Answers

Chapter 1 8 a BCE stands for Before the Common Era and CE

stands for the Common Era.
SkillCheck b Traditionally, the zero for time is when Jesus
Christ was born. BC, meaning Before Christ,
1 a 16 b 8 c 28 d 4 refers to the time before Christ. AD, meaning
e 21 f 25 g 22 h 5 Anno Domini (‘in the year of our Lord’ in
i 13 j 8 k 15 l 6 Latin), refers to the time after Christ was born.

2a 49 b 604 c 70 d 33 9 BCE C B H J D A E I F G CE
500 0 500
e 237 f 128 g 23 h 2
i 28 j 400 k 12 l 32 10 a Teacher to check. b Teacher to check.
m 9 n 25 o 64 p 1

3a T b T c F d T
Exercise 1-02
e F f F g T h T
i F
1 A ¼ 4, B ¼ 9, C ¼ 11, D ¼ 17, E ¼ 20, F ¼ 27
4 a 1, 2, 3, 4, 8 2a A ¼ 2, B ¼ 10, C ¼ 13, D ¼ 15
b 2, 3, 5, 7, 16, 18 b A ¼ 10, B ¼ 16, C ¼ 28, D ¼ 34, E ¼ 37
c 27, 38, 49, 51, 54, 66 c A ¼ 8, B ¼ 15, C ¼ 32, D ¼ 41, E ¼ 49, F ¼ 56
5 a 18, 17, 11, 6, 5, 3 d A ¼ 4, B ¼ 36, C ¼ 52, D ¼ 66, E ¼ 90, F ¼ 116
b 31, 23, 14, 8, 7, 5, 2 e A ¼ 10, B ¼ 20, C ¼ 35, D ¼ 55, E ¼ 63,
c 91, 89, 69, 46, 41, 37, 3 F ¼ 89, G ¼ 111
3 a Missing values are 5, 4, 2, 4, 5, 7, 8
Exercise 1-01 b Missing values are 50, 40, 30, 20, 30, 50,
60, 70
1 a 100C b body temperature c Missing numbers are 35, 30, 25, 20, 15,
c 74C d water freezes 10
e 117C d Missing numbers are 400, 300, 200, 200
e Missing numbers are 33, 30, 27, 24, 21,
2 a 6 b 1 c 10 18, 15, 12, 9, 6
d 11 e 0 f 2
4a
3 a down b less c up –5 –4 –3 –2 –1 0 1 2 3
d right e after f north
g deposit h increase i east b
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
4 a i about 38 metres
ii about 73 metres 5 a 29 b 35 c 32
iii about 111 metres d 20 e 12 f 5
b ‘þ’ signs measure height above water level and
6a 1 b 4 c 6
‘’ signs measure depth below water level
d 6 e 12 f 15
5 $410
Exercise 1-03
6a depositing $25 in the bank
b losing $12 1a > b < c > d >
c walking 2 steps forward e > f > g < h <
d increasing the temperature by 3 i < j < k < l >
e driving 5 km east m > n > o < p <
f decreasing the price by $8
g going down 3 floors 2a 7 b 8 c 8, 6, 4, 2, 1, 3, 5, 7
h 5 seconds after take-off
70
534 9780170188777
 Answers

3a 3, 1, 2, 3 Mental skills 1A

b 8, 5, 3, 2, 5
c 10, 6, 4, 3, 0 2a 155 b 221 c 317 d 1764
d 5, 3, 2, 4, 6 e 48 f 726 g 283 h 952
e 48, 24, 11, 0, 8, 36 i 722 j 631 k 215 l 163
f 26, 10, 2, 3, 12, 15 m 394 n 466 o 937 p 295
4a 5, 4, 3, 1, 2
b 8, 0, 2, 4, 7
c 4, 1, 1, 3, 5, 11 Exercise 1-05
d 8, 3, 2, 4, 18
e 1, 3, 6, 15, 48 1a 2 b 2 c 10 d 6
f 33, 1, 36, 58, 100 e 13 f 1 g 0 h 10
i 9 j 1 k 7 l 6
5a 2 b 2 c 4 d 3
m 5 n 6 o 12 p 9
e 6 f 20 g 7 h 7

6D 2B

7 a 4 b 6 c 4 3 a No, 10  4 ¼ 6, 4  10 ¼ 6
d 2 e 12 b No, 5  9 ¼ 14, 9  (5) ¼ 14
c No, they give different answers.

Exercise 1-04 4a 11 b 11 c 29 d 29

e 31 f 23 g 16 h 10
1a 4 b 5 c 1 d 2 i 50 j 50 k 42 l 42
e 0 f 4 g 3 h 4 m 12 n 5
i 20 j 4 k 8 l 0
m 2 n 2 o 11 p 6 5 You get the negative of double the integer.

2C 6 a (þ) b () c (E)

d (þ) e (E)
3 a Yes, 4
b Yes, integers can be added in any order. 7a 4 b 4 c 3 d 3
e 1 f 1 g 4 h 4
4a 12 b 0 c 20 d 23
i 2 j –2
e 15 f 0 g 3 h 9
i 19 j 10 k 32 l 9
8a 7 b 3 c 8
m 0 n 5
d 8 e 1 f 6
5 The answer is always zero.
9 Teacher to check.
6 a (þ) b () c (E)
7 a 4 b 7 c 3
d 7 e 3 f 7 Exercise 1-06

8 Teacher to check. 1a 18 b 24 c 21 d 32

e 63 f 45 g 42 h 42
9 Teacher to check. i 24 j 6 k 1 l 54
m 10 n 42 o 44 p 81
q 60 r 60 s 100 t 56

2a C b A c D

9780170188777 535
 Answers

3a × –3 5 b × –5 5 Exercise 1-08
–3 9 –15 5 –25 25
5 –15 25
1a 7 b 22 c 1 d 7
–5 25 –25
e 6 f 4 g 25 h 8
c × 6 –4 d × –1 1 i 21 j 12 k 200 l 28
–4 –24 16 –1 1 –1 m 15 n 5 o 3
6 36 –24 1 –1 1 2C
e × 7 –3 f × –3 –6 3a 7 b 25 c 36
4 28 –12 8 –24 –48 d 10 e 14 f 3
–6 –42 18 2 –6 –12 g 5 h 16 i 2
j 8 k 11 l 2

