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

9 The two right-angled triangles shown have their hypotenuses and one side equal in length.

a Write down Pythagoras’ Theorem for

c each triangle.
a b m b By rearranging the formula, show that

a = m.

c Are the triangles congruent?

bc

Questions 8 and 9 have shown us that two right-angled triangles are congruent if the
hypotenuse and one side of one triangle are equal to the hypotenuse and one side of
the other triangle. This is the fourth condition, and is abbreviated to RHS.

Summary • SSS means ‘side,
side, side’.
• Two triangles are congruent if three sides of one triangle are
equal to three sides of the other (SSS). • SAS means
‘side, angle,
• Two triangles are congruent if two sides and the included angle side’.
of one triangle are equal to two sides and the included angle of
the other (SAS). • AAS means
‘angle, angle,
• Two triangles are congruent if two angles and a side of one side’.
triangle are equal to two angles and the corresponding side of
the other (AAS). • RHS means
‘right angle,
• Two right-angled triangles are congruent if the hypotenuse and hypotenuse,
one side of one triangle are equal to the hypotenuse and one side side’.
of the other triangle (RHS).

76 INTERNATIONAL MATHEMATICS 2

APPENDIX H
H:01 | Similar Triangles

The following exercise is an investigation into the conditions necessary for two triangles to be
similar. In appendix A:07B, the construction of triangles using protractors, compasses and ruler is
revised. You will need this knowledge here.

Exercise H:01 (Some practical work is included)

You will need: protractor, compasses, ruler, set square, pencil, eraser, tracing paper.

1
Equal angles
have the same
symbols.

A BC

a Which two triangles have the same shape?
b Measure the angles of the two similar triangles.

What do you find?

2 The triangles pictured below have been drawn with
the same-sized angles.

C

F

AB

D E

a Are the triangles the same shape (similar)? 77APPENDIX H

b Name the side that corresponds to (ie matches) side:

i AB ii BC iii AC

c Measure the length of each side.

d Are the ratios of matching sides equal?

3 Construct two equilateral triangles with sides of 2 cm and 6 cm
respectively.

a Are the triangles the same shape?
b Are the matching angles equal?
c Are the ratios of matching sides equal?

4 F For the two triangles shown,
C 80° answer the following questions:

40° 60° 40° a What is the size of ∠ACB?
A 4 cm B D b What is the size of ∠DEF?
c Are the angles of ∆ABC equal
6 cm
to the angles of ∆DEF?
E d Are the triangles similar?

e What is the ratio DE : AB?

The exercises above illustrate the following result.

Two triangles are similar if their angles are equal.

5 Identify the triangles that are similar in each of the following. Look for triangles with
a the same angles.

70° 80° 50°

A 50° B C
60° 60° 40° 70° 60°

b 60° 60°
80° C 40°
60°
B 60° D
A
60° 60° 50° 50° 70° 70°

c

50° 50° 60° 80°
C
A 50° B 50° 40° D 40°
80° 80° 80° 60°

d

60° 35°

A 40° C D
75° 65° 80° 60° 45°
B
e 75° 55°

80° 40° 60° 65°

A C D
B

45° 80° 60° 45°

78 INTERNATIONAL MATHEMATICS 2

6 There are ten pairs of similar triangles in the triangles shown below. Each of the triangles A to
J is similar to one of the triangles L to W. Select the triangle that is similar to triangle:
aA bB cC dD eE fF gG hH iI jJ

60° 60° 80° 100°

A BC D
60° 60°
40° 80° 50° 50° 40° 40°

30° F G H 25°
E 30° 60° 50° 110°

120° 30°

I Can you find the Elementary, Watson!
105° missing angle, Holmes? The angles of a triangle
always add up to 180°.

35° J

70° 70°

60° M
40° 40°
L
80° 40°

80° 30° P 45° 70°
N O 110° Q
50° 80° 70° R
30° 60°

S T U 30° V 60° 60°
70° 70° 70° 60° 105° 40° W
60°

79APPENDIX H

7C 2 cmF a Are the two triangles similar?
4 cm 2·5 cm
5 cm D 3 cm E b Name the side that matches the
side:
A 6 cm B i AB ii BC iii AC.

The two biggest ...and so are c Are the ratios of matching sides
sides are the two equal?

corresponding... smallest sides. d Carefully trace or construct
one of these triangles on a
piece of paper and cut it out.
By matching, find whether
matching angles are equal.

8 a On a piece of paper construct triangles with sides of:

i 2 cm, 3 cm, 4 cm ii 4 cm, 6 cm, 8 cm

b Are the ratios of matching sides equal?

c Cut the triangles out and check to see whether matching angles are equal.

Are they? Are the triangles similar?

Questions 7 and 8 illustrate the following results.

If two triangles have matching sides in the same ratio, they are similar.
This means that matching angles are equal.

9 Identify the triangles that are similar in each of the following. Are the
a sides in the
same ratio?
5 10 6 10
3A 6 C 8

4 B

8 12

b 5 7 7·5
A 6 16
4
6 B
8 6
C

9

c 6 4
B
6 C
A3 8 12

4

d 6 3 4 C2 54
B 5 D
10
A4 4 6

8

80 INTERNATIONAL MATHEMATICS 2

This could ■ middleB
help you long
figure it out. middle A short
long short

Triangle A is similar to Triangle B if:
l--o---n----g----s--i--d---e-----o---f---A-- = -m----i--d---d----l-e----s---i-d----e----o---f---A--- = -s--h---o---r---t---s--i--d---e----o----f---A--
long side of B middle side of B short side of B

10 Below are shown ten pairs of similar triangles. Each of the triangles A to J is similar to one of
the triangles K to U. By checking the ratios of matching sides, find the triangle that is similar to:
aA bB cC dD eE fF gG hH iI jJ
(All measurements are in cm.)

8 6 55 12 8
A B C
5 66 88
10 16 D E

3 6

5 F3 66 4·5 5 10 8
6 G H I
9 3·5 87
J
12 5

44 4 M3 6N 4 44
K 5 8 P
4
2 16
16

L 15 44
9 Q R
6
12 18
14 10
9 10 65 U
S T
7 16
4

81APPENDIX H

11 D a Are these triangles similar?

b Calculate the ratios:

A i -D----E-- ii -E----F--
2 cm AB BC

4 cm c What would you expect the

ratio -D----F-- to equal?
AC

60° C 60°
B 3 cm E

6 cm F

Question 11 illustrates the third condition for two triangles This appears to be a
to be similar. mixture of the two
other conditions.

Two triangles are similar if an angle of one triangle is equal
to an angle of the other and the lengths of the matching
sides that form the angles are in the same ratio.

12 Identify the pair of similar triangles in each of the following.
a

6 cm A 4 cm 2 cm
40° 8 cm B C

40° 40°
6 cm 3 cm

b Don’t be fooled by the
triangles’ orientations.
9 cm
C 6 cm

8 cm 6 cm 3 cm B
4 cm
A

13 Find two similar triangles in each of the following.

State which condition could be used to show that

the triangles are similar.

aA bA B cD

C 4
E

DE 5

DE 50° B 4·8 C
BC A6

82 INTERNATIONAL MATHEMATICS 2

H:02 | Drawing Enlargements

Fun Spot H:02 | Drawing enlargements fun spot

• The following questions illustrate a simple way of constructing similar figures by the H:02
enlargement method.

ABCD is similar to EFGH.

EH a Which angle matches:

i ∠A? ii ∠B? iii ∠C? iv ∠D?

b Which side matches side:

AD i AB? ii BC? iii CD? iv AD?

c By measurement, calculate the ratios:

B O i -E---F-- ii F----G--- iii G-----H--- iv -H----E--
F AB BC CD DA

d i How far is E from O?

ii How far is A from O?

C iii Is EO = 2 × AO?

e i Is FO = 2 × BO?

ii Is GO = 2 × CO? ■ Each point
iii Is HO = 2 × DO? has doubled

G its distance

from O.

• To draw a figure similar to ABCD by BЈ AЈ
enlargement, follow these steps. B A
Step 1 Select a point O to be the centre of O
enlargement. C D
Step 2 Draw rays from O through each of the
vertices A, B, C and D. CЈ DЈ
Step 3 Decide on an enlargement factor, say 2.
Step 4 Move each vertex to a new position on
its ray which is twice its present distance
from O. For example, if A is 18 mm from
O, then A′ becomes 36 mm from O.

• Trace each of the figures below and then make a similar figure by the enlargement
method, using an enlargement factor of 2.

a b c

A D D

O E OC C

BC O

AB A B

83APPENDIX H

APPENDIX I
I:01 | The Pictogram or Picture Graph

Yearly Sales of Jazzy Jeans

2000

2001

2002

2003

represents 1000 pairs
of jeans

Features
1 The pictogram is attractive and catches the attention of the reader.
2 It seeks to create an impression rather than give detailed information. The pictogram is not

intended to convey detailed information.
3 The pictogram allows you to compare the size of each category easily.
4 It is easy to understand.

Details
1 The pictogram must have a title or heading.
2 Only one axis is necessary.
3 Each symbol stands for a definite number of items. This information will be shown on the

graph, usually at the bottom.
4 The axis will be given a label or name, unless the meaning is obvious.

84 INTERNATIONAL MATHEMATICS 2

I:02 | The Column Graph

Percentage of all drug-related deaths Drug-related Deaths Features
100 1 The column graph is easy to read and
90
80 to understand.
2 It is easy to draw.
70 3 The graph allows comparisons to be

60 made at a glance.
4 The column graph shows more detail
50
than most other graphs and is impressive
40 in its appearance.

30 Details
20 1 The column graph must have a title

10 or heading.
2 Both vertical and horizontal axes
0
Alcohol Tobacco Other drugs are used.
3 Axes must be given labels (or names)
This represents 18·7% of all deaths recorded, or
7352 of 39 316. unless the meaning is obvious.
Source: Australian Bureau of Statistics 4 The columns are rectangles, although

vertical lines are sometimes used as
columns.
5 An axis may represent non-numerical
data.
6 Where numbers are used, care must
be taken to choose a suitable scale for
the axis.

85APPENDIX I

Appendixes

Appendix B

Challenge B:01

1 xy 2 xy 3 xy
12
15 3 13 7 2 11 9
3 26 15
28 2 2 10 4 4 47 21 6
5 74 27 6
5 11 6 107 33 6
6
3 13 2 3 21 4

7 15

4 20 2 4 36 4

9 19

5 29 2 5 55 4

11 23

6 40 6 78

4 xy 5 xy The connection is that the

16 15 final difference is always twice
the number multiplying the x2.

