clock has a
diameter of 25 cm?

Fun Spot 15:03 | What happened to the wooden car with wooden wheels and

a wooden engine?

Find the circumference of each circle. Match the letters to the answers.

D r = 12 E d=6 G r=8 I d=9 N r = 11

O d = 18 T r=7 W d = 20

28·3 44·0 62·8 56·5 56·5 75·4 18·8 69·1 50·3 56·5

Answers can be found in the Interactive Student CD. 37 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

13:02 Congruent Shapes

Name: Class:

Exercise

1 Match the congruent shapes by joining them with a line.

12 3 45 6

A BC D EF

2 For each part, which shapes are congruent? C
a C
AB
C
b B D
A

c B
A

d

C
AB

Fun Spot 13:02 | How much does it cost a pirate to get earrings?
Match the letter with the congruent shape below.

AB C ENR U

Answers can be found in the Interactive Student CD. 38 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

13:03 Congruent Figures

Name: Class:

Exercise

1 List five pairs of congruent shapes. E GJ H
A K
D

F BC

2 Complete the following. b Shape C ≡ shape … c Shape F ≡ shape …
a Shape A ≡ shape …

3 Match any congruent shapes.

1 35 6 7 10 11
2 4
13
9 12
8

4 Complete the following. b Figure 3 ≡ c Figure 5 ≡
a Figure 1 ≡ figure … d

5 State whether each pair is congruent. c
ab

Fun Spot 13:03 | During which battle was General Custer killed?
Match the letter with the congruent shape below.

A EH I

L

NO S T

Answers can be found in the Interactive Student CD. 39 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

14:03 Working with Data

Name: Class:

Examples 2 Find the mode, median and mean.
Mode = 2 (most popular outcome)
1 Complete the table below using these scores.
1, 2, 4, 5, 3, 2, 2, 3, 1, 4, Median = 3 (middle outcome is
3, 2, 5, 4, 3, 2, 2, 1, 3, 4 between 10th and 11th
for 20 outcomes)
Outcome Tally Frequency ( f ) f × outcome
Mean = -----t-o---t--a---l---o---f---o---u---t--c---o---m-----e--s-----
1 ||| 3 1 × 3 = 3 number of outcomes
2 |||| | 6 2 × 6 = 12
3 |||| 5 3 × 5 = 15 = -5---6- = 2·8
4 |||| 4 4 × 4 = 16 20
5 || 2 5 × 2 = 10
Add this column to find
Total 20 56 the total of all the scores.

Exercise

1 a Complete the table for these scores. Outcome Tally Frequency (f)
7, 6, 6, 8, 8, 10, 9, 6, 7, 8, 9, 8
6
b Find the mode, median and mean. 7
8
9
10

2 a Complete the table for the number of Goals Tally Frequency (f)
goals kicked per game.
2, 3, 0, 2, 2, 1, 4, 5, 0, 1, 3, 3, 0
2, 1, 4, 5, 1, 5, 2, 0, 2, 4, 1 1
2
b Find the mode, median and mean. 3
4
5

3 a Complete this table for the number of Matches Tally Frequency (f)
matches in 25 boxes.
49, 49, 48, 47, 48, 49, 50, 52, 50, 47
49, 50, 50, 51, 50, 50, 49, 50, 49, 48
51, 51, 52, 51, 48, 49, 50 49
50
b Find the mode, median and mean. 51
52

4 a Complete the table given these daily Temperature Tally Frequency (f)
temperatures.
16, 17, 14, 15, 16, 17, 16, 15, 14
15, 14, 15, 16, 17, 15, 15 15
16
b Find the mode, median and mean. 17

Answers can be found in the Interactive Student CD. 40 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

14:04 Frequency Distribution Tables

Name: Class:

Exercise

1 Complete the frequency distribution table for Outcome Tally Frequency (f)
the given scores.
1, 3, 0, 4, 3, 4, 5, 2, 3, 2, 0, 2, 2, 0
3, 5, 4, 3, 3, 3, 1, 3, 4, 2, 1, 3 1
2
3
4
5

2 Use the scores in question 1 to complete Class Tally Frequency (f)
this table.
Less than 3
3 or more

3 Group these test scores to complete this table. Group Tally Frequency (f)
46, 76, 63, 64, 47, 69, 57, 45, 63,
56, 59, 52, 60, 66, 51, 73, 69, 57, 40–49
64, 62, 58, 56, 52, 74, 49, 77, 62 50–59
60–69
70–79

4 Complete the grouped frequency distribution Height Tally Frequency (f)
table for these heights of a Year 8 class.
156, 168, 163, 166, 156, 163, 149, 152, 140–149
163, 170, 166, 151, 144, 152, 164, 170, 150–159
152, 167, 148, 169, 160, 167, 163, 171, 162 160–169
170–179