4 a Yes, both give 24. b Yes 4a 8 b 5 c 3

d 2 e 3 f 12
5 You always get the negative of the integer squared. g 2 h 2 i 19
6a 9 b 9 c 49 d 49 j 9 k 3 l 25
e 25 f 25 g 1 h 1
5a Correct
7 a (þ) b (þ) c () b Incorrect, 32 4 (4) 3 (2) ¼ 16
d (þ) e (þ) c Incorrect, 6 3 (2)  8 ¼ 4
d Correct
8 a 5 b 4 c 3 e Correct
d 7 e 5 f 2 f Incorrect, (2 þ 6) 3 2 ¼ 8
g Incorrect, 7  6 þ 10 ¼ 3
9 Teacher to check.
h Incorrect, (12  3) 4 (3) ¼ 5
i Incorrect, 12  3 3 5 ¼ 3
Exercise 1-07 j Incorrect, 2  9 3 (3) – (18) ¼ 47
6a 4 3 [ 7 – 2 þ (3)] ¼ 8
1a 4 b 2 c 4 d 3 b (4 3 7) – [2 þ (3)] ¼ 27
e 9 f 3 g 3 h 10 c (4 3 7) – 2 þ (3) ¼ 33
i 4 j 7 k 9 l 6 d 40 4 [10 3 (2)] þ 15 ¼ 13
m 9 n 8 o 4 p 6 e (40 4 10) 3 [(2) þ 15] ¼ 52
f 40 4 [10 3 (2) þ 15] ¼ 8
2a A b B
7 Teacher to check.
3 a 6 b 2 c 6 d 16
e 7 f 9 g 20 h 9
Mental skills 1B
4 a × –6 –3 3 6 b × 8 –8 32 –32
–6 1 –1
2
1
––
2
–1 –2 –4 4 –16 16 2a 17 b 35 c 114 d 261
–3 2 1 –1 –2 4 2 –2 8 –8 e 132 f 128 g 56 h 418
i 74 j 123 k 88 l 112
m 36 n 549 o 185 p 317
5 a You get 1
6 a (þ) b (þ) c ()
Exercise 1-09
7 a 8 b 3 c 7 1a 7 b 6 c 4 d 1
d 44 e 50 f 32 e 5 f 14 g 26 h 28
i 30 j 48 k 44 l 30
8 Teacher to check. m 65 n 8 o 15 p 4
q 25 r 64 s 48 t 2

536 9780170188777
 Answers

2 Same answers as question 1. 8 a 5, 2 b 3, 5 c 4, 2

2 2 2
d 3, 2 e 3, 10
3 (5) means 5 3 5 ¼ 25, 5 means (5 ) ¼ 25.
4a 18 b 71 c 1
d 6 e 3960 f 192 Chapter 1 revision
g 5 h 60 i 5
j 38 k 61 l 16 1a 2 b 23 c 56
d 10 e 8 f 0
5 a 13 b 10 c 2
d 15 e 56 f 8 2a
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7
6 Teacher to check.
b
–4 –3 –2 –1 0 1 2 3 4
Exercise 1-10
c
1 13C 2 4 km –5 –4 –3 –2 –1 0 1 2 3

3 a 6610 m b 2316 m c 311 m d 9237 m

3a F b F c F d T
4a 2009, 2010, 2013, 2014 e T f T g T h F
b 2011, 2012 i F j T k T l F
c $100 million
d Profit, $200 million 4 14, 3, 0, 1, 5, 9, 10

5 1 km north 6 $7 7A 5 a 1 b 10 c 3

d 4 e 10 f 3
8 59 9 4602 m 10 280 cm g 11 h 1 i 8
11 155 m below the surface
6a 7 b 4 c 4 d 12
12 $109.00 13 11 m e 0 f 12 g 7 h 6
i 11
14 a 14th day b $60
7 a 18 b 48 c 10 d 44
e 63 f 48 g 24 h 42
Power plus i 40
1a 1 b 1 c 1 8a 3 b 3 c 1
d (1) 3 (1) 3 (1) 3 (1) 3 (1) ¼ 1 d 4 e 2 f 100
e (1) 3 (1) 3 (1) 3 (1) 3 (1) 3 g 2 h 3 i 8
(1) ¼ 1
f (1) 3 (1) 3 (1) 3 (1) 3 (1) 3 (1) 3 9 a 12 b 14 c 13
(1) ¼ 1 d 18 e 0 f 19
g 7 h 2 i 0
2 (1)n ¼ 1 when n is even, (1)n ¼ 1 when n is
odd 10 a 9 b 6 c 12
3 a 4 or 4 b 10 or 10 c 2 d 87 e 52 f 5

4 Yes, no number squared gives a negative answer. 11 16C 12 $820

5 Teacher to check.
6a 2 b 9 c 1
7 a True b False c True d False
e True f True g False h True
i True

9780170188777 537
 Answers

Chapter 2 b \NCD, \NCY, \DCY

c A straight angle
SkillCheck d \ANY or \YNA

1 a 20 b 25 c 15 d 20 7A

e 40 f 80 g 60 h 57 8a • \DBC or \CBD 3 \ADB or \BDA
i 70 j 94 k 28 l 81 b • \PSR or \RSP 3 \PRQ or \QRP
c • \MRQ or \QRM 3 \RNP or \PNR
2 a I and J b A and H, B and I d • \EIF or \FIE 3 \FGI or \IGF
3 a E and F b D and E c C and E e • \DCF or \FCD 3 \GBC or \CBG
d B and E e F and H f D and J f • \WXY or \YXW 3 \YWZ or \ZWY
g A and I h A and J 9 Teacher to check

Exercise 2-01
Exercise 2-02
1a \QPK, \P or \KPQ
1 a 64 b 133 c 85 d 87
b \OCR, \C or \RCO
e 129 f 175 g 157 h 112
c \GVE, \V or \EVG
d \TAG, \A or \GAT 2a \AOB ¼ 38 b \PDQ ¼ 162
e \PQD, \Q or \DQP c \XPY ¼ 84 d \MAN ¼ 121
f \RDC, \D or \CDR e \TQS ¼ 175 f \XYZ ¼ 38
2C g \LMN ¼ 82 h \GFD ¼ 121
i \ADM ¼ 162 j \BPZ ¼ 47
3 a \CAD or \DAC b \PMQ or \QMP k \ABC ¼ 122 l \EFG ¼ 38
c \TQR or \RQT d \WXY or \YXW
e \AED or \DEA f \FGE or \EGF 3 d, a, h, f, c, b, g, e
4 a \ABC ¼ 213 b \XYZ ¼ 300
4 The following are examples, the sizes of the angles c \LMN ¼ 248 d \GHK ¼ 330
will differ.
5B
a P b T 6 Teacher to check
A
7 Teacher to check

O T 8a E b H
F 145°
c A d B
G
H
65°
D R
E
F C
c T d

5 a \SQP b \CBE c angle b d angle q 32°

R G 45°
A B
6 a \NAY, \AYN or \AYC, \ANY or \ANC,
e Q f 265°
\AND, \AYD, \NCD, \NDY, \NCY, \DNC or N
\DNY, \DCY, \CDY, \NYD or \CYD, \NDC M
(Remember that \NAY and \YAN are two ways
of naming the same angle.) 110°
S A
H