14 14

2 20 8 2 19 10

22 24

3 42 8 3 43 10

30 34

4 72 8 4 77 10

38 44

5 110 8 5 121 10

46 54

6 156 6 175

Appendix C

Prep Quiz C:01

1 16 28 3 81 43 5 64 6 64 7 m5 8 a2b3
9 30a4 10 12y3z2
c n10 d q10 e a4 f p7 g x8 h y5
Exercise C:01 b m7 k n12 l x10 m h11 n f4 o m9 p t7
j w8 s x7 t q20
1 a x5 r p14 e 6p5 f 8x6 g 21a5 h 50m3
i t2 c 4x4 d 7q4 m 3w8 n 36m4 o 35n10 p 12x7
q w12 k 18x5 l 8p6
s 120b5 t 56y15 e m6n8 f a6b8 g x9y5 h t3w4
2 a 2x7 b 5p5 m k4l9 n x5y6 o a5b4 p m13n3
i 24a5 j 56t4 c a4b6 d p6q4
q 15p4 r 63a9 k m5n5 l a3b5 e 18x9y6 f 24p5x5 g 6a6b4 h 14x3y6
s t2w5 t a20b9 m 24a2b3 n 42a4b6 o 40a2b4 p 48p4q5
3 a a6b b p2q5
i x5y j a5m4 c 12x4y4 d 14t7w4
q a6b2 r p5q6 k 5p5q7 l 6m3n6

4 a 12a6b b 15p2q5

i 32m7n10 j 6a9b5

1 INTERNATIONAL MATHEMATICS 2

Exercise C:02 b a3 c m2 d n2 e a3 f y4 gy hk
j b2 k x2 l m5 mt n w5 o a4 p l3
1 a x3 r m5 s t12 t w12
i z2 e 5m4 f 5a g 4n2 h 4b4
q x6 c 7k3 d 8y2 m t6 na o m2 pw
k 4l3 l 4n3
2 a 5x4 b 6m2 s 2y4 t 3p8 e 6m2 f 10m g 2a2 h 3t2
j 2y5
i 3x r 5n12 c m2 d t8 g mn3 h k3m
q 3a5 k 5m l 4n4 o p3q4 p c2d6
w 2y2 x 3a5
3 a x2 b a3 c y6z d t2w5
i 5n2 j 2a6 k t7w l f2h5
s 4p6q t 8tw3
4 a a2b5 b m3n6 e p2q f a2b2
i a4x3 j m2n7 m m2n3 n a5b3
r 2mn3 u 10m3n3 v 2ab7
q 6ab

Exercise C:03 b x12 c m10 d n6 e y28 f t12 g x9 h w21
j y20 k h15 l b4 m n27 n m20 o w12 p x100
1 a a8
i x14 e 16n10 f 32y5 g 27p6 h 64q6

2 a 4x6 b 9a8 c 25m6 d 8x12 e m2n8
i 100a6 j 49p6 k 216n3 l 1000a15 m 16p4q6

3 a a4b2 b m12n6 c a16x8 d p2q10 f t8w8 g k12m6 h x12y9
i 4a4b2 j 9x4y6 p 125a9b6
k 100m2n8 l 25x2y8 n 1000m12n9 o 16p16q8

Exercise C:04 B C
a5 p8q4
1A
a x11 27m3 2m
b a15 p8
c 18n5 1
a5b4 25p4
d 3pq 8m6n 30x5y5
e 4w3
f a8 2q3 4a
g 16a8b2 32p5q10
h x11 x
i a2 a10 p18
x2
j 2p t6 36m8
k 3a3 36x10 2n2
l 80a11 2x2
m p5q3 4m2 30a2b2
n 5x4y2 6m10 t3
6a4b2
2a 1 b1 8m3n3 d1 e1 f1 g1 h1
i2 j5 l 25 m5 n4 o 12x2 p9
c1

k3

Exercise C:05

1 Approximately 549 755 813 900 coins would need to be placed on the 40th square. The last two digits are not given,

as the number is too big to fit on the screen. The pile is worth approximately $27 487 000 000. The pile would be

about 700 000 km high.
2 9·4608 × 1012 km

2ANSWERS

Appendix D 3 ∠DCE 4 ∠ACD 5 ∠ACD 6 ∠ACD and ∠DCE
D 7 b 8 180 – a 9 c 10 a = c
Prep Quiz D:01

1 and 2

A

B CE b ∠XYE = a° (corresp. ∠s // lines)
∠XYE = b° (vert. opp. ∠s)
Exercise D:01 ∴a=b

1 a ∠AEF = x° (vert. opp. ∠s) b ∠DBC = x° (vert. opp. ∠s)
∠AEF = y° (corresp. ∠s // lines) ∠BDE = 180° – x° (co-int. ∠s, BC//DE)
∴x=y ∠BDE = 180° – y° (co-int. ∠s, DB//EC)

2 a ∠ACD = x° (corresp. ∠s, BD//AC) ∴ 180 – x = 180 – y
∠ACD = y° (corresp. ∠s, AB//CD) ∴x=y
∴x=y
b a + x = 180 (co-int. ∠s, AB//DC)
3 a a + x = 180 (co-int. ∠s, AB//DC) b + x = 180 (co-int. ∠s, AD//BC)
a + y = 180 (co-int. ∠s, AD//BC) ∴a=b
∴x=y
b a + 90 = 180 (co-int. ∠s, AB//DC)
4 a ∠FAB = ∠EGB (corresp. ∠s, AF//GE) ∴ a = 90
∠ECD = ∠EGB (corresp. ∠s, BG//DC)
c + 90 = 180 (co-int. ∠s, AD//BC)
∴ ∠FAB = ∠ECD ∴ c = 90
b = 90 (opp. ∠s of a parallelogram)
c ∠BAC = 2p°
∠ACD = 2q° b ∠ABC + a° + b° = 180° (∠ sum of ∆ABC)
∠ADC + a° + b° = 180° (∠ sum of ∆ADC)
∠BAC + ∠ACD = 180° (co-int. ∠s, AB//CD) ∴ ∠ABC = (180 – a – b)°
∴ 2p + 2q = 180 and ∠ADC = (180 – a – b)°
∴ p + q = 90 ∴ ∠ABC = ∠ADC

Now ∠AEC + (p + q)° = 180° (∠ sum of ∆)
∴ ∠AEC + 90° = 180°
∴ ∠AEC = 90°

5 a a + x = 90 (adj. comp. ∠s)
b + x = 90 (comp. ∠s)
∴a=b

c Let ∠BCA = x°
∴ ∠DBC = (90 – x)° (comp. ∠s)
∴ ∠ABD = 90° – (90 – x) (adj. comp. ∠s)
= x°
∴ ∠BCA = ∠ABD

3 INTERNATIONAL MATHEMATICS 2

Appendix F

Exercise F:01

2 b They are all the same distance from the circumcentre.
4 parallelogram
5 a The bisectors of the chords meet at the centre.

b Draw two chords and construct the perpendicular bisector of each chord. The point where the bisectors meet is the
centre of the circle.
6 c yes
7 b isosceles; because AO = OB
d yes
10 c yes
d yes
11 c rhombus
d rhombus
12 b 90°

Prep Quiz F:02 3 90° 4 45° 5 60
8 90° 9 45° 10 30°
1 cut in half 2 30°
6 equilateral 7 60°

Exercise F:02

4 b 90° c AB = 20 mm; AC = 35 mm

5 b 30° c AC = 50 mm; BC = 86 mm

6 b 60° c AD = 54 mm; DC = 29 mm

7 a CD should be 36 mm b CD should be 20 mm c CD should be 35 mm

8 a DE should be 3 cm; ∠CED should be 45°

b ∠MLN should be 75°; LM should be 29 mm; LN should be 36 mm

Exercise F:03

Note: Answers to construction questions can be checked using the answers given.

2 a AC = 22 mm; BC = 44 mm b AB = 32 mm; BC = 48 mm; CD = 53 mm

c BC = 31 mm; AC = 70 mm; AD = 45 mm; BD = 65 mm

8 a BD = DC = 4 cm b AD = 3 cm; CD = 5 cm c AD = 29 mm

Prep Quiz F:04

13 2 3 34 44 56
8 90° 9 60° 10 45°
6 360° 7 120°

Exercise F:04

2 c equilateral triangle

5a 5 b 72°

6a 8 b 45°

11 a x = 54 b x = 75

Prep Quiz G:01

1 ∆PQR 2 ∆TUV 3 ∠J and ∠M, ∠K and ∠N, ∠L and ∠O

4 JK and MN, KL and NO, JL and MO 5 ∠X and ∠P, ∠Y and ∠R, ∠Z and ∠Q

6 XY and PR, XZ and PQ, YZ and RQ 7 yes 8 no 9 yes 10 no

Exercise G:01

1 a yes b yes, they are congruent c yes

2 a yes b yes c yes

3 a BC gets longer b no

4 a 4·6 cm b no c yes

5 a yes b The triangles are congruent

6 a I and V, II and IV, III and VI b The 5 cm side is opposite the same-sized angle.

7 a i 80° (∠A) ii 60° (∠D) iii 40° (∠L) b ∆DEF c The 4cm side is opposite the 60° angle in both triangles.

8 a BC and EF, AB and DF, AC and DE b yes

9 a c2 = a2 + b2,c2 = m2 + b2 b a2 = c2 – b2 and m2 = c2 – b2 c yes

∴ a2 = m2

∴a=m

4ANSWERS

Appendix H

Exercise H:01

1 a B and C b Corresponding angles are equal.

2 a yes b i DE ii EF iii DF

c AB = 6 cm; BC = 3 cm: AC = 4·5 cm; DE = 8 cm; EF = 4 cm; DF = 6 cm d yes
gR
3 a yes b yes c yes
gR
4 a 80° b 60° c yes d yes e 6 : 4 or 3 : 2

5 a A and C b A and C c A and B; also C and D d A and D e B and C

6a W bL cN dM eP fU hQ
hS
iV jT

7 a yes b i DE ii EF iii DF

c yes d Matching angles are equal.