5 Use this list of raffle ticket sales to complete Tickets sold Tally Frequency (f)
the frequency distribution table.
5, 15, 11, 20, 3, 6, 14, 13, 7, 17, 1–5 Tally Frequency (f)
12, 16, 14, 18, 8, 9, 6, 17, 15, 12, 6–10
8, 10, 12, 19, 13, 8, 11, 14, 12, 6 11–15
16–20
6 Complete the table using the given outcomes.
3, 8, 6, 2, 3, 5, 5, 8, 5, 3, 7, 4, 5, 8, Outcome
7, 2, 5, 1, 8, 6, 4, 6, 9, 7, 7, 4, 3,
7, 10, 7, 6, 5, 4, 6, 8, 9, 3, 6, 2, 9 1–2
3–4
5–6
7–8
9–10

Answers can be found in the Interactive Student CD. 41 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

14:05 Dot Plots and Column Graphs

Name: Class:

Exercise

1 How many pencils had the following lengths?

a 11 cm b 8 cm

c 13 cm d 10 cm 7 9 11 13 15
Length of pencils (cm)
2 a How many students watched TV for the
0123456789
following times? Weekend TV watched by our class (hours)

i 4 hours ii 7 hours

iii 9 hours iv 2 hours

b List any outliers.

c Which time is the mode?

3 Draw a dot plot to show this information on the number of children per family in my street.

4, 3, 5, 2, 1, 0, 2, 3, 2, 4, 0, 2, 3, 1, 8, 5, 4, 2, 3, 1, 0, 1, 2, 3, 5, 4, 2, 2

a What is the mode?

b What is the range? 0 123 4 5 6 7 8

c Which is the outlier? Number of children

4 Draw a column graph of the dot plot shown
in question 2.

Frequency

Number of hours

5 The number of pets owned by students of a

Year 8 class are:

5, 3, 0, 3, 4, 2, 1, 3, 5, 2, 1, 4, 3, 2, 01234 5
Number of pets

2, 0, 3, 4, 2, 2, 1, 1, 0, 4, 3, 2, 2, 1

a Draw a dot plot and a column graph of this

information. Frequency

b What is the mode?

c How many children had the following?

i 4 pets ii no pets

iii less than 2 pets

Number of pets

6 Listed below are the number of goals scored each game by my team.

5, 3, 2, 6, 7, 4, 3, 2, 10, 4, 7, 6, 4, 5, 2, 3, 4, 5, 4, 3

a Draw a dot plot. b What is the range?

c What is the outlier? d What is the mode?

Answers can be found in the Interactive Student CD. 42 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet Class:

15:02 Probability

Name:

Examples Probability of an event = -n---u---m-----b----e--r----o---f----f--a---v---o---u---r---a---b---l--e----o---u---t--c---o---m-----e---s-
number of possible outcomes

In a class of 30 students, 9 are blonde, 6 black-haired, 10 brown-haired and 5 red-haired.

A student is chosen at random. Find the probability of the following.

1 The person is blonde. 2 The person is black- or brown-haired.
P = --9--- = --3--- P = 6-----+-----1---0-- = 1----6- = --8---
30 10 30 30 15

3 The person is red-haired. 4 The person is not red-haired.

P = --5--- = -1- P = -3---0----–-----5- = -2---5- = -5-
30 6 30 30 6

Exercise

1 One of these balls is chosen at random. What is the probability G
R YY
of choosing the following?
RYR
a a green ball b a yellow ball GR P

c a red ball d a purple ball

2 Josie’s CD rack contains 20 CDs. If 8 are by the Beatles, 2 by the

Beach Boys, 3 by ABBA, and the rest are compilations, find the

probability of randomly choosing the following.

a a Beatles CD b an ABBA CD

c a compilation CD d a CD that is not a compilation

3 Veronica has 4 horses: Nejma (female), The Butcher, Big Tom and Coster

who are males. After saddling them up, she chooses one to ride. What is

the probability she rides the following?

a a female b a male c Nejma or The Butcher

4 A hundred tickets are sold in a raffle at the local club. 0236 0236
Jenny buys 10 tickets and her brother Paul buys 5. Find
the probability of the following. Name: The prize
a Jenny wins b Paul wins c someone else wins Address: A mystery prize

5 A letter is chosen from the alphabet at random. What is the I E S PW L
probability of the following? B OM AG J
a the letter starts your name b the letter is a vowel C KT N Y
c the letter is a consonant R U X H V F

D ZQ

6 List the months of the year. If a month is chosen at random find April

the probability of the following. S MTWT F S
123456
a it begins with a J b it contains an a
7 8 9 10 11 12 13
c it contains your birthday d it ends in ber 14 15 16 17 18 19 20
21 22 23 24 25 26 27
e it is a summer month 28 29 30

Answers can be found in the Interactive Student CD. 43 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

15:04 Using Probability

Name: Class:

Probability = n----u---m-----b----e--r----o---f----f--a---v---o---u---r---a---b---l--e----o---u---t--c---o---m-----e---s-
number of possible outcomes

Exercise

1 Six runners are to run in a race. If one is chosen at random, what is the probability of the

following?

a the one chosen will win b the one chosen will not win

2 Our school has 12 prefects this year: 4 boys and 8 girls. If one prefect is selected at random to

be a captain, what is the probability of the following?