538 9780170188777
 Answers

g Y h e f ¼ 165 f a ¼ 45
180° g t ¼ 90 h a ¼ 32, b ¼ 148
28° L N
L K M i x ¼ 70, y ¼ 90 j j ¼ 132, k ¼ 48, l ¼ 132
k x ¼ 62, y ¼ 105 l c ¼ 60
i K L
90°
Mental skills 2
2 a 117 b 740 c 138 d 140
e 174 f 100 g 436 h 109
Y
i 200 j 312

Exercise 2-03 3 a 160 b 700 c 90 d 2200

e 72 f 1600 g 2100 h 480
1a acute b obtuse c obtuse i 132
d acute e reflex f reflex
g acute h obtuse i reflex Exercise 2-05
j obtuse k reflex l acute
m acute n reflex o obtuse 1a c b u c a
d f e i f p
2 Teacher to check.
2 a m ¼ 50 b q ¼ 120 c x ¼ 211
3a acute b obtuse c reflex d y ¼ 145 e a ¼ 98 f d ¼ 151
d reflex e acute f straight g w ¼ 90 h f ¼ 57 i n ¼ 110
g obtuse h obtuse i revolution
j acute k reflex l obtuse 3D
m acute n reflex o right
p reflex q obtuse r acute 4 a \MDQ b \NDP
c \NDQ, \MDP d Teacher to check
4D 5a m ¼ 90 b x ¼ 135
5 a obtuse b acute c acute d acute c f ¼ 25 d w ¼ 133
e n ¼ 29 f q ¼ 62
g t ¼ 163 h h ¼ 20, g ¼ 160
Exercise 2-04 i q ¼ 90, r ¼ 90, s ¼ 90
1 a 57 þ 33 ¼ 90 b 147 þ 33 ¼ 180 6a y ¼ 100 b p ¼ 120
c a ¼ 120 d x ¼ 41
2 a 60 b 20 c 65 e h ¼ 170 f y ¼ 53
d 52 e 1 f 33 g d ¼ 135 h e ¼ 68, f ¼ 112
g 48 h 24 i p ¼ 60

3 Teacher to check Exercise 2-06

4 a 162 b 30 c 145 d 55
e 118 f 93 g 69 h 176 1 AB, AC, AD, BD, BC, CD
2 a AD and CF, GB b BG and CF
5 a c ¼ 84 b y ¼ 90 c p ¼ 126 d a ¼ 180 c Teacher to check
e x ¼ 12 f x ¼ 40 g a ¼ 15 h a ¼ 46
3 a AD ’ CF, GB b BG || CF
6 a \PQR and \RQS b 67 þ 23 ¼ 90
c right angle 4 Teacher to check

7 a a ¼ 60 b a ¼ 20 5D 6C
c m ¼ 135 d m ¼ 71 7-12 Teacher to check

9780170188777 539
 Answers

Exercise 2-07 Exercise 2-08

1a f b c c c 1a g b d c d
2 a b 2a b

c
c

3 Pairs of alternate angles are marked in the same

way.
3 Pairs of corresponding angles are marked in the
same way. a b

a b

× ×

× c
×

c
×
4A
×
5a 2
b a ¼ 94, b ¼ 86, c ¼ 94, d ¼ 86, e ¼ 94, f ¼ 86,
4B g ¼ 94
5a a ¼ 120 b y ¼ 28 c They are equal
c m ¼ 63 d c ¼ 108 6a
e t ¼ 74 f a ¼ 50 and b ¼ 60 ×
g m ¼ 110, n ¼ 70 h x ¼ 105, y ¼ 105
×
i a ¼ 40, c ¼ 40, d ¼ 140, y ¼ 140 ×

6a 4 ×
b a ¼ 75, b ¼ 105, c ¼ 75, d ¼ 105, e ¼ 75,
f ¼ 105, g ¼ 75 b They are equal
7 Teacher to check
8a Vertically opposite angles
b Corresponding angles
c Both b and c equal a
d They are equal
9a m ¼ 110 b a ¼ 50
c n ¼ 80 d b ¼ 122
e h ¼ 20 f m ¼ 50, n ¼ 130, p ¼ 50
g a ¼ 140, b ¼ 40 h a ¼ 130, b ¼ 130
i a ¼ 136, b ¼ 136, c ¼ 44

540 9780170188777
 Answers

Exercise 2-09 8a a ¼ 130 b m ¼ 90

c b ¼ 105 d d ¼ 68
1a d b d c c e m ¼ 112 f a ¼ 82, b ¼ 98
g f ¼ 50, g ¼ 130 h j ¼ 125, k ¼ 125
2a b i a ¼ 51, b ¼ 129, c ¼ 51

Exercise 2-10
1 a \WXQ b \XWP c \WXS
d \AWV or \XWP e \XWA f \XWP
c
2a 65, co-interior b 71, alternate
c 105, corresponding d 120, corresponding
e 110, co-interior f 132, alternate
g 28, alternate h 72, corresponding
i 95, co-interior j 93, corresponding
3 a
k 81, alternate l 30, co-interior
m 128, corresponding n 114, co-interior
or
× o 109, alternate

3a a ¼ 113, b ¼ 113
b b j ¼ 133, k ¼ 133, l ¼ 133
c m ¼ 52, n ¼ 52, p ¼ 128
or d y ¼ 42, z ¼ 42
×
e l ¼ 95, m ¼ 85
f b ¼ 45, c ¼ 30
c g p ¼ 105, q ¼ 105
h k ¼ 85, m ¼ 85
i p ¼ 63, w ¼ 117
or
j k ¼ 50
×
k x ¼ 118, y ¼ 55
l a ¼ 72, b ¼ 108
m m ¼ 97, n ¼ 83, p ¼ 83
4a 2 b A n g ¼ 132
c a ¼ 59, b ¼ 121, c ¼ 59, d ¼ 59, e ¼ 121,
o a ¼ 153, b ¼ 153, c ¼ 27
f ¼ 59, g ¼ 121
d They add up to 180 4C
5 Both sums are 180
6 a 180, Angles on a straight line Exercise 2-11
b
1 a \BEF and \CFE
×
AB || CD, alternate angles are equal
× b \AGH and \GHD
AB || CD, alternate angles are equal
× c \BEF and \EFC
AB is not parallel to CD, alternate angles are not
equal
c They add up to 180 d \GEB and \DFE
AB is not parallel to CD, corresponding angles
7a 180, Angles on a straight line
are not equal
b Alternate angles
e \AEF and \CFG
c 180
AB || CD, corresponding angles are equal
d They add up to 180