8 b yes c yes, yes

9 a A and B b A and C c B and C d A and C

10 a M bP cN dK eL fQ

iT jU

11 a yes b i 2:1 ii 2 : 1 c 2 : 1

12 a B and C b A and B

13 a ∆ABC and ∆ADE (3 angles) b ∆ABC and ∆EDC (3 angles)

c ∆ABE and ∆ACD (sides about an equal angle in same ratio)

Fun Spot H:02 ii ∠F iii ∠G iv ∠H
ii FG iii GH iv EH
1 a i ∠E ii 2 : 1 iii 2 : 1 iv 2 : 1
b i EF ii 10 mm iii yes
c i 2:1 ii yes iii yes
d i 20 mm
e i yes

5 INTERNATIONAL MATHEMATICS 2

Foundation Worksheet

2:02 Solving Problems

Name: Class:

Exercise

1 In how many different orders can you write the words red, white and blue?

2 Three coins are tossed. In how many ways could they fall? (One way is three heads.)

3 A heater costs 30c to run for the first minute, while it warms up, then 20c for each minute
after that. How much would it cost to run for 20 minutes?

4 The outside of this block is painted blue.
How many of the small cubes will have
exactly two sides blue?

5 A company wants to give each employee a personal code to access the file room. How many
choices are there if each code consists of a letter (A–Z) followed by a number (0–9)?

6 There are six players in a golf competition. Each golfer plays the others once before the
winner is decided. How many matches will there be?

7 Josie needs 40c from her piggy bank to give to her sister Veronica. How many ways could this
be made up if the piggy bank contains 5, 10 and 20 cent coins?

8 Farmer Mark has to replace three strands of wire in the fence around a 200 m by 300 m
rectangular paddock. How long will it take for the job if he lays 100 m of wire every
15 minutes?

9 There are four children on a particular cruise. How many 2-HOUR BOAT
adults are there if the total paid is $228? CRUISES

Adult: $12
Child: $9

10 Kerrie thinks a great way to save would be to put $1 aside this week, $2 aside next week,
$4 the third week and so on, doubling each time.
a How much would she put aside in the 10th week?
b How much would she have put aside altogether by the 10th week?

Answers can be found in the Interactive Student CD. 1 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

3:03 Percentage Conversions

Name: Class:

Examples • To change to a percentage, × 100.
• To change to a decimal, ÷ 100.
1 0·64 = 0·64 × 100%
= 64% 3 --3---7--- = --3---7--- × 100% 4 0⋅675 = 0·675 × 100%
= 67·5%
2 --6--- = --6--- × 100% 100 100
7 90% = 90 ÷ 100
25 25 = 37% = 0·9

= 24% 6 54% = 54 ÷ 100
= 0·54
5 2% = 2 ÷ 100
= 0·02

Exercise

1 Change to percentages.

a 0·23 b 0·07 c 0·3 d 0·57 e 0·1
h 0·92 i 0·8 j 0·31
f 0·85 g 0·01 m 0·5 n 0·255 o 0·78

k 0·817 l 0·007 c 60% d 40% e 4%
h 99% i 9% j 15%
2 Change to decimals. m 3% n 150% o 102%

a 12% b 25% c --1--- d 3----7- e --7---

f 66% g 38% 10 50 10

k 55% l 81% h --7--- i --8---3--- j -3-

3 Change to percentages. 20 100 4

a --1---3--- b -1- m --3--- n 1----9- o --4---4---

100 2 25 20 100

f -1- g 1----8-

4 25

k 4-- l 2----9-

5 50

Fun Spot 3:03 | What’s bright orange and sounds like a parrot?

Change to percentages. Match the letters with the answers.

A --9--- C 0·4 O 1----1- R 0·04 T -2---4-

20 25 50

!

45% 40% 45% 4% 4% 44% 48%

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

3:04 Foundation Worksheet

Finding a Percentage of
a Quantity

Name: Class:

Examples Remember:
• % means ‘out of a 100’.
1 43% means 43 out of 100. • of means ‘×’.
2 8% means 8 out of 100.
3 Find 6% of 100 m. 4 Find 6% of 300 m. (× 3)
= 6 out of 100 m
= 6 out of 100 m = 18 out of 300 m
=6m = 18 m

5 Find 23% of $300. 6 Find 60% of $450.
= (23 ÷ 100) × 300 = 60 ÷ 100 × 450
= $69 = $270

Exercise

1 Complete. b 19% means … out of … c 87% means … out of …
a 6% means … out of … e 48% means … out of … f 25% means … out of …
d 30% means … out of …
b 15% of $200 c 8% of 100 kg
2 a 15% of $100 e 21% of 100 t f 21% of 500 t
d 8% of 300 kg h 54% of $600 i 30% of 290 L
g 3% of $700 k 12% of $90 l 44% of 7000 m
j 60% of 50 kg n 25% of 800 t o 50% of 78 g
m 5% of $3000 q 99% of 2200 m r 1% of 85 000 t
p 72% of $650

3 Write as decimals.

a 18% b 10% c 3% d 50% e 26%
h 71% i 38% j 90%
f 83% g 45%

Fun Spot 3:04 | What’s tall, hairy, lives in the Himalayas and does

500 sit-ups a day?

Write these percentages as fractions. Match the letters with the answers.

A 20% B 50% D 33 1-- % E 5% H 10% I 25% L 60%

3

M 75% N 6% O 30% S 45% T 34% W 52%

1----7- --1--- --1--- 1-- -1- 1-- --3--- 3-- -1- --3--- 1-- 3-- --9--- --3--- --3--- -1---3- 3-- -1- --3---
50 10 20 5 2 3 10 4 4 50 5 5 20 50 10 25 4 5 50

Answers can be found in the Interactive Student CD. 3 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

3:05 Applications of Percentages

Name: Class:

Examples When calculating using percentages, either
1 17% of $600 = 0⋅17 × 600 change to a decimal before multiplying, or
2 17% of $600 = 17÷100 × 600 divide by 100 before multiplying.

Exercise

1 I earned $100. I wish to give 15% of this to my mother. How much should I give her?

2 3% of the computers are not working. If there are 200 computers, how many are not working?

3 39% of the students in a school have brown hair. How many students is this, if there are 900
in the school altogether?

4 Phill bought a bike for $90. After fixing it up, he wants to re-sell it to make a 40% profit.
What will his profit be?

5 Jamie is a farmer with 450 calves. If 56% are male, how many calves are males?

6 Hannah’s pay is currently $580 per week. How much extra will she get when she receives her
5% pay rise?

7 Justine must save the 20% deposit for her first car. If the car is priced at $8000, how much
must she save?

8 John is one of the 12% of people surveyed when leaving a CD shop who like hip-hop music.
If 300 were surveyed, how many liked hip-hop?

9 Angus is treasurer of the local church which decides to donate 10% of its offertories for
March to various missionary groups working in Africa. How much will be donated if the
offertories were $11 700?

10 A cordial drink is made from 25% raspberry cordial and water. How many millilitres of cordial
are required to make up 5 litres of the drink?

11 Jemma wants to buy a new wardrobe priced at $670. How much will she save if she buys the
display unit at a discount of 8%?

Answers can be found in the Interactive Student CD. 4 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet Class:

3:06 Percentages

Name:

Examples • Make the first amount a fraction over the second.
• Multiply by 100 to make a percentage.

What percentage is each of these?

1 17 of 100 2 8 of 25 3 29 of 50
= 2----9- × 100%
= --1---7--- × 100% = --8--- × 100%
50
100 25
= 58%
= 17% = 32%

1 What percentage is shaded? Exercise c
a
b

2 What percentage is each of these?

a 3 of 100 b 6 of 10 c 74 of 100 d 90 of 100
g 43 of 50 h 1 of 10
e 3 of 20 f 11 of 50 k 1 of 2 l 3 of 4
o 27 of 50 p 3 of 10
i 17 of 20 j 16 of 25 s 9 of 50 t 1 of 20
w 24 of 25 x 21 of 50
m 3 of 25 n 11 of 100

q 7 of 20 r 1 of 25

u 1 of 100 v 11 of 20

Fun Spot 3:06 | When is it bad luck to see a cat?

Change the percentages to decimals. Match the letters with the answers below.

A 14% E 4% H 35% M 1% N 40% O 76%

R 7⋅6% S 11% U 25% W 60% Y 100%

0·6 0·35 0·04 0⋅4 ’

1 0·76 0⋅25 0·076 0·04 0⋅14 0·01 0·76 0·25 0·11 0·04

Answers can be found in the Interactive Student CD. 5 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

3:07 Percentage Change

Name: Class:

Examples To change a percentage to a decimal, ÷ 100
or move the decimal point two places to the left.
1 73% = 0·73
3 60% = 0·60 = 0·6 4 112% = 1·12
2 8% = 0·08
6 84% of 600 kg 7 30% of 40 t
5 9% of $300 = 0·84 × 600 kg = 0·3 × 40 t
= 0·09 × $300 = 504 kg =2t
= $27

Exercise

1 Change to decimals.

a 13% b 103% c 2% d 88% e 50%
h 135% i 91% j 7%
f 26% g 44% m 66% n 75% o 59%

k 120% l 10% c 0·7 × 500 kg
f 1·5 × 88 g
2 Use a calculator to find the following. i 1·35 × $4000
l 0·08 × 15 000 m
a 0·13 × $400 b 1·03 × $400
c 70% of 500 kg
d 0·39 × 2000 L e 0·05 × $520 f 110% of $90
i 42% of $600
g 0·62 × $750 h 0·25 × 620 m l 190% of $340

j 0·44 × 800 t k 0·95 × $260

3 Use the method you used in question 2 to find the following.

a 13% of $400 b 103% of $400

d 25% of $60 e 75% of 180 t

g 6% of 6000 kg h 50% of 34 g

j 55% of 200 L k 1% of $1000

Fun Spot 3:07 | Why do birds fly south for the winter?

Change these decimals to percentages. Match the letters with the answers.

A 0·4 F 0·04 I 0·25 K 0·14 L 1·4

O 0·75 R 0·5 S 1·04 T 0·55 W 0·57

’ 55% 75% 75% 4% 40% 50% 55% 75% 57% 40% 140% 14%

25% 55% 104%

Answers can be found in the Interactive Student CD. 6 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet Class:

3:09 Commission

Name:

Examples

1 Helen receives $7 for every $100 of plastic ware she sells. What does she get for selling

$400 worth in 1 week? $7 for $100

= $7 × 4 for $400

= $28

2 John is paid a commission of 3% on his car sales. What is his commission on a $35 000 car?
3% of $35 000

= 0·03 × $35 000
= $1050

Exercise

1 For every $100 worth of goods I sell, I am paid $4. How much can I keep if I sell goods to

the following values?

a $200 b $300 c $500 d $150

2 Bill’s company allows him to take $15 for every $100 profit the company makes. How much

does he take when the profit is the following?

a $200 b $400 c $4000 d $700

3 Margaret is a frame maker who is paid $25 for every $100 worth of frames she makes. What is

her pay when she makes frames with the following values?

a $300 b $800 c $1000 d $3000

4 Janet earns a 5% commission on her carpet sales. How much is her commission from sales
of $1300?

5 Lawrie works in a furniture store and earns an 8% commission for selling lounge suites. What
does he get for selling a $2400 leather lounge?