a a boy is chosen b a girl is chosen

c a particular girl, Maria, is chosen

3 Cards numbered 1 to 20 are placed in a container. If one card is chosen at random, what is the

probability of the following?

a it is an even number b it is less than ten

c it is a prime number d it is a multiple of 3

4 A black bag contains 40 marbles—10 red, 10 black, 15 white, 5 blue. What is the probability

that a marble, selected at random, will be the following?

a white b red or black

c blue d not blue

5 Jenni thinks she has a 60% chance of getting a certain job. What is her chance of missing out
on the job?

6 Craig Lowndes calculates his chance of winning the next V8 race is 0·2. What is the
probability someone else wins?

7 A card is chosen from a standard pack of 52 cards. Find the probability of the following.

a it is a king b it is a red card

c it is a heart d it is a red 7

8 Keira has 15 tops in her wardrobe: 3 are white, 2 are pink, 4 are red, 6 are black, 10 are short-

sleeved and 5 are long-sleeved. If her father picks one for her to wear, what is the probability

that it will be the following?

a pink b short-sleeved

c not black d long-sleeved

e red or white

Answers can be found in the Interactive Student CD. 44 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Challenge Worksheet

1 : 12 The Bridges of Königsberg

Name: Class:

Exercise

The Prussian city of Königsberg had seven bridges. The people of the city wondered if it was
possible to walk across all seven bridges without crossing any bridge more than once.
Use the map below to solve their problem. Explain your answer.

• Euler’s solution of this problem was the origin of network theory.

Answers can be found in the Interactive Student CD. 1 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Challenge Worksheet

2 : 02 This Puzzle is Good ‘Training’

Name: Class:

Exercise

This is a diagram of Michelle’s model railway. The engine and the two goods wagons are in the
positions shown.

Tunnel

AB

The engine can pass through the tunnel but the goods wagons are overloaded and cannot pass
through the tunnel without losing some of their load.
Can you use the engine to interchange the positions of the two wagons and return the engine to
the siding?
If a ‘move’ is counted every time the engine stops, how few moves are necessary to solve the
problem? Note that a wagon may be picked up as the engine moves to it but the engine must stop
to uncouple a wagon.

Answers can be found in the Interactive Student CD. 2 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

7 : 06 Challenge Worksheet

Name: Oranges for Sale

Class:

Exercise

In Luigi’s grocery store, a fresh case of oranges was brought in. Soon after, a man entered the
store and bought half the case plus three oranges. Then a woman entered the store and bought
half the remaining oranges plus three oranges. An old lady then entered the store, liked the look
of the oranges, and so bought half the remaining oranges plus three oranges. A young man then
bought half the remaining oranges plus three oranges. Finally, a boy entered the store and
bought the last orange. How many oranges were there originally?

Answers can be found in the Interactive Student CD. 3 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Challenge Worksheet

10 : 07 The Logical Prisoner

Name: Class:

Exercise

The sheriff of a small country town kept three condemned mathematicians in separate cells
where each prisoner could see the other two.

The sheriff confronted the three prisoners and said: ‘If you can solve my riddle you will go free.’
The sheriff showed them three green stickers and three red stickers. He then blindfolded the
prisoners, put a green sticker on the forehead of each and then said: ‘If you can see a green sticker
raise one hand but if you know the colour of the sticker on your own forehead raise both hands.’

When the first prisoner’s blindfold was removed he raised one hand. When the second prisoner’s
blindfold was removed he also raised one hand. When the third prisoner’s blindfold was removed
he thought for a moment and then raised both hands.

Given that no prisoner could see his own sticker and the prisoners did not communicate, explain
how the third prisoner knew that his sticker was green.

Answers can be found in the Interactive Student CD. 4 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Challenge Worksheet

11 : 05 Practical Applications of
Surface Area

Name: Class:

Exercise

1 Holly’s dad, John, has made her the glory box shown here. 0.7 m
It needs three coats of stain.
a Find its surface area. 0.6 m
b Calculate the cost of the stain required, if each can covers 1m
3 m2 and costs $7.80.

2 A room is 5 metres long, 4 metres wide and 3 metres high.
a Find the surface area of the four walls and ceiling.
b Find the cost of painting at $7.20 per square metre.

3 A cake of soap has dimensions 10 cm by SLIPPERY'S SLIPPERY'S
7 cm by 2·5 cm.
a How much plastic is needed to snugly SOAP SOAP
hold one cake?
b How much plastic is needed for a pack 175 g SLIPPERY'S
of five cakes?
SLIPPERY'S SOAP

SOAP SLIPPERY'S

SOAP

SLIPPERY'S

SOAP

SLIPPERY'S

SOAP

4 Glenn has a rectangular haystack, in his paddock, which is 6 metres long, 4 metres wide and
2 metres high. What area of tarpaulin is needed to cover the exposed sides against the
weather?

5 Christina’s bathroom is to be tiled to a height of 1·6 metres. The room is 4 metres long and
2·5 metres wide. Calculate the area for tiling, if you allow 3 m2 for the door and vanity unit.