9780170188777 541
 Answers

f \CEF and \AFG 4a G b A

AB is not parallel to CD, corresponding angles
are not equal
g \AEF and \EFC 117°
84°
AB || CD, co-interior angles add to 180 U J Q R
h \BEF and \EFD c T d E
AB is not parallel to CD, co-interior angles do
not add to 180. 150°
i \AEF and \EFC 41° D G
P O
AB || CD, co-interior angles add to 180
e R f
210°
2 a MN || PQ, co-interior angles add to 180 X
D
b PQ || MN, corresponding angles are equal
c MN || PQ, alternate angles are equal, 96°
S A W
corresponding angles are equal
d PQ is not parallel to MN, corresponding angles g h
are not equal, \PCB ¼ 115 and \MAD ¼ 120 270°
195° P
M L
e MN is not parallel to PQ, alternate angles are not N
equal B
f MN || PQ, co-interior angles add to 180 i 300°
O
3B M
A

Power plus P

1 a 360 b 15 c 120 d 2.5 5a \WHI or \IHW, acute angle

b \DAR or \RAD, obtuse angle
2 a left b front c behind d front
c \GLU or \ULG, acute angle
3 a m ¼ 51, vertically opposite, corresponding d \PVR or \RVP, acute angle
angles e \NPE or \EPN, right angle
b x ¼ 62, alternate angles; y ¼ 62, alternate angles f \SAM or \MAS, obtuse angle
c a ¼ 55, alternate, co-interior g \MTV or \VTM, straight angle
d m ¼ 58, alternate, straight angle, or co-interior h \XYZ or \ZYX, reflex angle
e y ¼ 75, teacher to check (corresponding) i \MPQ or \QPM, reflex angle
f k ¼ 65, straight angle, angle sum of a triangle;
6a i 55 ii 12 iii 86
c ¼ 35, alternate angles b i 135 ii 80 iii 2
g x ¼ 85, alternate angles
h m ¼ 255, teacher to check (corresponding 7 a m ¼ 62 b k ¼ 133 c x ¼ 58, y ¼ 122
angles)
8a a ¼ 220 b m ¼ 65 c y ¼ 325
i k ¼ 105, teacher to check (corresponding,
d a ¼ 100 e m ¼ 44 f a ¼ 95, b ¼ 85
co-interior, and vertically opposite)
g p ¼ 145 h x ¼ 42 i f ¼ 70
4 Teacher to check j t ¼ 83 k p ¼ 155, q ¼ 155, r ¼ 25
l x ¼ 30

Chapter 2 revision 9 a AB and GH

b EF and GH, EF and AB
1 Teacher to check. c AB and CD, AB and EF, GH and CD,
GH and EF
2 a \ABD b \QOS
10 Teacher to check
3 Teacher to check.

542 9780170188777
 Answers

11 Teacher to check 3a 21 b 30 c 32 d 18
e 36 f 40 g 49 h 54
12 a b i 64 j 63 k 24 l 56
m 9 n 81 o 25 p 16

4 a 1, 2, 4, 5, 10, 20 b 1, 2, 3, 4, 6, 12
c 1, 19
5 Yes, the last digit is even.
13 a b
6a 8 b 5 c 6 d 6
e 4 f 8 g 6 h 8
i 4 j 9 k 6 l 9

7 a 8, 16, 24, 32, 40 b 7, 14, 21, 28, 35

c 12, 24, 36, 48, 60
14 a b
8 No, it does not end with a zero.

Exercise 3-01

15 a alternate b co-interior 1 a 3100 b 49 000 c 2600 d 4 934 300

c corresponding d corresponding 2 a 24 000 b 45 000 c 63 000 d 48 000
e alternate f corresponding
3 a 45 820 b 1700 c 8310 d 71 260
16 a a ¼ 115 b m ¼ 35
c k ¼ 115 d d ¼ 125 4 a 64 000 b 64 200 c 64 220 d 60 000
e x ¼ 50 f q ¼ 62
5 a 1 328 000 b 1 330 000
g x ¼ 37, y ¼ 37
c 1 327 510 d 1 000 000
h m ¼ 62, p ¼ 118, z ¼ 118
i a ¼ 112, d ¼ 68, t ¼ 112 6 Your answers should be close to the following exact
j x ¼ 50, y ¼ 50 answers.
k x ¼ 26, m ¼ 64 a 331 b 157 c 1587
l a ¼ 72, c ¼ 70, z ¼ 38 d 255 e 421 f 203
m a ¼ 38, c ¼ 142 g 413 h 734 i 6723
n x ¼ 35, y ¼ 88, z ¼ 92 j 15 744 k 276 l 72.43 (to two decimal
places)
17 a AB || CD, co-interior angles add to 180
b AB is not parallel to CD, alternate angles are not 7 27 800 8 $17 500
equal
c AB || CD, corresponding angles are equal 9 Teacher to check. 10 104 000
11 a 1000 km b 1000 km c 1000 km
Chapter 3 12 23 582 000
SkillCheck
Exercise 3-02
1 Odd, the last digit is an odd number.
2 Yes, the last digit is a zero. 1 a 238 b 1095 c 448 d 6825
2 $294

9780170188777 543
 Answers

3 a 112 b 714 c 3096 d 3542 e Last digit is not a 0.

e 3252 f 630 g 1600 h 3424 f 1 is not divisible by 2.

4 552 km 5 1140 8C 9 12

6 a 170 b 78 c 128 d 228 10 a 75, 90 b 60, 80 c 84

e 112 f 176 g 128 h 264 d 54, 60, 66, 72, 78, 84, 90, 96

7 a 110 b 70 c 140 d 180 11 a Yes b No c Yes d No

e 270 f 410 g 80 h 240
12 a Yes b Yes c No d Yes
8 a 306 b 459 c 243 d 171
e 450 f 1800 g 360 h 4100 Mental skills 3A
9C 10 2604 2a 1800 b 26 000 c 770 000
Exercise 3-03 d 1000 e 315 000 f 1 000 000
g 2940 h 47 500 i 240
j 1600 k 300 l 210
1 a 11 b 34 c 12 d 70
m 12 000 n 9900 o 1600
e 15 f 78 g 147 h 123
p 3500 q 400 r 500
2 a 452; 2712 ¼ 452 3 6 b 124; 1116 ¼ 24 3 9 s 18 000 t 3 600 000
c 495; 1980 ¼ 495 3 4 d 466; 3728 ¼ 466 3 8
Exercise 3-05
3a 12 14; 49 ¼ 12 3 4 þ 1
b 229 13; 688 ¼ 229 3 3 þ 1 1 a 12 b 21 c 43
c 158 56; 953 ¼ 158 3 6 þ 5 d 25 e 147 f 6
d 259 27; 1815 ¼ 259 3 7 þ 2
2 a 36; 900 ¼ 36 3 25 b 29; 667 ¼ 29 3 23
4C 5 $34 each. c 214; 6848 ¼ 214 3 32
6 a 32 b 80 c 600 d 180 5
3 a 28 12 ; 341 ¼ 28 3 12 þ 5
e 82 f 18 g 46 h 120 1
b 36 14 ; 505 ¼ 36 3 14 þ 1
7 a 72 b 116 c 324 d 485 c 38 11
26; 999 ¼ 38 3 26 þ 11
e 54 f 122 g 109 h 26
4 11 5 26 cm 6 25 weeks
Exercise 3-04 Exercise 3-06
1 a No b Yes c Yes d No 1a XXVII b LII c LXXIX
e No f Yes g Yes h No d XCIII e MMDC f CCCXIV
g CMXXVIII h MMMCDLXXVI i CLXV
2 a No b No c Yes d Yes j CCXXX k MMCDLXXXII l CIX
3 a No b Yes c No d No
2 a 26 b 40 c 264 d 54
e No f No g Yes h Yes
e 77 f 45 g 339 h 528
4 a Yes b No c No d No i 2162 j 1990 k 98 l 1507
e Yes f Yes g Yes h No
3 a Teacher to check.
5 a No b No c Yes d Yes b They are cumbersome to use, and they take too
e Yes f No g Yes h No long to write.