6 Nita runs a CD shop where she is allowed a commission of 17% on certain CD sales. How
much will she receive in a week where she sells $2000 of these CDs?

7 Jack is on a basic wage plus 2% commission on orders. What will his total commission be on
orders of $1100, $700, $500 and $2000?

8 Con charges 12% commission on sales of insurance policies. How much will he get for
policies costing $8600?

9 Tony, as senior partner, receives 20% commission on profits, while Phil receives 15%
commission. How much will they each get if profits are $60 000?

10 Jamie receives 10% commission on the newspapers he sells. What is his commission on
$470 worth of sales?

Answers can be found in the Interactive Student CD. 7 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

3:10 Finding a Quantity if a
Percentage is Known

Name: Class:

Examples

1 If 210 students is 25% of 2 40% of my savings is $120. 3 The 15% deposit for a car

the school, how many are What are my total savings? is $1800. How much is the

in the school altogether? 40% of savings = $120 car?

25% of school = 210 ∴ 1% of savings = $120 ÷ 40 15% of car = $1800

∴ 100% of school = 210 × 4 = $3 ∴ 1% of car = $1800 ÷ 15

= 840 ∴ 100% of savings = $3 × 100 = $120

∴ 840 students in school = $300 ∴ 100% of car = $120 × 100

∴ my savings are $300 = $12 000

Remember that the original ∴ car costs $12 000

quantity is 100%.

Exercise

1 50% of my mass is 35 kg. What is my mass?

2 10% of my money is $5. How much do I have?

3 20% of Kerrie’s farm is natural bush. How big is Kerrie’s farm if there are 60 ha of bushland?

4 Josie scored 30% of her team’s goals for the season. If Josie scored 198 goals, how many did
the whole team score?

5 Concrete contains 12% cement. How much concrete will contain 36 kg of cement?

6 A solution contains 25% active ingredients. If there are 200 mL of active ingredients, how
large is the solution?

7 Veronica received a $90 discount in a ‘15% off’ sale at the local bookstore. What was the
original price for the books?

8 A metal alloy contains 60% copper. What mass of alloy will have 30 kg of copper?

9 Mr McMath told his class that 75% of Year 8 passed the term test. If 90 passed, how many
were in Year 8?

10 24 teenagers couldn’t name a Beatles’ song when surveyed. If this was 8% of the total, how
many were surveyed altogether?

11 40% of all money raised for charity in the school’s lamington drive went to cancer research.
What was the total raised if $1400 went to cancer research?

12 55% of a rugby league team’s mass was with the six forwards. If they weighted 660 kg how
much did the whole team weigh?

13 In 2003, Jamie decided to put away 2% of his pay to saving for his daughters’ weddings. If he
put away $1000 that year, what was his pay?

Answers can be found in the Interactive Student CD. 8 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet Class:

4:03 Ratio Problems

Name:

Examples

1 Simplify each ratio.

a 5 : 20 (÷ 5) b 24 : 16 (÷ 8) c 40 : 50 (÷ 10)

= 1:4 = 3:2 = 4:5

2 Duncan and his sister Hannah have lollies in the ratio 1 : 4. If Duncan has 13 lollies, how
many does Hannah have? Hannah has 4 × Duncan
= 4 × 13
= 52 lollies

Exercise

1 Simplify each ratio.

a 4:2 b 20 : 30 c 9 : 12 d 15 : 5 e 6 : 10
h 6 : 30 i 18 : 9 j 30 : 21
f 4 : 18 g 16 : 20 m 25 : 35 n 20 : 80 o 16 : 12
r 12 : 32 s 24 : 10 t 8 : 80
k 8 : 14 l 60 : 50 w 9 : 24 x 9 : 72 y 25 : 20

p 22 : 33 q 6 : 26

u 28 : 4 v 14 : 20

2 A map has a scale of 1 : 1000. Two places are 1 cm apart on the map. What is the distance
between these places?

3 The ratio of blonde to brown-haired students in Year 8 is 1 : 3. If there are 25 blondes, how
many students have brown hair?

4 Holly and Brianna shared their father’s record collection in the ratio 5 : 1. If Brianna took
36 records, how many did Holly take?

5 A drink uses cordial and water mixed in the ratio 1 : 15. How much cordial should be mixed
with 300 mL of water?

6 Paul and Jenny share the driving on a holiday in the ratio 2 : 1. If Paul drives for 280 km, how
far should Jenny drive?

Fun Spot 4:03 | Why do tigers eat raw meat?

Simplify each fraction. Match the letters with the answers.

A 6-- B --5--- C --8--- E --4--- H 1----0- K --9---

9 10 20 12 12 15

N --3--- O --4--- S --6--- T --9--- U --8--- Y --2---

18 20 14 30 10 20

’ !

1-- -1- -2- 2-- -4- 3-- -1- --3--- -5- 1-- --1--- 2-- -2- -1- --3--- 2-- -1- 1-- -3-
2353573 10 6 3 10 536 10 5555

Answers can be found in the Interactive Student CD. 9 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet Class:

4:05 Rates

Name:

Examples

1 Simplify each rate. (÷ 5) b 15 minutes for 10 laps (÷ 10)
= 1·5 min for 1 lap
a $60 for 5 T-shirts = 1·5 min/lap
= $12 for 1 T-shirt
= $12/T-shirt

2 8 kg of potatoes cost $4. How many kg do I get for $7?
8 kg for $4 = 2 kg for $1 (÷ 4)
= 14 kg for $7 (× 7)

Exercise

1 Simplify each rate. b 20 km in 2 h c $30 for 6 kg
a $80 for 8 e 40 kg for 5 adults f 60 t in 15 min
d 12 L in 3 h h 600 km in 20 days i 800 m in 25 min
g $6 for 4 pens k 300 m in 40 s l 75 g for $5
j 80°C in 16 min n 35 laps in 5 min o 200c for 40 g
m $240 for 6 m2 q 150 students in 6 groups r 75 girls in 5 teams
p 40 kg for $80

2 a I can buy 10 apples for $2. How many apples can I buy for $5?
b If 60 peaches fit into 3 boxes, how many will fit into 7 boxes?
c Jack rides 40 km in 5 hours. How far will he ride in 8 hours?
d Keira makes 6 toys in 3 hours. How many will she make in 40 hours?
e 6 kg of carrots cost $4. How much could I buy for $10?
f Josie swims 24 laps in 10 minutes. How many laps would she do in 15 minutes?
g Veronica spends $200 on 8 doses of worming paste for her horses. What would be the cost
of 5 doses?

Fun Spot 4:05 | Have you read this book?

Calculate the following. Match the letters to the answers.

B 20 ÷ 5 × 6 E 120 ÷ 8 × 3 F 68 ÷ 4 × 7 G 16 × 3 ÷ 6

H 32 ÷ 8 × 12 I 15 × 8 ÷ 10 K 9 ÷ 3 × 20 L 50 ÷ 10 × 8

N 6 × 18 ÷ 12 O 10 × 8 ÷ 16 R 12 ÷ 5 × 40 T 16 ÷ 10 × 35 Y 30 × 7 ÷ 6

‘ 12 9 56 48 45 96 5 ’

48 5 40 45 5 119

24 35 40 45 45 60 12 9 8

Answers can be found in the Interactive Student CD. 10 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

6:01 Patterns and Rules

Name: Class:

Examples

Use the rule to fill in the table.

1 y=x+3 2 n = 4m − 1 3 b=8−a

x3456 m1 2 3 4 a0123
y6789 n 3 7 11 15 b8765

y=3+3=6 n=4×1−1=3 b=8−0=8
y=4+3=7 n=4×2−1=7 b=8−1=7
y=5+3=8 n = 4 × 3 − 1 = 11 b=8−2=6
y=6+3=9 n = 4 × 4 − 1 = 15 b=8−3=5

Exercise

1 Use the rule to fill in the table.

a y=x+1 b y = 2x + 1 c y=5−x
x1234
x1234 x12 3 4 y

yy f g = 3f − 2
f 1234
d k = 4j e b=a+6 g
j 1234 a1234
k b i b = 5a + 2
a1234
g n = 10 − m h y = 10x b
m1 2 3 4 x1234
n y c q=3−p
p1234
2 Use the rule to fill in the table. q

a y = 3x + 1 b n = 6m f h = -1- g

x0123 m2 4 6 8 2

yn g2468
h
d c = −2b e y=x+7
i y = 2x + 3
b0123 x0369 x4321
c y y

g y = 2x − 4 h d = 4c − 5 © Pearson Education Australia 2006.
x0246 c0123 This page may be photocopied for classroom use.
y d

Answers can be found in the Interactive Student CD. 11

INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

6:02 Addition and Subtraction

Name: Class:

Examples Adding and subtracting like terms is
just counting how many.
1 a 5k − 3k = 2k
To find the value, substitute the
b 5ab + 7ab = 12ab number for the letter, then calculate.
c 10x2 + x2 = 11x2

(no number means 1)

2 a Find the value of 4c − 3 if c = 7.
4c − 3 = 4 × 7 − 3
= 25

b Find the value of y + 7 if y = 4 .
y+7=4+7
= 11

Exercise

1 Simplify. b 6a − 2a c 4b + 3b d y + 6y e 7x − x
a x+x g 4m − 3m h 3x + 5x i 7t − 6t j 14n − n
f 9y − 4y l 3ab + 2ab m 3h + 12h n 10q − 3q o 9a2 + 5a2
k 10p + 5p q c2 + c2 r 7xy − xy s 15m − 8m t 11f − 10f
p 6n − 5n v 6x + 12x w 4y + 10y x 4y − 10y y 7p + 11p
u 2abc + 7abc
c x+5 d x−8 e 2x + 1
2 Find the value when x = 10. h 2x − 8 i 4x − 3 j x2

a 3x b 3x + 4 c 6m d 10 − m e 3m + 5
h 1-- m i m − 10 j 4m − 1
f 5x g x+7
2
3 Find the value when m = 6.

a 2m b 2m − 8

f m+9 g 5m + 1

Fun Spot 6:02 | What do you call a Tyrannosaurus eating a taco?