6 Dean has built a storage box, for his firewood, which is a rectangular prism with a lid. The
outside dimensions are 90 cm long, 60 cm wide and 50 cm high, and it is made of wood which
is 2 cm thick. Calculate:
a the inside dimensions of the storage box
b the interior surface area.

7 Tara has to wrap two presents which are in boxes
20 cm by 10 cm by 10 cm and 25 cm by 20 cm by
15 cm. Calculate their surface area and decide if she
has enough wrapping paper if she bought a roll
advertised as 50 cm × 6 m.

Answers can be found in the Interactive Student CD. 5 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Challenge Worksheet

15 : 04 Probability: An Unusual Case

Name: Class:

Bradley Efron, a mathematician at Stanford

University, invented a dice game that involves

unexpected probabilities.

The faces of four dice are numbered as shown

below.

Die A (used by Andrew) 1, 2, 3, 9, 10, 11

Die B (used by Ben) 0, 1, 7, 8, 8, 9

Die C (used by Cassie) 5, 5, 6, 6, 7, 7

Die D (used by Diane) 3, 4, 4, 5, 11, 12

• Each player throws their die once. Die A
1 2 3 9 10 11
• Andrew beats Ben if the number on his die is 0 AAAAAA
1 TAAAAA
higher than the number on Ben’s die. 7 BBBAAA
8 BBBAAA
• The table of outcomes on the right can be 8 BBBAAA
9 BBBTAA
used to determine who has the greater
• A means die A wins.
probability of success. 11 Die B • B means die B wins.
P(A wins) = 2----2- • T means a tie occurs.
9 10
36

P(B wins) = 1----2- 8

36 87

P(tie) = --2---

36

Clearly, Andrew has the greater probability of

winning.

Exercise

1 Complete the tables of outcomes below.

a Die B b Die C c Die D

017889 556677 3 4 4 5 11 12
1
53 2
3
54 9
10
64 11
Die C
Die D
Die A
65

7 11

7 12

2 a Should Andrew beat Ben? b Should Ben beat Cassie?
c Should Cassie beat Diane? d Should Diane beat Andrew?

3 Explain why this situation is so unusual. b Should Ben beat Diane?

4 a Should Andrew beat Cassie?

Answers can be found in the Interactive Student CD. 6 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Worksheets

Answers

)2:02 Solving Problems

16 28 3 $4.10 48 5 260
8 7 1- hours 9 16
6 15 79
2

10 a $512 b $1023

3:03 Percentage Conversions

1 a 23% b 7% c 30% d 57% e 10% f 85%
j 31% k 81⋅7% l 0.7%
g 1% h 92% i 80%
d 0⋅4 e 0⋅04 f 0⋅66
m 50% n 25⋅5% o 78% j 0⋅15 k 0⋅55 l 0⋅81

2 a 0⋅12 b 0⋅25 c 0⋅6 d 74% e 70% f 25%
j 75% k 80% l 58%
g 0⋅38 h 0⋅99 i 0⋅09

m 0⋅03 n 1⋅5 o 1⋅02

3 a 13% b 50% c 10%

g 72% h 35% i 83%

m 12% n 95% o 44%

3:04 Finding a Percentage of a Quantity

1 a 6 out of 100 b 19 out of 100 c 87 out of 100 d 30 out of 100

e 48 out of 100 f 25 out of 100

2 a $15 b $30 c 8 kg d 24 kg e 21 t f 105 t
j 30 kg k $10.80 l 3080 m
g $21 h $324 i 87 L p $468 q 2178 m r 850 t

m $150 n 200 t o 39 g d 0⋅5 e 0⋅26
i 0⋅38 j 0⋅9
3 a 0⋅18 b 0⋅1 c 0⋅03

f 0⋅83 g 0⋅45 h 0⋅71

3:05 Applications of Percentages

1 $15 2 6 3 351 4 $36 5 252 6 $29
10 1250 mL 11 $53.60
7 $1600 8 36 9 $1170

3:06 Percentages

1 a 30% b 13% c 55%

2 a 3% b 60% c 74% d 90% e 15% f 22% g 86% h 10%
k 50% l 75% m 12% n 11% o 54% p 30%
i 85% j 64% s 18% t 5% u 1% v 55% w 96% x 42%

q 35% r 4%

3:07 Percentage Change

1 a 0⋅13 b 1⋅03 c 0⋅02 d 0⋅88 e 0⋅5 f 0⋅26
i 0⋅91 j 0⋅07 k 1⋅2 l 0⋅1
g 0⋅44 h 1⋅35 o 0⋅59
d 780 L e $26 f 132 g
m 0⋅66 n 0⋅75 c 350 kg j 352 t k $247 l 1200 m
i 5400 d $15 e 135 t f $99
2 a $52 b $412 j 110 L k $10 l $646
c 350 kg
g $465 h 155 m i $252

3 a $52 b $412

g 360 kg h 17 g

INTERNATIONAL MATHEMATICS 2 WORKSHEET ANSWERS 1 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.