7a 9 is not divisible by 2. 4 Teacher to check.

b Last digit is not a 0 or 5. 5 Teacher to check.
c 5 is not divisible by 2.
d 3 is not divisible by 2. 6 5000 and 10 000

544 9780170188777
 Answers

Exercise 3-07 5B
6 a 10 b 6 c 11 d 4 e 1
1a 84 b 76 c (5)3 f 9 g 8 h 12 i 5
d 15 e 134 f 101
7 0 and 1
g (4)2 3 93 h 22 3 122 i 32 3 114
j 152 3 (6)2 k 23 3 8 2 l 102 3 201 8a 7 b 9 c 25
d 22 e 42 f 19
2a 333333333 g 30 h 28 i 16
b 535 j 14 k 20 l 56
c 7373737 9 a 64 b 1331 c 1
d (6) 3 (6) 3 (6)
e 23232323434 10 a 343 b 4096 c 125
f 12 3 12 3 12 3 11 3 11 3 11 3 11 3 11 3 11 d 1000 e 8000 f 4913
g 42 875 h 512 i 125
3a 16 b 125 c 32
d 1 000 000 e 243 f 2401 11
g 1 h 16 i 27
Number, x 1 2 3 4 5 6 7 8 9 10 11 12
j 1 k 59 049 l 4096
Number
1 8 27 64 125 216 343 512 729 1000 1331 1728
4 See table below. cubed, x3

Exercise 3-08 12 B
13 a 8 b 9 c 5 d 1
1 a 81 b 289 c 100 e 3 f 12 g 4 h 11
2 a 49 b 169 c 324 i 10
d 1 e 25 f 400 14 a 8 b 20 c 35
g 256 h 1156 i 225 d 5 e 17 f 16

3 a 20 b 15 c 18 15 a 16 b 14 c 22
d 16 e 13 f 34 d 40 e 27 f 21
16 D 17 B
4 Number, x 1 2 3 4 5 6 7 8 9 10 11 12
Number
18 a 7.1 b 5.7 c 9.8
squared, x2
1 4 9 16 25 36 49 64 81 100 121 144 d 4.1 e 9.7 f 5.7

Exercise 3-07
4 Power of 10 Number Name
101 10 ten
102 100 hundred
103 1000 thousand
106 1 000 000 million
109 1 000 000 000 billion
1012 1 000 000 000 000 trillion
1015 1 000 000 000 000 000 quadrillion
1018 1 000 000 000 000 000 000 quintillion
1021 1 000 000 000 000 000 000 000 sextillion
1024 1 000 000 000 000 000 000 000 000 septillion
1027 1 000 000 000 000 000 000 000 000 000 octillion
1030 1 000 000 000 000 000 000 000 000 000 000 nonillion
1033 1 000 000 000 000 000 000 000 000 000 000 000 decillion
9780170188777 545
 Answers

Mental skills 3B Exercise 3-11

2a 20 b 60 c 450 d 30 1C
e 190 f 26 g 53 h 720
2 a 1, 3, 9 b 1, 2, 4 c 1, 3, 5, 15 d 1, 2
i 6 j 6 k 4 l 9
m 70 n 30 o 22 p 8 3a 4 b 3 c 2 d 4
q 40 r 5 s 800 t 6 e 14 f 4 g 5 h 6
i 25 j 8 k 30 l 13
Exercise 3-09 m 12 n 12 o 9 p 70

1a 1, 17 b 1, 3, 7, 21 4a 9
c 1, 2, 3, 4, 6, 8, 12, 24 d 1, 11
e 1, 5, 7, 35 f 1, 2, 4 5 a 162 b 12 c 35 d 4
g 1, 2, 3, 6, 9, 18 h 1, 23
i 1, 5, 25 j 1, 3, 9 Exercise 3-12
k 1, 3 l 1, 19
2 a 3, 11, 17, 19, 23 b 4, 9, 18, 21, 24, 25, 35 1 a 7, 14, 21, 28, 35

3C 2 16, 20, 24, 28, 32, 36, 40, 44

4 Primes: 17, 41, 59, 71, 101 Composites: 10, 27, 3 16

33, 62, 77, 129, 472, 999, 2064, 967 504 4 a 15 b 42 c 12 d 30
5f They are all prime numbers. e 40 f 20 g 10 h 8
i 18 j 21 k 60 l 60
6a 37, 41, 43, 47
b 66, 68, 69, 70, 72, 74, 75, 76, 77, 78 5 Teacher to check.
c 2, 3, 5, 7, 11, 13, 17, 19
6 a 24
d 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46
7 (Different factor trees are possible.)
7B 8 Teacher to check.
a 420 b 400 c 220 d 180
9 a Some possible answers: 1, 25, 9, 36, 4.
b Square numbers Power plus
Exercise 3-10 1 a 8, 9, 25, 32, 125, 243
b 25, 64, 216, 243, 256, 343
1 (Different factor trees are possible.) c 81, 125, 128, 10 000, 14 641
2D 2a 1 b 121 c 12 321 d 1 234 321
3 (Different factor trees are possible.) 3a 123 454 321
4 (Different factor trees are possible.) b 1 234 567 654 321
a 24 3 3 b 23 3 52 c 22 3 5 3 23 c 12 345 678 987 654 321
3
d 2 3 89 e 237 2
f 24 3 3 2 d 1 234 567.876 543 21
2 3
g 5 3 13 h 3 35 4a 6 b 60
5 a 22 3 112 b 22 5a 9 b 9 c 200
d 8 e 75 f 2
6 a 25 b 30 c 19 d 28
e 21 f 15 g 12 h 16

546 9780170188777
 Answers

6 a 50 b 90 c 100 2a 2 b 8 c 4
d 1000 e 1100 f 10 000
g 800 h 420 i 100 000 3 a 103 b 57 c 295
4a b
7 3 and 5, 5 and 7, 11 and 13, 17 and 19, 29 and 31,
41 and 43, 59 and 61, 71 and 73