Simplify these expressions. Match the letters to the answers.

A 4h + h + h E 12h − h M 9h + 4h + h N 3h × 5

O 10h − 3h − 4h R 3h3 + h3 S 2h2 + 2h2 T 8h + 5h − h

U 6h − 8h X −2 × 7h Y 15h − 10h + 2h

12h 7h 4h3 6h 15h 15h 3h 4h2 6h −2h 4h3 −2h 4h2 14h 11h −14h

Answers can be found in the Interactive Student CD. 12 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

6:03 Multiplication of Pronumerals

Name: Class:

Examples 2 a×b When simplifying, multiply the numbers
= ab and letters separately and omit the × signs.
1 15 × p
= 15p 4 3g × h 5 2m × 5n 6 8c × c
= 3gh = 10mn = 8c2
3 5 × 3x
= 15x

Exercise

1 True or false? b 2y = 2 × y c q × q = 2q d 3x + 2y = 5xy
a a + a = 2a f p + q + r = pqr g 4x × 3x = 12x h m + m + m = m3
e 5 × d × 3 = 15d
b 8 × 2x c 6×d d 3 × 4g
2 Simplify. f d×e g 4×a×2 h 8y × 2
a 3 × 5a j a×b×c k 3×7×c l 7t × 3
e 6q × 3 n 4u × 5 o 10 × 6k p 4 × 4y
i 5 × 6w r 9n × 5 s 3×9×x t 2×f×7
m m×3×6
q 2z × 5 b 3m × (−2) c 5a × b d −6 × 4c
f 3f × 4g g x × 4x h 7 × (−4t)
3 Simplify. j 2p × 8q k 7 × (−2q) l 3y × (−8)
a 2x × 5y n 9t × t o −3 × 10m p 3×a×4×b
e 4×m×n r −2p × 5q s 8 × 5y t −5w × (−4x)
i 2l × 5m
m 10c × 3d
q 2h × 3h

Fun Spot 6:03B | Why didn’t the dinosaur cross the road?

Simplify these expressions. Match the letters to the answers.

A 5 × 3j B 7×j C 2 × 6j D 5j × 2 E 3×6×j
S 3j × 5k
I 3 × 4k N j×k O 4 × j × k R 7 × 2k

T 3 × 7 × k U k × 9 × 2 V 6k × 2j W 2j × 7k

7j 18j 12j 15j 18k 15jk 18j 14k 4jk 15j 10j 15jk

14jk 18j 14k 18j ’ !

jk 21k 12k jk 12jk 18j jk 21k 18j 10j

Answers can be found in the Interactive Student CD. 13 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

6:04 Division of Pronumerals

Name: Class:

Examples • To show division, use words, the ÷ sign, or
write the expression as a fraction.
1 Find a quarter of 20x
= 20x ÷ 4 • Divide numbers and letters separately.
= 5x
2 Simplify 10q ÷ 2 3 Simplify -1---2---x---2-
= 5q 4

= 12x2 ÷ 4
= 3x2

Exercise

Simplify. b Half of 12y c Third of 18k d Tenth of 20a
1 a Half of 8m f Half of 14t g Fifth of 15p h Half of 18b

e Quarter of 16x b 12y ÷ 2 c 18k ÷ 2 d 20a ÷ 2
f 44t ÷ 2 g 40p ÷ 2 h 10b ÷ 2
2 a 8m ÷ 2
e 16x ÷ 2 b 20x ÷ 4 c 16q ÷ 4 d 3l ÷ 3
f 12q ÷ 6 g 24a ÷ 8 h 40c ÷ 10
3 a 15m ÷ 3 j 10y ÷ 5 k 35t ÷ 5 l 36b ÷ 9
e 14f ÷ 7
i 21y ÷ 3 b 8----a- c -1---2---f d 2----4---y-
4 4 3
4 a 1----6---x-
2 f 6----w-- g -1---6---r- h -2---8---n-
6 8 7
e 1----8---m---
9 j -3---6---c- k -3---0---p- l 4----8---d-
6 5 12
i 5----0---x-
5

Fun Spot 6:04 | What do dinosaurs put on their meat pies?

Simplify these expressions. Match the letters to the answers.

A 12v ÷ 6 M Half of 20v O 24v ÷ 8

R Third of 18v S 3----v- T -1---0---v- U 1----2---v-
3 2 3

5v 3v 10v 2v 5v 3v v 2v 4v 6v 4v v

Answers can be found in the Interactive Student CD. 14 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

6:05 Multiplication and Division
of Pronumerals

Name: Class:

Examples • Work from left to right if there is more than
one × or ÷ sign.
1 2p × 6 × 3 = 12p × 3
= 36p • For harder divisions, cancel top and bottom.

4 10k ÷ 2k = 5 -1---0---k- 2 4x × 5 ÷ 2 = 20x ÷ 2 3 10y ÷ 5 × 3 = 2y × 3
1 2k = 10x = 6y

=5 5 18mn ÷ 6n = 31----8---m-----n- 1
1 6n 1

= 3m

Exercise

Simplify. b 8 × 5 ÷ 10 c 18 ÷ 3 × 4 d 20 × 2 ÷ 10
1 a 6×2×5 f 8×4÷2 g 12 ÷ 4 × 7 h 14 ÷ 2 × 5

e 30 ÷ 3 ÷ 2 b 3x × 4 × 2 c 5 × 2m × 4 d 4 × 3 × 5g
f 2k × 4 × 4 g 8×m×3 h 4p × 2 × 9
2 a 10a × 3 × 6
e 7c × 2 × 3 b 12y ÷ 4 × 3 c 5t × 4 d 5t × 4 ÷ 10
f 24a ÷ 3 × 5 g 4p × 4 ÷ 2 h 7 × 6h ÷ 2
3 a 12y ÷ 4 j 10c × 4 ÷ 5 k 9q ÷ 3 × 5 l 24x ÷ 4 ÷ 3
e 24a ÷ 3 n 6x ÷ 6 × 8 o 3j × 8 ÷ 12 p 18m ÷ 9 × 4
i 5 × 6w ÷ 10 r 8u × 4 ÷ 2 s 10y ÷ 2 × 10 t 4c × 9 ÷ 6
m 6 × 10m ÷ 4
q 30c ÷ 3 ÷ 2 b 10ab ÷ 2b c 6x ÷ 2x d 11t ÷ t
f 5ab ÷ a g 20xy ÷ 10y h 12gh ÷ 3gh
4 a 8m ÷ m j 27q ÷ 3q k 18fg ÷ 2g l 10xy ÷ 2xy
e 4c ÷ 4c n 100n ÷ 25 o 40hc ÷ 8hc p 55jm ÷ 5j
i 30pq ÷ 6p
m 26cd ÷ 2c

Answers can be found in the Interactive Student CD. 15 © Pearson Education Australia 2006.
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INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet Class:

6:06 Using Algebra

Name:

Examples 12 m b 4a mm
1 Find the perimeter and area. a

3x m 6 mm 6 mm

5x m

Perimeter = 3x + 12 + 5x m 4a mm
= 8x + 12 m
P = 4a + 6 + 4a + 6 mm
Area = -1- × 12 × 3x m2 = 8a + 12 mm

2 A = 6 × 4a mm2
= 24a mm2
= 6 × 3x m2
= 18x m2

2 Ian had $2 to buy lollies at the local shop. If he bought a bag of mixed lollies for 50 cents
and a giant snake for 4y cents, what was his change?
$2 = 200 cents
∴ Change = 200 − 50 − 4y cents
= 150 − 4y cents

Exercise

1 Find the perimeter of each shape. Measurements are in metres.

a 4 b x c 10b
10b
3 7 4b 5p

5 20 4b
8
d e 4t f

7y 13 3t

2 Find the area of each shape. Measurements are in centimetres. 4

abc

23

6 x 10h
8t
d ef
5
5q 6c

79

3 a Helen bought 2 shirts priced at $3y each and 4 ties at $7 each. What was the total cost?

b Janet paid $10 for a game of ten-pin bowling and Clive paid $5d. What was the total cost

if Janet played 4 games and Clive played only 3?

c CDs cost $6x each and DVDs cost $8x each. If Tina bought 4 CDs and 5 DVDs, find:

i the total cost ii the change from $200.

Answers can be found in the Interactive Student CD. 16 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet Class:

6:09 Factorising

Name:

Examples • To factorise, take the HCF of each term to the
front of the bracket.

• Check your factorising by mentally expanding.

1 Complete. b 6p − 3 = 3(… − …) c 8p + 12q = 4(… + …)
a 5x + 15 = … (x + 3) Ask 6p = 3 × ? → 2p Ask 8p = 4 × ? → 2p
HCF of 5 and 15 is 5 Ask 1 = 3 × ? → 1 Ask 12q = 4 × ? → 3q
∴ 5(x + 3) ∴ 3(2p − 1) ∴ 4(2p + 3q)

2 Factorise. c 10m + 25n
HCF = 5
a 2a − 10 b 12 + 18x ∴ 5(… + …)
10m = 5 × ? → 2m
} {HCF = 2 You will HCF = 6 25n = 5 × ? → 5n
‘think’ these ∴ 6(… + …) ∴ 5(2m + 5n)
∴ 2(… − …) steps with 12 = 6 × ? → 2
2a = 2 × ? → a 18x = 6 × ? → 3x
10 = 2 × ? → 5 practice.

∴ 2(a − 5) ∴ 6(2 + 3x)

1 a Expand 2(x + 4) Exercise c Expand 6(4m + 1)
Factorise 2x + 8 Factorise 24m + 6
b Expand 5(a − 7)
2 Complete. Factorise 5a − 35 c 9k − 12 = … (3k − 4)
a 3x − 3 = 3(… − …) f 8p + 4 = 4(… + …)
d 10a + 15b = 5(… + …) b 10y + 18 = 2(… + …) i 20c + 16 = … (5c + 4)
g 6x − 10y = 2(… − …) e 6 + 15m = … (2 + 5m) l 14 − 35w = … (2 − 5w)
j 11d + 22 = 11(… + …) h 20t − 5 = 5(… − …)
k 12q + 30 = 6(… + …) c 8a − 8c
3 Factorise. f 10x − 10
a 8x + 16 b 6m + 6n i 5x + 45
d 7d − 14c e 3g + 6 l 6x + 8
g 9e − 27 h 4y + 24 o 9a + 21b
j 3b − 30 k 4z − 16 r 21a + 77
m 6m − 21 n 20y − 12 u 12 − 18h
p 45b + 72a q 30 − 12g x 40h + 32c
s 15r + 50 t 6m − 27n
v 8j + 6m w 24 − 18l

Answers can be found in the Interactive Student CD. 17 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

6:10A Algebraic Fractions 1

Name: Class:

Examples

1 -3- + -1- 2 3----a- + -4---a- 3 -5---x- − -4---x- 4 -7---c- + -9---c- 5 -1---9---m--- − 1----3---m---
55 10 10 12 12 12 12 20 20

= 4-- = -7---a- = --x--- = -1---6---c- (÷ 4) = 6----m--- (÷ 2)
5 10 12 12 20

• When the denominators (bottoms) are the = 4----c- = 3----m---
same, add or subtract the numerators (tops). 3 10

• If possible, then simplify by cancelling.