3:09 Commission b $12 c $20 d $6
1 a $8
2 a $30 b $60 c $600 d $105
3 a $75
4 $65 b $200 c $250 d $750
8 $1032 7 $86
5 $192 6 $340
10 $47
9 Tony $12 000, Phil $9000

3:10 Finding a Quantity if a Percentage is Known

1 70 kg 2 $50 3 300 ha 4 660 5 300 kg
9 120 10 300
6 800 mL 7 $600 8 50 kg

11 $3500 12 1200 kg 13 $50 000

4:03 Ratio Problems

1 a 2:1 b 2:3 c 3:4 d 3:1 e 3:5 f 2:9 g 4:5 h 1:5
l 6:5 m 5:7 n 1:4 o 4:3 p 2:3
i 2:1 j 10 : 7 k 4:7 t 1 : 10 u 7:1 v 7 : 10 w 3:8 x 1:8 y 5:4
q 3 : 13 r 3:8 s 12 : 5 5 20 mL 6 140 km
4 180
2 1000 cm = 10 m 3 75

4:05 Rates b 10 km/h c $5/kg d 4 L/h e 8 kg/adult
1 a $10 each g 5°C/min
l $1.50/pen h 30 km/day i 32 m/min j 5 c/g
f 4 t/min q
k 7⋅5 m/s b 140 15 g/$1 m $40/m2 n 7 laps/min o
p 0⋅5 kg/$
2 a 25 25 students/group r 15 girls/team

c 64 km d 80 e 15 kg f 36 g $125

6:01 Patterns and Rules

1 a 2, 3, 4, 5 b 3, 5, 7, 9 c 4, 3, 2, 1 d 4, 8, 12, 16 e 7, 8, 9, 10
h 10, 20, 30, 40 i 7, 12, 17, 22 e 7, 10, 13, 16
f 1, 4, 7, 10 g 9, 8, 7, 6 c 2, 1, 0, −1 d 0, −2, −4, −6
h −5, −1, 3, 7 i 11, 9, 7, 5
2 a 1, 4, 7, 10 b 12, 24, 36, 48

f 1, 2, 3, 4 g −4, 0, 4, 8

6:02 Addition and Subtraction

1 a 2x b 4a c 7b d 7y e 6x f 5y gm h 8x it
m 15h n 7q o 14a2 pn q 2c2 r 6xy
j 13n k 15p l 5ab v 18x w 14y x −6y y 18p
d2 e 21 f 50 g 17 h 12
s 7m tf u 9abc
d4 e 23 f 15 g 31 h3
2 a 30 b 34 c 15

i 37 j 100

3 a 12 b4 c 36
i −4 j 23

6:03 Multiplication of Pronumerals

1a T b T c F dF eT fF gF hF
e 18q f de g 8a h 16y
2 a 15a b 16x c 6d d 12g m 18m n 20u o 60k p 16y
l 21t
i 30w j abc k 21c t 14f e 4mn f 12fg g 4x2 h −28t
q 10z r 45u s 27x m 30cd n 9t2 o −30m p 12ab
d −24c
3 a 10xy b −6m c 5ab l −24y
t 20wx
i 10lm j 16pq k −14q
q 6h2 r −10pq s 40y

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6:04 Division of Pronumerals

1 a 4m b 6y c 6k d 2a e 4x f 7t g 3p h 9b
e 8x f 22t g 20p h 5b
2 a 4m b 6y c 9k d 10a e 2f f 2q g 3a h 4c

3 a 5m b 5x c 4q dl e 2m fw g 2r h 4n
l 4b
i 7y j 2y k 7t d 8y
l 4d
4 a 8x b 2a c 3f

i 10x j 6c k 6p

6:05 Multiplication and Division of Pronumerals

1 a 60 b4 c 24 d4 e5 f 16 g 21 h 35
e 42c f 32k g 24m h 72p
2 a 180a b 24x c 40m d 60g e 8a f 40a g 8p h 21h
m 15m n 8x o 2j p 8m
3 a 3y b 9y c 20t d 2t
i 3w j 8c k 15q l 2x e1 f 5b g 2x h4
q 5c r 16u s 50y t 6c m 13d n 4n o5 p 11m

4a 8 b 5a c3 d 11
i 5q j9 k 9f l5

6:06 Using Algebra

1 a 12 m b 27 + x m c 28b m d 28y m e 7t + 13 m f 10p + 16 m
20h cm2 d 35q cm2 e 54c cm2 f 20t cm2
2 a 12 cm2 b 3x cm2 c

3 a $(6y + 28) b $(40 + 15d)

c i $64x ii $(200 − 64x)

6:07 Factorising

1 a 2(x + 4) = 2x + 8 b 5(a − 7) = 5a − 35 c 6(4m + 1) = 24m + 6

2 a x−1 b 5y + 9 c3 d 2a + 3b e3 f 2p + 1
j d+2 k 2q + 5 l7
g 3x − 5y h 4t − 1 i4
f 10(x − 1)
3 a 8(x + 2) b 6(m + n) c 8(a − c) d 7(d − 2c) e 3(g + 2) l 2(3x + 4)
j 3(b − 10) k 4(z − 4) r 7(3a + 11)
g 9(e − 3) h 4(y + 6) i 5(x + 9) p 9(5b + 8a) q 6(5 − 2g) x 8(5h + 4c)
v 2(4j + 3m) w 6(4 − 3l)
m 3(2m − 7) n 4(5y − 3) o 3(3a + 7b)

s 5(3r + 10) t 3(2m − 9n) u 6(2 − 3h)