Chapter 3 revision c

1 a 88 000 b 87 500 c 87 530 d 90 000

2 Teacher to check
3 a 48 b 170 c 297 5 \PSA a vertex b arm
d 200 e 882 f 10 170
6 a 24 b 5 c 78
4 a 240 b 124 c 162
d 132 e 16 f 121 7 a 148 b 90 c 75
8
5 a Yes b No c Yes d No
e No f Yes g No h No

6B
7
7 a 256 12 b 26 c 124 9 Teacher to check
8 a XLII b XXXVIII 10 a 2500 b 17 200 c 807 900
c LXXXVIX d CCCXLVII
11 a 2 b 6 c 7 d 6
9 a 34 b 65 c 117 e 15 f 3 g 9 h 16
i 11 j 26 k 10 l 15
10 a 36 b 125 c 100 000 d 256
12 a m ¼ 130 b b ¼ 110
11 a 7 b 12 c 20 d 9 c p ¼ 142 d a ¼ 98
12 a 29, 31, 37, 41, 43, 47 e p ¼ 54 f a ¼ 88, b ¼ 92
b 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, g c ¼ 142 h m ¼ 55
63, 64, 65, 66, 68, 69 i m ¼ 37, p ¼ 87 j x ¼ 296
k x ¼ 30 l y ¼ 90
13 a 60 ¼ 22 3 3 3 5 b 200 ¼ 23 3 52
c 144 ¼ 24 3 32 13 a 36 b 27 c 5 d 11
14 a 16 b 18 14 18C
15 a 4 b 12 15 a 1, 2, 3, 6, 9, 18 b 1, 3, 5, 9, 15, 45
c 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30,
16 (Different factor trees are possible.) 81 36, 40, 45, 60, 72, 90, 120, 180, 360
17 a 24 b 90 16 a 18 ¼ 2 3 32 b 45 ¼ 32 3 5
c 360 ¼ 23 3 32 3 5
18 (Different factor trees are possible.) 400
17 a 12 b 9
Mixed revision 1 18 a 77 b 42

1a 0 b 31 c 11
d 52 e 46 f 60

9780170188777 547
 Answers

Chapter 4 9a C b D c C
SkillCheck 10 a 2 14 b 2 17 c 2 d 1 23
e 2 13 f 1 14 g 1 13 h 1 13
1a i 1 3
4 ii 4
b i 3
ii 3 11 a 1 12 b 3 16 c 4 14 d 6 34
6 6
7
7 5 e 17 20 f 100 11 g 1 27 h 5 13
c i 12 ii 12
16 50

d i 15 5 12 D
20 ii 20
e i 6 3
9 ii 9
f i 5
9 ii 4
9
Exercise 4-02
7 5 7
2 12
3 Teacher to check 1a 10 b 3 c 8
31
2
1 d 3 e 2 15 f 3 47
4 Teacher to check 5 3
3 9 1
6 a 12 b 19 c 7 2a 5 b 8 c 4
1
d 7 e 5 f 3 d 6 e 4 23 f 1 15

7 Teacher to check 3C
1
8a 3 b 3 c 8 4a 2 > 13 b 2
3< 4
3
c 3
8< 2
1

9 a 12 b 10 c 24 d 2 35 < 2 10
7
e 5
6> 2
1
f 5
12 > 3
1

17 6 11 2
g 20 > 10 h 15 > 3 i 2 37 < 5 25
10 Teacher to check
13 3 1 5 Teacher to check
11 a 60 b 4 c 6
1 6a
12 1–
3 0
4
–3
4
1 1 1–2 2 2 1–4

Exercise 4-01 b
0 –2
5
3–
5
1 1 1–5 1 3–5 1 4–5 2
c
1a M b P c M 0 1 5 1
– –1 — 3
–
d M e P f I 6 3 12 4
1 1
g P h P i I — – –2 11
— 1 12– 1 –34
10 5 3 12
j P k M l I d
6
0— 12
—
60 60
40
—
60
55
—1
60
1 30
—
60
1 45
—
60
2
2a 4 13 b 3 14 c 3
1 10 d 4 15 —1 3– —9
–3 7–
3 16 8 16 4 8
e 1 35 f 4 38 g 5 h 7 15 e
0 5 30 45 60 70 1
— — — — —
i 4 j 10 10
11 k 3 15
19 l 1
10 10 80 80 80 80 80
3---
3 13 9 10 3
3a 2 b 8 c 7 d 3
7 a
e 9
f 37
g 37
h 38 0 2
–
3
1 1 1–3 2 7
–
3
2 10 6 5 5---
5
4 Mixed numeral b
0 1–
5
3– 1 1 3–5 9–
5
2 2 –25
5
5 a 12 b 25 c 8 c
d 56 e 72 f 75 –1–16 –1 – –13 0 1
–
5
– 1
2 6
g 6 h 3 i 9
d
–1 –7 – –1
–10 2
– –14 0 –2
5
—9 1
10
6 Teacher to check 7D
8a 3
b 1
c 4
d 3 8C 9 Teacher to check
8 4 5 4
3 4 1 2
e 7 f 5 g 4 h 3

548 9780170188777
 Answers

Exercise 4-03 Exercise 4-05

2 9 4 1a 7 b 7 c 20 d 8
1a 3 b 10 c 1 d 3
e 2
f 1
g 2
h 1 e 5 f 22 g 3 h 30
5 2 5 4
i 15 j 50 k 75 l 12
5 13 1 1
2a 6 b 15 c 4 d 8
2 1 20 3
2 a $21 b $8 c $8 d 20c
e 3 f 20 g 63 h 4 e $0.30 f $2.50 g $135 h 36c
7 3 1 5
i 8 j 10 k 9 l 1 24 i $2.50 j $12 k $3200 l $240
27
m 40 n 1 11
20 o 7
24
2
p 1 35
3a 30 mins b 135 mins c 18 h
3D d 18 mins e 73 days f 45 secs
1 11
g 200 secs h 18 mins i 32 h
4a 6 b 12 j 8 months
1
5 2 4 a 27 b 18
6 a 4 12 b 2
3 c 4 d 5 24 ¼ 5 12
5a 250 m b 2250 m c 45 mm
e 3 25 f 6 38 g 2 23 h 6 d 10 cm e 750 g f 3500 mL
g 320 m h 3 mm i 2700 g
7
7 20 8 Teacher to check j 1000 L k 4800 mm l 40 000 kg

Exercise 4-04 6D 7 24 pencils

8 a 12 2
b 3
1a 3 b 4 14 2
c 3 15 d 3 18
1
e 4 12 f 1
4 10 g 2 12 h 3 56 9 54
i 2 18 j 3
4 20 k 1
2 12 l 5 10
21 10 a Ashleigh 9, Bethany 6, Thomas 2
b Only 17 horses are given to the children
2C c Teacher to check
3 a 2 12 b 1 25 c 3
7 d 3 13
e 1 34 f 7
2 12 g 7
1 10 h 3 Mental skills 4A
4
i 1 21
40 j 1 19
20 k 5
6 l 7
1 10
2a 14 b 9 c 7 d 8
m 1 12 n 2 45 o 1 11
12 p 3
4 e 3 f 8 g 10 h 5
i 33 j 5 k 15 l 18
4 3 11
12 or 3h 55 mins m 26 n 6 o 36 p 6
1
5 a 2 10 b 3 58 q 14 r 160 s 14 t 2