Exercise

Simplify. b -7- − 6-- c --1--- + 1----0- d --9--- − --3--- e 5-- + -2-
1 a -1- + -1- 88 12 12 10 10 66

33 b -7---x- − 6----x- c --a--- + 1----0---a- d -9---y- − -3---y- e -5---m--- + 2----m---
88 12 12 10 10 66
2 a -x- + -x-
33 g -7---k- − -3---k- h 2----t + 3----t i 5----t − 4----t j -3---p- + 4----p-
10 10 77 99 55
f -c- + 2----c-
55 l -5---w-- + -1---1---w-- m 5----x- + -x- n -8---y- − --y--- o -2---p- + -p-
12 12 88 13 13 qq
k -6---w-- − 3----w--
11 11 q 3----q- − -2---q- r -7---p- + -6---p- s 3----x- + 7----x- t --n--- + -7---n-
88 10 10 88 15 15
p -c- + -c-
44 b --9----x-- − --3----x-- c --k--- + -7---k- d -4----t + -7----t
100 100 20 20 25 25
3 a 1----4---m--- + -1---3---m---
100 100 f 1----3---b- + -5---b- g 1----2---y- − -2---y- h 1----9---c- − -1---7---c-
20 20 25 25 20 20
e 1----9---a- + 1----1---a-
100 100 j -5---1---h- − ----h---- k -7---x- + -5---x- l -6---0---y- − --5----y--
100 100 20 20 100 100
i 3----9---m--- + ---m-----
100 100

Fun Spot 6:10A | How do you make a hotdog stand?

Simplify each fraction. Match the letters to the answers.

A 3----x- C 5----x- E -3---x- H 6----x- I -8---x-
12 10 9 16 12

L -2---x- R 1----5---x- S 1----2---x- T -1---5---x-
10 18 20 20

3----x- 3----x- -x- -x- -x- 2----x- -3---x- -3---x- -x- -3---x- -x- 2----x- 5----x-
54345 345 28436

Answers can be found in the Interactive Student CD. 18 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

6:10B Algebraic Fractions 2

Name: Class:

Examples When multiplying fractions:
• cancel if possible (divide top and bottom)
• multiply top and bottom.

1 -3- × 1-- 2 4-- × -1---4- 3 5-- × -2---4- 4 3----x- × -1---0- -1---0- 2
5 9x 9x 3
54 79 6 25 = 13----x- ×
15
(nothing cancels) = 4-- × 1----4- 2 = 1 -5- × -2---4- 4 = 2--
= --3--- 71 9 1 6 25 5
3
20 = 8-- = 4--

9 5

Exercise

Simplify. b -1- × 2-- c 5-- × --1--- d 1-- × 1----0-
1 a -1- × -1-
45 6 15 57
33
f -7- × -2- g -3- × 1-- h 7-- × 2--
e -3- × -2-
83 54 93
53
j -1- × -1---0- k 1-- × 3----0- l 3-- × -7-
i --1--- × 5--
5 11 6 37 49
10 6
n --7--- × 2-- o -6- × --5--- p -1- × --1---
m -2- × 4--
10 3 7 12 2 10
95
b --3--- × --1--- c -4- × -3- d 1-- × --9---
2 a -1- × -4-
10 10 98 6 10
25
f -8- × 3-- g -2- × -1---5- h 1----3- × -6-
e -7- × -6-
94 58 20 7
87
j --7--- × 5-- k -5- × 1----2- l --9--- × --5---
i --3--- × --5---
20 7 85 20 18
10 18
n --3--- × --6--- o --3--- × --5--- p 1----6- × 3--
m -4- × -5-
10 21 25 12 92
58
b -a- × 1----0- c -3---m--- × -5-- d --3--- × -4---y-
3 a 2----x- × -6- 5a 10 m 2y 5
3x
f -l- × -9--- g 1----2- × -k- h 8-- × -3---h-
e -5---j × ---1---- 3 2l k4 h8
6 15j

Fun Spot 6:10B | What lies down a hundred feet in the air?

Simplify each fraction. Match the letters to the answers.

A --4--- C --5--- D 1----0- E -1---0-
12 25 12 15

I -1---6- N --6--- P --9--- T -1---2-
20 20 18 30

-1- -1- 2-- --3--- -2- -4- 1-- -2- 5-- 2--
3 5 3 10 5 5 2 3 6 3

Answers can be found in the Interactive Student CD. 19 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet Class:

7:01 Algebra Review

Name:

Examples • When adding or subtracting, count, as with numbers.
• When multiplying or dividing, omit the × and ÷ signs.
1 10k + 3k
= 13k 2 15x − 2x 3 4×h
= 13x = 4h
4 −7 × m
= −7m 5 a÷4 6 3×p÷2
= -a- = 3----p-
4 2

Exercise

1 a 5×x b a÷2 c −3 × p d m÷7 e c÷3
f 10 × d g g÷4 h 8×k i 9×z j 6y ÷ 7
k t÷8 l 3×x÷5 m 2 × 6p n −20 × a o 4t ÷ 3

2 a 2x + 3x b 7y − y c 5a + a d 6q − 3q e 2c + 8c
f 4t + 7t g 8m − 5m h 12x − 11x i 6h + 2h j 4d − 3d
k 9f − 4f l 9g + 4g m 3y + 8y n 4b + 15b o 7n − 2n

3 a a+3−3 b b×4÷4 c m−8+8 d y÷2×2
e x×7÷7 f p + 10 − 10 g 3×a÷3 h m−6+6
i w+8−8 j y×5÷5 k t−9+9 l 10 × g ÷ 10
m x÷4×4 n y ÷ 13 × 13 o k + 11 − 11 p 2m − 3 + 3

Fun Spot 7:01 | What can jump higher than a house?

Use a = 6, b = 3, c = 10 to find each of the following. Match the letters to the

answers.

A a+b C b+c E b + c − a G 2b + c H a + 4c

I 7a J c − b + 10 M a + b + c N 4c O ab

P a-- S -c- T c − b − a U 5b Y a2
b 2

,

9 40 36 1 46 42 40 16

46 18 15 5 7 5 ’ 17 15 19 .

13 9 40 1 2

Answers can be found in the Interactive Student CD. 20 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

7:02 Solving Equations 1

Name: Class:

Examples The basic rule for solving
1 Solve: equations is do the opposite.

a − 3 = 10 b + 8 = 12 c 5 × = 40 d ÷6=3

opposite of − 3 is + 3 opposite of + 8 is − 8 opposite of × 5 is ÷ 5 opposite of ÷ 6 is × 6

∴ = 10 + 3 ∴ = 12 − 8 = 40 ÷ 5 =3×6
= 13 =4 =8 = 18

2 Check if = 14 is a solution. To check your solution (or answer), put it
into the equation to see if it makes it true.

a × 2 = 28 b −6=8 c + 4 = 10 d ÷2=7

Check 14 × 2 = 28 Check 14 − 6 = 8 Check 14 + 4 = 10 Check 14 ÷ 2 = 7
True True False True

Exercise

1 Solve these equations. −1=6 c 6× = 18 d ÷2=3 e −3=4
a + 7 = 10 b

f × 8 = 24 g ÷5=4 h + 9 = 12 i 4 × = 12 j + 6 = 10

k −3=3 l ÷3=5 m −7=5 n ÷ 2 = 10 o × 3 = 21

p + 10 = 20 q ÷ 4 = 8 r 6 × = 48 s + 8 = 15 t − 2 = 12

u × 9 = 36 v − 5 = 15 w ÷ 11 = 3 x + 9 = 20

2 Which of the numbers 2, 7 and 10 are solutions to these equations?

a + 4 = 11 b 3 × = 30 c 20 ÷ = 10 d − 3 = 4

e × 6 = 42 f − 7 = 3 g + 8 = 10 h ÷5=2

i ×3=6 j −7=0 k ÷7=1 l + 2 = 12

Fun Spot 7:02B | Why did the bacteria cross the microscope?
Solve these equations. Match the letters with the answers.

D + 5 = 16 E 3 × = 12 G −2=6 H ÷3=4

I + 9 = 12 L × 3 = 6 O − 8 = 10

R + 8 = 15 S 5 × = 25 T ÷8=5

40 18 8 4 40 40 18 40 12 4 18 40 12 4 7 5 2 3 11 4

Answers can be found in the Interactive Student CD. 21 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

7:03 Solving Equations 2

Name: Class:

Examples • The basic rule for solving equations is do the opposite.
• ‘Reading’ the equations can help also.
1 x + 8 = 14
− 8 is opposite 2 7c = 21 3 30 ÷ k = 3 4 y−5 =6
∴ x = 14 − 8 ÷ 7 is opposite 30 ÷ something gives 3 something takeaway 5
=6 ∴ c = 21 ÷ 7 30 ÷ 10 = 3 gives 6
=3 11 − 5 = 6
∴ k = 10 ∴ y = 11

Exercise

Solve these equations by inspection. d -x- = 7
2
1 a x + 15 = 16 b a−9=2 c 4m = 32
h m--- = 6
e a + 8 = 13 f x−3=6 g 2c = 16 3
k -a- = 5
i 7x = 28 j b + 11 = 20 l m−4=8
n -h- = 3 2
m c − 12 = 3 o n + 3 = 14 p 3b = 12
3 s -d- = 10
q 8m = 32 r f − 3 = 14 t x + 7 = 15
u -t- = 9 4
v 5y = 30 w g−7=6 x g+1=1
2
2 a 3+a=9 b 10 + y = 11 c m×3=6 d 10 ÷ x = 2
f y × 5 = 35 g x÷5=6 h y + 20 = 30
e 10 − x = 3 j 7 + b = 20 k 13 − n = 3 l 12 ÷ k = 12
i 6×h=6 n x−6=8 o p + 5 = 15 p 8 × t = 48
m 40 ÷ q = 8 r u × 9 = 72 s 15 − y = 0 t f + 9 = 15
q d÷4=9

Fun Spot 7:03 | Why did the golfer wear two pairs of pants?