6:10A Algebraic Fractions

1 a 2-- b 1-- c 1----1- d -3- e 7--
5 6
3 8 12
d 3----y- e 7----m---
2 a -2---x- b -x- c -1---1---a- 5 6 f 3----c- g 2----k- h 5----t
8 12 5 5 7
3 l 4----w-- m -3---x-
3 4 n -7---y- o 3----p- p -c-
i -t- j 7----p- k 3----w-- 13 q 2
9 5 11 t 8----n-
15
q -q- r -1---3---p- s -5---x-
8 10 4 2----k-
5
3 a -2---7---m--- b 3----x- c 2----m--- d -1---1---t e -3---a- f -9---b-
50 i 5 25 10 10
100
g 2----y- h ---c-- j -h- k 3----x- l 1----1---y-
10 2 5 20
5
e 2--
6:10B Algebraic Fractions 5

1 a 1-- b --1--- c --1--- d 2-- m --8--- f --7--- g --3--- h -1---4-
10 18 7 45 12 20 27
9
l --7--- e -3- n --7--- o --5--- p --1---
i --1--- j --2--- k --5--- 12 4 15 14 20
12 11 37
d --3--- m -1- f -2- g 3-- h 3----9-
2 a -2- b ----3---- c 1-- 20 2 3 4 70
100 6
5 l -1- e --1--- n --3--- o --1--- p -8-
8 18 35 20 3
i --1--- j 1-- k 3--
12 4 2 d 6-- 3 f -3- g3 h3
5 2
3a 4 b2 c -3-
2

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7:01 Algebra Review

1 a 5x b -a- c −3p d -m-- e -c- f 10d g -g- h 8k
2 7 3 4
i 9z k -t- n −20a hx
2 a 5x j 6----y- 8 l -3---x- m 12p o 4----t
7 5 f 11t 3 hm
i 8h c 6a e 10c n 19b p 2m
b 6y k 5f d 3q m 11y fp g 3m
jd cm l 13g ex ny o 5n h3
kt mx p 10
3a a bb dy ga x 11
iw jy lg ok h 10

7:02 Solving Equations 1

1a 3 b7 c3 d6 e7 f3 g 20
i3 j4 k6 l 15 m 12 n 20 o7
q 32 r8 s7 t 14 u4 v 20 w 33

2a 7 b 10 c2 d7 e7 f 10 g2
l 10
i 2 j 7 k7

7:03 Solving Equations 2

1a 1 b 11 c8 d 14 e5 f9 g8 h 18
l 12 m 15 n9 o 11 p4
i 4 j 9 k 10 t8 u 18 v6 w 13 x0

q4 r 17 s 40 d5 e7 f7 g 30 h 10
l1 m5 n 14 o 10 p6
2a 6 b 1 c 2 t6

i1 j 13 k 10
q 36 r8 s 15

7:04 Solving Equations 3

1 a 19 b 26 c9 d 33 e 2 f 11 g9 h9

i 1 j 9 k 5 l 40 d 7p − 28
h 6k + 8
2 a Yes b No c Yes d No e Yes f Yes l 18h − 12

3 a Yes b No c No d No e Yes f Yes

4 a 6x + 15 b 5x − 35 c 8a − 6
g 6m + 21
e 18h − 6 f 45q + 72 k 15y − 20

i 20t − 12 j 16w − 24

7:05 Formulae

1 a 20 b 70 c 24 d 54 e4 f 240
15 c7 d 7⋅5 e 4⋅6 f 17
2a 5 b 44 c 79 d 19 e 46 f 127
8 c2 d 25 e5 f 6⋅25
3 a 17 b 78⋅5 c 314⋅2 d 265⋅9 e 1256⋅6 f 10⋅2

4 a 10 b

5 a 201⋅1 b

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7:07 Number Line Graphs b
1a −4 −3 −2 −1 0 1

−1 0 1 2 3 4

c d
−1 0 1 2 3 4 0 1 234567

e f
−6 −5 −4 −3 −2 −1 0 −3 −2 −1 0 1 2 3

g h
−1 0 1 2 3 4 5 −4 −3 −2 −1 0 1 2 3

i j
−4 −3 −2 −1 0 1 2 3 4 5 6 7 8 −4 −3 −2 −1 0 1 2 3 4 5 6 7

k 2 l
−6 −5 −4 −3 −2 −1 0 1 −4 −3 −2 −1 0 1 2 3 4 5 6 7

2 a {0, 1} b {−3, −1, 3, 4} c {−1, 0, 1} d {4, 5, 6, 7}

e {−4, −2, 0} f {−6, 0, 2} g {−3, −1, 1, 2} h {−2, −1, 0, 1}

3 a all numbers greater than 4 b all numbers less than −4

c all numbers greater than 0 d all numbers less than 1

e all numbers greater than or equal to 2 f all numbers greater than or equal to −3
h all numbers less than or equal to −5
g all numbers less than or equal to 20