6a b Exercise 4-06
4 1 1– –1
2 6
2 9 35 9
1 1a b c d
– 4 1– 2
– 15 20 48 80
2 2 3 5 9 20 21
e 16 f 64 g 63 h 160
1–
3 1 1– 2B
3 6
1 3 1
3a 7 b 10 c 18 d 1
Add into empty cells in grid i: top row 2, second row 5 4 3 5
e f g h
2 12, third row 312 and 1 16 21 20 32
3
i j 15 k 2 27 l 2
Add into empty cells in grid ii: top row 1 and 56, second 25 25
11 1 3 9
row 113 and 0, third row 12 m 24 n 64 o 5 p 16

7 56 hour 4 42 58 hours

9780170188777 549
 Answers

1 5 3
5a 2 b 1 21 c 6 40 Exercise 4-08
d 6 17
24 e 2 79 f 5 49
1 258
6 8 eggs, 20 cups of flour, 2 cups of sugar
2 a 66 b 7
7a 1
þ 14 þ 14 b 3
þ 35
4 5 11 4
3 a Anthony b 15 c 15
1 3
¼ 33 4 ¼ 23 5
¼ 34 ¼ 65 ¼ 1 15 4 127 12 5 20
5
c 3
þ 38 þ 38 þ 38 þ 38 d 5 3 17 ¼ 57 6a 6 b 50 minutes
8
¼ 5 3 38
72 8 40 9D
¼ 15
8 ¼ 18
7

21 24 10 6 34 hours 11 21
40 12 1
9
e 73 3
20 ¼ f 8 3 35 ¼
20 5
13 a 24 b 4
1
¼ 1 20 ¼ 4 45
1
8a 7
b 2
c 4
d Teacher to check 14 280 15 30
8 3 5

9 17 12 hours Exercise 4-09

10 Teacher to check
2 1 1
1a 3 b 2 c 3
4 6 4
Exercise 4-07 d 5 e 7 f 5

11 16 30
1a 3
b 5 c 8
d 10 2a 4 b 3 c 7
2 5
33 31 53
e 1
f 2
g 4
h 1 d 5 e 3 f 6
7 5 7 9

2a 1 b 0 c 7 3 a 3 35 b 3 27 c 5 58
10
2 3 1
d 7 11 e 12 10 f 19 12
3 a 12 b 10 c 21 d 15
e 42 f 80 g 16 h 8 1 1 4 1
4a 10 b 1 14 c 1 15 d 14
e 1 12 f 1 11
24 g 4
15 h 21
32
4C 5 38 25 hours i 1 16 j 6 k 3 56 l 2 58
3
6a 8 b 4 c 1 12 m 4 18 n 15 19 o 1
10 p 9
3 20
9 21 24
d 1 16 e 25 f 25
11 1
5 a 68 b 56 c 25
g 18 h 2 i 2 d $510 e $1680 f $88
j 1 14 k 1
5 l 3
4
6 0.015g 7 17 13
7 a It equals 1
b Your answer is the number squared 8 a 12 34 h b $159.38
8B 9 208
9a 1 5 1 5
7 b 49 c 12 d 12

10 a 3 34 b 2 45 c 7
8 d 1 13 Exercise 4-10
11 8 1a 1
b 7
c 2
d 9
20 50 25 10
2 7 7 7 31 23
12 a 21 b 10
e 100 f 200 g 300 h 400

13 Teacher to check 2 a 0.28 b 0.06 c 0.161 d 0.213

e 0.02 f 0.2 g 0.7807 h 0.265

550 9780170188777
 Answers

3 a 9% b 17% c 62 12% d 90% 3 16 4 7 eggs

e 22% f 30% g 20% h 55%
5a 2 b 1 14 c 3
5
i 75% j 48% k 42 12% l 82%
6 a 33 13% b 16 23% c 14 27% d 11 19%
m 6 14 % n 33 13% o 150% p 22 29%
1
e 9 11 % f 8 13% g 66 23% h 44 49%
4 a 24% b 50% c 86% d 57.1%
e 6% f 34.5% g 240% h 0.7% 7 a $262.50 b 2 kg c 12 L
i 130% j 0.1% k 31.5% l 2.6%

5A 6C Chapter 4 revision
Exercise 4-11 1 a 74 b 22
9 c 28
5 d 22
7
2 a 1 34 b 8 23 c 3 27 d 1 12 1
24 ¼ 12
1a 6 b $204 c 7.5
1 5 3
d 84 mm e 148 kg f 7.2 g 3a 3 ¼ 15 b 4 ¼ 12
16 c 4 16
5 ¼ 20
g $165 h $10.80 i $96 5 15 1 25 3 15
d 12 ¼ 36 e 2 ¼ 50 f 20 ¼ 100
j 224 mL k $1.30 l 405 m
5 3 3
m $15.40 n 2.7 ha o 15 mins 4a 6 b 4 c 4
4 1 4
d 3 e 2 f 7
2B 3 42 4 312 girls
5a 3 2 7 4 1 1 7 11
5 124 chickens 6 148 7D 10 , 5 , 10 , 5 b 3 , 2 , 12 , 12
7 1
8 a $150 b $160 6 a 1 b 10 c 6
d 11
20 e 5
6 f 1
8
Mental skills 4B
7 a 9 23 b 4 13 c 5
6
2a 15 b 6 c 3 d 2 3
d 4 10 e 1 13 f 3 23
e 9 f 19 g 16 h 80
i 16 j 7 k 17 l 54 8 a A 9, B 8, R 12, O 7, T 20, H 3 12
m 30 n 7 o 9 p 18 b 3 12, 7, 8, 9, 12, 20; H O B A R T
Exercise 4-12 9 a 16 hours b 1600 m
c 2 14 hours or 135 mins d 105 mm
1a 4
b No (only got 80%)
5 e 50 seconds f 125 cm
2C 2 5
10 a 15 b 6 c 14
2
3a 5 b 20% c 12, 40% d 1
e 3
f 1
21 4 2
4 a 74% b 70% c 83 13 % g 2 14 h 8 i 1 15
d 62 12 % e 65% f 92% 1
11 a 50 b 6 c 1 12
32
5 a 40% b 25% c 70% d 25% d 2 e 6 f 35
e 5% f 3% g 25% h 25% g 3 h 2 i 1 12
i 70% j 45% k 15% l 20%
7
12 6 12 litres 13 1 spotted
Power plus 25
14 a 72 b 1 19
30 c 1
2
1 5
1 a 4
b 1
c 1
d 49 d 40 e 1 12 f 10 89
25 27 8 100
27 2 5 9
e 64 f 3 g 7 h 10 15 a i 13
ii 0.13
100
3 3
i 4 j 4 2
b i 25 ii 0.08
c i 3
2 a 75 m b 45 m 40 ii 0.075