Solve each equation, then match the letters to the answers.

A x + 10 = 14 C 7x = 14 E x − 8 = 11 G 8−x=3
N x+8=8
H 4x = 40 I 9 + x = 18 L -x- = 5
O x÷6=1 S -x- = 4 3

5 T 5x = 15

90 2 4 20 19 10 19 563

4 10 6 15 19 9 0 6 0 19

Answers can be found in the Interactive Student CD. 22 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

7:04 Solving Equations 3

Name: Class:

Examples

1 Solve these equations. 2 Is x = 5 a solution 3 Expand 5(3c − 7).
5 × 3c − 5 × 7
a a − 7 = 13 b 4x = 24 to 3x − 4 = 10? = 15c − 35
Substitute x = 5.
opposite is + 7 opposite is ÷ 4
3 × 5 − 4 = 10
a = 13 + 7 x = 24 ÷ 4 11 = 10

= 20 = 6 ∴ No

Exercise

1 Solve these equations.

a a + 11 = 30 b b − 5 = 21 c 4x = 36 d y ÷ 3 = 11
g t÷3=3 h 6x = 54
e g−1=1 f r + 9 = 20 k y + 8 = 13 l a÷8=5

i 7u = 7 j m−4=5

2 Is x = 8 a solution? b 4x = 48 c x−8=0
a 2x + 1 = 17 e 3x − 5 = 19 f 2(x + 3) = 22
d -x- = 16
2 b 3(x − 2) = 18 c x-----+-----2- = 3
3
3 Is x = 4 a solution? -x-
a 3x + 4 = 16 e 4 +3=4 f 5x = 3x + 8

d 16 − 3x = 2 b 5(x − 7) c 2(4a − 3) d 7(p − 4)
f 9(5q + 8) g 3(2m + 7) h 2(3k + 4)
4 Expand. j 8(2w − 3) k 5(3y − 4) l 6(3h − 2)
a 3(2x + 5)
e 6(3h − 1)
i 4(5t − 3)

Fun Spot 7:04 | Why was the centipede an hour late for the soccer match?

Solve the equations and match the letters to the answers.

A a + 7 = 13 E 3a = 21 H 7−a=2 I -a- = 2 K 5a = 50 N a − 8 = 4
R 10a = 10 4
O -a- =4 P a + 4 = 13 T a − 15 = 0 U -a- = 5
8 S 7=a+7 6

8 15 15 32 32 10 8 15 6 12 5 32 30 1

15 32 9 30 15 8 15 0 0 5 32 7 0 .

32 12

Answers can be found in the Interactive Student CD. 23 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet Class:

7:05 Formulae

Name:

Examples • Substitute the values given into the formula.
• Calculate the answer—you may have to
1 Use the formula A = LB to
find A when L = 4, B = 10. solve the equation.
A = 4 × 10
∴ A = 40 2 Use F = ma to find m if 3 If v = u + at, find u when
F = 50, a = 8. v = 40, a = 3, t = 5.
50 = m × 8 40 = u + 3 × 5
∴ m = 50 ÷ 8 = u + 15
u = 40 − 15
m = 6 -1- = 25

4

Exercise

1 If F = m × a, find the value of F if:

a m = 4 and a = 5 b m = 10 and a = 7 c m = 3 and a = 8
f m = 12 and a = 20
d m = 6 and a = 9 e m = 8 and a = 0·5

2 If A = C + P, find the value of P if:

a A = 12 and C = 7 b A = 20 and C = 5 c A = 8 and C = 1
f A = 40 and C = 23
d A = 10 and C = 2·5 e A = 6·3 and C = 1·7

3 Use v = u + at to find v when: b u = 20, a = 6, t = 4 c u = 7, a = 8, t = 9
a u = 5, a = 4, t = 3 e u = 22, a = 4, t = 6 f u = 50, a = 7, t = 11
d u = 4, a = 3, t = 5

4 Use A = LB to find the value of L when:

a A = 50, B = 5 b A = 24, B = 3 c A = 12, B = 6
f A = 25, B = 4
d A = 100, B = 4 e A = 100, B = 20

5 Use A = πr2 to find the value of A when:

a r=8 b r=5 c r = 10 d r = 9·2 e r = 20 f r = 1·8

(Use the π button on your calculator, and answer to one decimal place.)

Fun Spot 7:05 | Why do firemen wear red suspenders?

Calculate the following. Match the letters with the answers.

A 4+3×2 E 3 × 22 H 16 − 4 × 2 I 5×3+4
P (2 × 3)2
K 5×3×2 N 2+4×3 O 20 − 12 ÷ 4 U 10 + 20 ÷ 4

R 7×3 S 42 T 50 − 3 × 8

26 17 30 12 12 36 26 8 12 19 21 36 10 14 26 16 15 36

Answers can be found in the Interactive Student CD. 24 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

7:07 Number Line Graphs

Name: Class:

Examples

• To graph numbers on a number line, mark them with a dot.
• The notation {2, 4, 6, 8} means the set of numbers 2, 4, 6 and 8.

1 Graph each set of numbers. b {−2, −1, 0, 2}
a {2, 4, 6, 8}

02 468 −4 −3 −2 −1 0 1 2 3 4

2 Write down the set of numbers. 4 b
a
0 1 234567
−4 −3 −2 −1 0 1 2 3
{0, 1, 2}
{−2, 0, 2, 4}

3 Express each inequality in words.

a aϽ5 b x Ͼ −3 c h р 10
All numbers less
All numbers less All numbers greater than or equal to 10

than 5 than −3

Exercise

1 Graph each set on a separate number line.

a {1, 2, 3} b {−3, −2} c {0, 2, 4} d {1, 3, 5, 7}
g {5, 2, −1} h {2, −4, 0, −1}
e {−6, −4, −2, 0} f {−3, 3} k {−6, −2, 0} l {5, 3, 1, −1, −3}

i {8, 4, 0, −4} j {0, −4, −2, 6}

2 Write the set shown on each number line. b
a
−3 −2 −1 0 1 2 3 4 5
−2 −1 0 1 2 3

c d

−3 −2 −1 0 1 2 3 4 0 1 234567

e f

−5 −4 −3 −2 −1 0 1 −7 −5 −3 −1 0 1

g h

−2 0 2 −3 −2 −1 0 1 2 3

3 Express each inequality in words.

a kϾ4 b x Ͻ −4 c qϾ0 d mϽ1
g c р 20 h y р −5
e xу2 f h у −3

Answers can be found in the Interactive Student CD. 25 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

7:08 Solving Inequations

Name: Class:

Examples

1 Is x = 2 an answer to the following? 2 Is a = 10 an answer to the following?
a -a- Ͻ 4
a x + 5 Ͻ 10 b 4x у 10 No 5 b a−6Ͼ7
2 + 5 Ͻ 10 4 × 2 у 10 10 − 6 Ͼ 7
7 Ͻ 10 1----0- Ͻ 4
Yes 8 у 10 5

2 Ͻ 4 Yes 4 Ͼ 7 No

3 Solve. b -x- у 3

a m − 6 Ͻ 10 4x у 3 × 4 c h+5р4 d 6v Ͼ 18
v Ͼ 18 ÷ 6
m Ͻ 10 + 6 h р4−5

∴ m Ͻ 16 ∴ x у 12 ∴ h р −1 ∴vϾ3

Exercise

1 Is x = 5 an answer to the following?

a x+1Ͼ3 b 3x р 12 c x−4Ͻ8 d 5x Ͼ 10

2 Solve.

a x+1Ͼ3 b 3x р 12 c x−4Ͻ8 d 5x Ͼ 10 e c − 5 р 10
f -c- Ͼ 5 g c + 6 Ͻ 10 h -c- Ͻ −2 i 7m Ͻ 28 j m+8Ͻ3

3 l 2m Ͼ −8 4 n -y- у 10 o y + 7 р 10
k m−1у5 q -t- Ͼ 2 m -y- Ͻ 6 3 t t−7у6

p y−4Ͼ7 3 4 s 3t Ͼ 18

r t + 3 р 10

3 Is t = 12 an answer to the following?

a -t- Ͼ 2 b t + 3 р 10 c 3t Ͼ 18 d t−7у6
3

4 Is m = 3 an answer to the following?

a 7m Ͻ 28 b m+8Ͻ3 c m−1у5 d 2m Ͼ −8

Fun Spot 7:08 | What do you call a monkey with a banana in each ear?

Calculate the following. Match the letters with the answer.

A 10 + 5 C 7 × 4 E 9−2 G −3 × 4 H 15 ÷ 5 I 11 − 9

N 30 ÷ 3 O 19 − 11 R 16 + 9 T −3 + 4 U 8 × (−2) Y 20 ÷ 4

,

15 10 5 1 3 2 10 −12

37 ’ 3 7 15 25 .