7:08 Solving Inequations

1 a Yes b No c Yes d Yes
c x Ͻ 12 d xϾ2
2 a xϾ2 b xр4 i mϽ4 j m Ͻ −5 e c р 15 f c Ͼ 15
o yр3 p y Ͼ 11 k mу6 l m Ͼ −4
g cϽ4 h c Ͻ −8 q tϾ6 r tр7
c Yes d No
m y Ͻ 25 n y у 30 c No d Yes

s tϾ6 t t у 13

3 a Yes b No

4 a Yes b No

8:06 Graphing Straight Lines

1a O bD cR dJ eM fI
jG kH lC
gA h B i K
12
2a x 0 1 2 3 b x 0 57 3 cx 0 1 3 5
y 3 9 y −1 3 11 19
y5432

3a x 0 1 2 3 bx 0123 cx 0123
y 0369 y 4 2 0 −2
y5678
y y
y (3, 9) (0, 4)

(3, 8) (2, 6) (1, 2)
(2, 7)
(1, 6) (1, 3)
(0, 5)

(2, 0)

x x
x

(3, −2)

4 a x=2 b y = −3 c y=4 d x = −1

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9:01 Picture Graphs and Column Graphs

1 a 1 symbol = 4 crates b i passionfruit ii cola c i 16 ii 2

2 a 21 b i6 ii 7
d jumpers
c Keira’s wardrobe etc.

3 a number of books b novels c 16 d gardening e 2 f 5 g 55

4 a i April ii October

b i 100 mm ii 110 mm iii 50 mm

c i August ii February iii September, November, December

9:02 Reading Graphs

1a i 6 ii 18 b archery – 4, athletics – 25 c squash

2 a column graph b type of pet c 12 d2

e i cats ii carpet snakes

3 a pie chart/graph b 28

c i 36° ii 72° iii 90°

d wages e $20 000 f $4000

4 a 50 b 225 c 25 d 350 e 25

9:05 Travel Graphs

1 a i 1 km ii 2 km iii 3 km iv 3 km v 0⋅5 km

b i 3 pm ii 2.30 pm
c Check with teacher—perhaps stopped for a coffee with a friend or watched a movie.

2 a 5 km b i 2 km ii 4 min c 40 min

3 a 10 am b 140 km c 70 km/h d The motorist was stopped.

e i 200 km ii 160 km

4 a 300 km b at noon c at 10 am for 1 hour and at 1 pm for half an hour

d 6h e 300 km f 50 km/h g 100 km h 150 km

i Brown. Even though he often travelled faster than Smith, he took regular breaks and his speed wasn’t excessive.

10:02 Angle Relationships

1 a 60 b 100 c 205 d 235 e 180 f 127
i 135 j 215 k 115 l 130
g 270 h 54 c 134 d d = 53, e = 47 e 95 f 117

2 a 37 b 113

g 50 h 60

10:05 Triangles and Quadrilaterals

1 30 2 70 3 110 4 25 5 160 6 94
10 31 11 91 12 118
7 20 8 112 9 24 16 52 17 25 18 85

13 75 14 45 15 248

19 75 20 77

10:07 Finding the Angles

1 70 2 120 3 120 4 100 5 40 6 70
9 134 10 83 11 123 12 318
7 29 8 43 15 38 16 50 17 57 18 78
21 107 22 40 23 45 24 115
13 130 14 253 27 32 28 17

19 60 20 50

25 48 26 57

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11:02 Finding the Area

1 a 40 cm2 b 25m2 c 136 cm2 d 40 m2 e 84⋅68 cm2 f 1000 m2
c 72 cm2 d 56 mm2 e 54 m2 f 42⋅78 cm2
2 a 20 cm2 b 120 m2 c 224 m2 d 2⋅76 m2 e 110⋅76 cm2 f 250 m2

3 a 40 cm2 b 117 m2

11:04 Volumes of Prisms

1 a 12 cm3 b 12 cm3 c 27 cm3 d 30 cm3

2 a 45 cm2 b 84 m3 c 330 m3 d 893 cm3

3 a 48 cm3 b 1350 m3 c 343 cm3 d 1120 m3
e 1440 m3 f 90 cm3 g 1331 mm3 h 420 m3
i 120⋅744 m3 j 1185⋅84 cm3 k 489⋅19 m3 l 438⋅976 cm3

11:05 Surface Area

1 160 cm2 2 432 cm2 3 600 cm2 4 950 cm2 5 262 cm2
8 520 cm2 9 2200 cm2 10 712 cm2
6 660 cm2 7 226 cm2

11 253⋅5 cm2 12 1392 cm2

12:03 Solving Circle Problems

1 9 cm 2 25 cm 3 15.71 m 4 232 mm
7 78⋅5 cm
5 251 m, 39⋅8 laps 6 96 m, 1536 m

13:02 Congruent Shapes

1 1 = C, 2 = A, 3 = F, 4 = B, 5 = D, 6 = E

2 a A=B b A=C c B=C d A=C=D

13:03 Congruent Figures

1 A = K, B = F, C = J, D = G, E = H

2a K bJ c B

3 1 = 8, 2 = 11, 3 = 12, 4 = 9, 5 = 7 figure 7
No
4a 8 b figure 12 c

5 a No b Yes c d Yes

14:03 Working with Data

1 a Outcome f 2 a Goals f 3 a Matches f 4 a Temp. f

63 03 47 1 14 2
72 15 48 3 15 6
84 26 49 7 16 4
92 33 50 8 17 3
10 1 43 51 4
53 52 2 b mode = 15
b mode = 8 median = 15
median = 8 b mode = 2 b mode = 50 mean 7 15⋅5
mean 7 7⋅6 median = 2 median = 50
mean 7 2⋅3 mean = 49⋅68

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14:04 Frequency Distribution Tables

1 Outcome f 2 Class f 3 Group f

02 Less than 3 10 40–49 4
13 3 or more 15 50–59 9
25 60–69 10
39 70–79 4
44
52

4 Height f 5 Tickets sold f 6 Outcome f

140–149 3 1–5 2 1–2 4
150–159 6 6–10
160–169 13 11–15 9 3–4 9
170–179 3 16–20
13 5–6 12

6 7–8 11

9–10 4

14:05 Dot Plots and Column Graphs

1a 2 b 2 c 4 d0
iv 0
2a i4 ii 6 iii 3 b 0 hours is an outlier. c mode = 7 hours

3

012345678
Number of children

a2 b8 c8
4 Frequency

6

5
4
3
2
1

0123456789
Number of hours

5 a Frequency

8

7

6

5

012345 4
Number of pets 3
2

1

b2 c i 4 ii 3 iii 8 012345
6a Number of pets

2 3 4 5 6 7 8 9 10 b8 c 10 d4
Number of goals
8 © Pearson Education Australia 2006.
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15:02 Probability

1 a -1- b --3--- c -2- d --1--- 2 a 2-- b --3--- c --7--- d -1---3-
10 5 10 20 20 20
5 5
c -1- 2 a -1- b --1--- c -1---7- d -1- e -1-
3 a 1-- b -3- 2 4 a --1--- 20 20 34
4 3
4 c -2---1- c 2-- 10 b 1-- c --1---
26 2 12
5 a --1--- b --5--- 5 6 a -1-
26 c 1--
26 4
8
15:04 Using Probability c 1--

1 a 1-- b 5-- 4 b -2- c --1---
6 c 3-- 3 12
6
5 d --3--- e --7---
3 a 1-- b --9--- 10 15
20
2 d -7-
b 1-- 8
4 a -3- 2
d --1---
8 6 0⋅8 26

5 40% or 0⋅4 d 1--
3
7 a --1--- b 1--
2
13

8 a --2--- b -2-
3
15

Challenge

1:12 The Bridges of Königsberg

It is not possible. Consider each body of land to be a vertex. The network cannot be travelled because it has
four odd vertices.

2:02 This Puzzle is Good ‘Training’

16 moves. The engine leaves the siding and reverses to couple with B. Then both return to the siding and B is
unhooked. The engine leaves the siding and goes anticlockwise around the track and picks up A and pushes it
into the siding and picks up B again. The engine then pulls out of the siding and reverses to uncouple B in its
original position. A is then returned to the siding and uncoupled. The engine then travels clockwise around the
track and pushes B to A’s original position and is then uncoupled. The engine then picks up A from the siding
and shunts it into B’s original position. The engine then returns to the siding.

7:06 Oranges for Sale
There were 106 oranges originally.

10:07 The Logical Prisoner

The second prisoner would have known the colour of his sticker if the sticker on the third prisoner had been
red, as the first prisoner had seen a green sticker. As the second prisoner did not raise both hands, the third
prisoner concluded that his sticker must be green as he could assume that it was not red.

11:05 Practical Applications of Surface Area

1 a 3⋅44 m2 b $31.20

2 a 74 m2 b $532.80

3 a 225 cm2 b 565 cm2

4 64 m2 5 7⋅4 m2

6 a 86 cm long, 56 cm wide, 46 cm high b 22 696 cm2

7 3350 cm2. Wrapping paper area = 30 000 cm2. Yes.

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15:04 Probability: An Unusual Case b Die C c Die D
1 a Die B 556677 3 4 4 5 11 12
3C C C C C C
017889 4C C C C C C 1D D D D D D
5 CCB B B B 4C C C C C C
5 CCB B B B 5T T CCCC 2D D D D D D
6 CCB B B B 11 D D D D D D
6 CCB B B B 12 D D D D D D
7 CCTB B B
7 CCTB B B
Die C 3T DDDDD
Die D
Die A 9A A A A DD

10 A A A A D D

11 A A A A D

2 a Yes b Yes c Yes d Yes

3 It doesn’t seem logical that Diane (D) is more likely to win against Andrew (A), since A should beat B,

B should beat C and C should beat D.

4 a No. They have exactly the same chance of winning. b No

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