28 15 10 1 5 8 −16

Answers can be found in the Interactive Student CD. 26 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

8:06 Graphing Straight Lines

Name: Class:

Exercise

1 Write the name of the point with the following y

coordinates. 4

a (0, 0) b (1, 3) c (3, −2) 3D

d (−1, 2) e (−3, 0) f (−1, −2) G J2B N

g (3, 1) h (0, 2) i (2, −1) 1A

ME O C

j (−3, 2) k (2, −3) l (2, 0) −4 −3 −2 −1 0 1 2 3 4x
−1 K

Q I −2 F R P

−3 L H

−4

2 Substitute the given value of x to find the value of y. Complete the table.

a y=5−x b y = 2x + 3 c y = 4x − 1

x = 0, y = 5 x = 0, y = 3 x = 0, y = …

x = 1, y = … x = 1, y = … x = 1, y = …

x = 2, y = … x = 2, y = … x = 3, y = …

x = 3, y = … x = 3, y = … x = 5, y = …

x0123 x0123 x0135
y5 y3 y

3 Complete each table. Draw each line on a number plane.

a y=x+5 b y = 3x c y = 4 − 2x
x0123
x0123 x0123 y
y y

4 Write down the equation of each line. by
ay
1
2
1 2 3x
1

−2 −1 1 2 3x −2 −1
−2 −2
−3

y y

c4 d3

3 2
2 1
1

−3 −2 −1 1 2x
−2
−2 1 2 3x −3
−1
−2

Answers can be found in the Interactive Student CD. 27 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

9:01 Picture Graphs and Column
Graphs

Name: Class:

Exercise Crates on the truck

1 A truck carries 100 crates of soft drink. The graph = 4 crates
gives the number of crates of each different type
of drink. Lemonade
a What is the key to this picture graph? Cola
b What type of drink has the following?
i the least number of crates Orange
ii the greatest number of crates Lime
c i How many crates of lime are there?
ii How many crates of passionfruit are there? Passionfruit
Bitter lemon

Dry ginger
Soda water
Pineapple

2 After her spring clean-out, Keira counted the different

clothes in her wardrobe, as shown on this graph.

a How many pieces of clothing are

represented in the picture graph?

b i How many jeans?

ii How many T-shirts? = 2 pieces of clothing

c Put a heading on the graph. Jeans
T-shirts
d What does Keira have three of? Jumpers

Skirts
Jackets

3 The local bookshop’s sales for a week are shown in Book sales
this column graph.
a Label the vertical axis. 16
b What was the most popular type of book? 14
c How many of these were sold? 12
d What was the least popular? 10
e How many of these were sold?
f How many autobiographies were sold? 8
g How many books were sold altogether? 6
4
2
0
Rainfall (mm)
4 a In which month would you expect the Autobiographies
Biographies
Novels
Recipe books
Travel books
Gardening books
Dietary books
Children’s books
following? Monthly rainfall in Pepperland

i the most rain ii the least rain 140
120
b What was the rainfall for the following? 100

i February ii June 80
60
iii October 40
20
c Which months had the following rainfall?
0
i 70 mm ii 100 mm J F M A M J J A S O N D Month

iii 60 mm

Answers can be found in the Interactive Student CD. 28 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

9:02 Reading Graphs

Name: Class:

1 This picture graph shows the number of students District competitors

who entered district sports competitions.

a How many competitors were there for

the following?

i bowling ii swimming

b Which sports had the least and most = 5 competitors
competitors? How many students were
Swimming
there for each? Tennis

c Which sport had 12 competitors? Archery
Athletics
Bowling

Squash

2 The results of a survey in our street concerning the Pets in our street

number and type of pets kept by each household 12 Dogs
are shown here. 10 Cats
a What type of graph is this? Birds
b What is on the horizontal axis? 8 Fish
c How many cats are in our street? 6 Carpet snakes
4 White mice
2 Horses
0 Rabbits

d How many horses?

e i Which pet was the most popular?

ii Which pet was the least popular?

3 This is a sector graph showing the budget for a A small business budget

small business with gross takings of $200 000. Stock Insurance
20% 10%
a What is another name for a sector graph? Electricity
b What percentage is missing for wages? 2% Profit Equipment
10% 5%

c What angle is needed for these sectors?

i insurance ii stock iii rent

d What was most money spent on? Wages Rent
25%
e How much is the expected profit?

f How much is expected to be spent on electricity?

4 This divided bar graph is the result of a survey of 400 vehicles passing a roundabout.

a 1 cm represents … vehicles. Vans and
utes
b How many cars passed the roundabout?
Motor cycles
Cars Trucks

c How many motor cycles passed the

roundabout?

d How many vehicles were not vans and utes?

e What percentage of vehicles were trucks?

Answers can be found in the Interactive Student CD. 29 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

9:05 Travel Graphs

Name: Class:

Exercise

1 a How far from home was Jim at: Distance from home (km) Jim’s walk
3
i 2 pm? ii 3 pm? iii 4 pm? 2
1
iv 5 pm? v 1.30 pm? 0

b At what time was Jim: 1234 56
Time (pm)
i 2 km from home?
5 Tim’s journey
ii 1·5 km from home? 4

c What might have happened from 4 to 6 pm? 3

2 This graph shows Tim’s journey when he calls Distance in kilometres 2
to see his friend.
a How far away does his friend live? 1
b He stopped on the way for refreshment.
i How far from home was this?
ii For how long did he stop?
c How long did it take Tim to reach his friend?

0 10 20 30 40
200 Time in minutes

3 a When did the motorist begin her trip? Travel graph of motoring trip
b How far did the motorist travel in the first
2 hours? Distance in kilometres 160
c What was her speed on this section?
d What do the horizontal sections on the graph 120
mean?
e How far from home was the motorist at: 80
i 1.30 pm? ii 3 pm?
40
4 Smith is travelling from A to B, while Brown leaves B
to go to A. 0
a How far apart are A and B? 10 am 11 am noon 1 pm 2 pm 3 pm 4 pm 5 pm
b When do Smith and Brown pass each other?
c When did Brown stop and for how long? Time of day
d How long did it take Smith for the journey?
e How far did Smith travel? Smith and Brown’s graphs
f What was Smith’s average speed? 300 B
g How far had Brown travelled by 10 am?
h How far did Smith travel between 9 am and noon? 250
i Who had the safest journey and why?
Distance in kilometres 200

150

100 Smith

50

0A
9 am 10 am 11 am noon 1 pm 2 pm 3 pm

Time of day

Answers can be found in the Interactive Student CD. 30 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

10:02 Angle Relationships

Name: Class:

Examples

• The angles at a point add to 360°. (They form one revolution.)
• When two lines cross, the vertically opposite angles are equal.

1 2 3 4

x° 95° m° c°
140° a° 94° 35°
132°
200°

x + 140 = 360 a + 95 + 200 = 360 m = 132 c + 35 = 94
x = 360 − 140 a = 360 − 200 − 95 ∴ c = 59
= 220 = 65

Exercise

1 Find the value of each pronumeral. c d
ab
155° 85°
100° c° 40°
160°
a° d°
300° b°
h
e f g
216°
e° 40° 103° g° h°

180° f° l

i j k 120°
110° l°
110° 145° j° 80°
i° 80° 70° d

35° k° 95° e° 53°

2 Find the value of the pronumerals. d° 47°

ab c h

37° b° 134° c° 35°
a° 113° 50° 25°

e f g h°

95° e° 27° 95° 45°
g°
f°

Answers can be found in the Interactive Student CD. 31 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

10:05 Triangles and Quadrilaterals

Name: Class:

Examples • The angles in a triangle add to 180°.
• The angles in a quadrilateral add to 360°.

1 110° 36° 2 53° 3 100° y° 4 40° 35°
m°
a° 70°
25°
65°
a + 36 + 110 = 180 x° m + 25 + 40 + 35 = 360
m + 100 = 360
∴ a = 180 − 110 − 36 y + 70 + 65 + 100 = 360
= 34 x + 53 + 90 = 180 y + 235 = 360 ∴ m = 260
∴ x = 180 − 53 − 90 ∴ y = 360 − 235

= 37 = 125

Exercise

Find the value of each pronumeral.

1 2 b° 3 c° 4 24° p°
43°
60° 27° 131°

a° 110°

5 70° 6 80° 7 g° 8 68°
h°
50° t° 94° 140°
80° y°
92° 20°

9 10 11 115° 12 y°

66° 74° k° 28°

x° 220° 67° 34°
35° c° 87°

13 14 15 16 t°

m° 62° 34° 38°

120° 73° p° q° 20
75° 57° 21°
18 x° 13°
17 27° 19 95°
69°
160° 46° 100°

128° y°

x° w°

Answers can be found in the Interactive Student CD. 32 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

10:07 Finding the Angles

Name: Class:

Exercise

Find the value of each pronumeral. 3 4 d° 90°
12
50° c°
70° a° 120°

b° 70° 100°
70°
5 50° 6 7
8
x° 110° 132° m°
a° 93° 106° 137° p°

9 10 11 12

w° y° 27° c° 42°
134° 83° h°

30°

13 14 15 16

160° 70° 52° 75°
70° k°
14° r°
t°
23° 55°
17 v°
18
u° 33° 19 a° 40° 20
x°
21 78° y°

q° 73° 22 100° 65°

25 100° 23 24 t° 110°

48° a° 2x° 75° 60°
h°
26 n° 47° 27 60° 28

76° x°
28°
j°
73°

Answers can be found in the Interactive Student CD. 33 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS

Foundation Worksheet

11:02 Finding the Area

Name: Class:

Examples Area of a triangle = 1-- bh Area of a parallelogram = bh

Area of a rectangle = lb 2 3
1
2 5m
7 cm
6 cm
15 cm
10 cm 20 m
Area = 15 m × 7 m
= 105 m2 Area = -1- × 10 cm × 6 cm Area = 20 m × 5 m
= 100 m2
2

= 30 cm2

Exercise

Find the area of each figure. b c
1a
5m 8 cm
4 cm

10 cm 5m 17 cm

d e f

8m 11·6 cm 20 m

5m 7·3 cm 50 m

2a b 20 m c

4 cm 12 m 9 cm
8 mm
10 cm e 16 cm

d 6m f 13·8 cm

14 mm 18 m

6·2 cm

3a b c
d
4 cm 9m

14 m

10 cm e 13 m f 16 m
2·3 m 25 m
15·6 cm 7·1 cm

1·2 m 34 10 m

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

Foundation Worksheet

11:04 Volumes of Prisms

Name: Class:

Examples Volume = area of each layer × number of layers
1 = cross-section area × height

2 A = 23 m2 3 10 m

4m

6m

Area of layer = 4 × 5 cm2 Volume = 23 m2 × 16 m Area of top = 10 m × 4 m
= 20 cm2 = 368 m3 = 40 m2

Volume = 20 cm2 × 3 cm Volume = 40 m2 × 6 m
= 60 cm3 = 240 m3

Find the volume of each prism. Exercise

1a 3 cm b 3 cm c d

3 cm

2a 2 cm b A = 12 m2 c d A = 47 cm2
A = 15 cm2 19 cm
3 cm 7m A = 30 m2 11 m

3a 6 cm b 10 m c 7 cm d

9m 15 m

4 cm 7 cm
7 cm
2 cm 10 m 14 m
8 cm
e f 9 cm g
h
20 m 2 cm 5 cm

j k 11 mm 15 m

8m 7m
4m
9m
l
i

2·7 m 8·6 m 13·5 cm 7·2 cm 7·1 m 7·6 cm
5·2 m 12·2 cm 5·3 m
13 m

Answers can be found in the Interactive Student CD. 35 © Pearson Education Australia 2006.
This page may be photocopied for classroom use.
INTERNATIONAL MATHEMATICS 2 FOUNDATION WORKSHEETS