9780170188777 551
 Answers

16 a 70% b 92% c 22 12% 2a 170 b 810 c 1400

d 80% e 36.1% f 4% d 640 e 140 f 150
g 48 h 400 i 80
17 Fraction Decimal Percentage j 600 k 90 l 1400
(simplest form)
3
3a 7000 b 10 000 c 270 d 2800
5 0.6 60% e 400 f 1200 g 160 h 24 000
4 i 24 000 j 3300 k 1800 l 2500
5 0.8 80%
41 m 320 n 400 o 21 000 p 210 000
50 0.82 82%
4D 5D
18 a 36 b $72 c 6 6a F b T c T d F
d $23.10 e 51 kg f 234 m e T f F g F h T
4 i F j T k T l F
19 13.2 mins 20 13 21 20%
22 a 17
20 b 85% Exercise 5-02
1a 18 3 12 ¼ 18 3 ð10 þ 2Þ
Chapter 5 ¼ 18 3 10 þ 18 3 2
SkillCheck ¼ 180 þ 36
¼ 216
1a 8 b 4 c 6 d 15 b 16 3 9 ¼ 16 3 ð10  1Þ
e 2 f 30 g 6 h 9
¼ 16 3 10  16 3 1
i 3 j 3 k 1 l 7
¼ 160  16
2a 6 b 6 c 10 ¼ 144
d 7 e 4 f 7
c 21 3 11 ¼ 21 3 ð10 þ 1Þ
3 a 11 b 20 c 11 d 9 ¼ 21 3 10 þ 21 3 1
e 4 f 7 g 25 h 1 ¼ 210 þ 21
i 2 j 32
¼ 232
4 a 150 b 252 c 140 d 15 3 8 ¼ 15 3 ð10  2Þ
d 80 e 130 f 26
¼ 15 3 10  15 3 2
5 Yes ¼ 150  30
6 a 11 b 17 c 1 d 14 ¼ 120
e 16 f 6 g 13 h 21
2 a 135 b 162 c 234 d 279
7 a 3 b 5 c 12 d 2 e 128 f 104 g 176 h 112
e 3 f 11 g 36 h 3 i 243 j 360 k 304 l 261
i 10 j 8 k 9 l 72
3 a 187 b 264 c 165 d 319
Exercise 5-01 e 300 f 168 g 288 h 396
i 480 j 132 k 108 l 209
1a 25 b 118 c 48 4a 6 3 22 ¼ 6 3 ð20 þ 2Þ
d 150 e 150 f 80
g 10 h 65 i 14 ¼ 6 3 20 þ 6 3 2
j 119 k 100 l 84 ¼ 120 þ 12
¼ 132

552 9780170188777
 Answers

b 12 3 19 ¼ 12 3 ð20  1Þ Exercise 5-04

¼ 12 3 20  12 3 1
N
¼ 240  12 1 a NþN b 2 c 3N d N7
N
¼ 228 e 10 f N–1 g 5N h N þ 21
iN–1 j N
k Nþ3 l N3
c 40 3 41 ¼ 40 3 ð40 þ 1Þ pffiffiffiffi 8
m N
¼ 40 3 40 þ 40 3 1
¼ 1600 þ 40 2 No difference except the N would be replaced by
¼ 1640 the X. The letter used makes no difference to the
expression.
d 25 3 48 ¼ 25 3 ð50  2Þ
¼ 25 3 50  25 3 2 3 a xþyþz b b – c or c – b c uv
2 C ðm þ nÞ
¼ 1250  50 d uv e d f 2
pffiffiffiffiffiffiffi
¼ 1200 g 10a h b–3 i 5–c
j c–5 k e43 l t2
5 a 160 b 204 c 1188 d 816 m 9xz n k – 12
e 174 f 252 g 270 h 539 1
o 2 ð20  gÞ or 12 ðg  20Þ
6D
4 a bþg b 4n c d–r
d $2s e $a 4 3 f 2x þ 2y or 2(x þ y)
Exercise 5-03 g xy h $(4m þ 2i)

1 a u4u¼1 b pþp¼23p 5C
c a þ (a) ¼ 0 d p30¼0
e uþ0¼u f a 3 (a) ¼ a2 Mental skills 5A
2
2 a 3w b b c 9acd d 6a
e
2 a 160 b 130 c 60 d 140
e 5 f 2f g 7m h 6wh e 210 f 270 g 190 h 220
i 3m j 4f 2 k d l 10abc i 300 j 170 k 80 l 290
m 16
n n 2g2 o 9x p h
q 8q r 8mn s 12pr 2 t 3a þ 2b Exercise 5-05
3 2
u ab
1 a 15 b 51 c 122 d 18
16 e6
3a 5a b 7 þ 3n c 2 2 a 40 b 58 c 17 d 0
d 4s – 8 e c2 þ d 2 f k
9 þ m 3a 8 b 44 c 16 d 2
g k
9þm h 12  2r i 7 þ 7u2
4 a 16 b 19 c 101 d 36
4A 5 a 73 b 53 c 8 d 10
5 a x3y b 23n4r c 13x¼x 6a 5 b 11 c 3 d 19
6B 7 a 22 b 26 c 4 d 34
7a 12 3 r 3 s b 2 3 n 3 n 8 a 16 b 3 c 24
c 84f d r3rþt3t
9 a 10 b 22 c 50
e 93a3a3b f 53m3n–23a
g (x þ 1) 4 3 h q3q3q 10 a 14 b 35 c 28
i 14  2 3 d 3 d j 4 3 c 4 5
k x3x3y3y l 43j84k 11 $3740 12 27 m2 13 10 12

8D 14 86F 15 $149

9780170188777 553
 Answers

Exercise 5-06 5a x¼8 b m¼9 c k ¼ 20

d a ¼ 16 e n ¼ 16 f h ¼ 35
1a x¼3 b x¼9 c a¼5 g m¼6 h k ¼ 15 i x ¼ 12
d m ¼ 20 e b ¼ 10 f c¼4 j a¼9 k h ¼ 15 l x ¼ 14
g k¼6 h d ¼ 13 i m ¼ 15
j x¼5 k y ¼ 15 l n ¼ 25 Mental skills 5B
2B 2 a 108 b 243 c 414 d 171
e 306 f 567 g 189 h 135
3a x¼5 b p¼7 c k¼5
d x¼4 e x¼3 f x¼8 4 a 187 b 242 c 418 d 440
g m ¼ 28 h a ¼ 12 i d¼2 e 275 f 209 g 594 h 341
j n¼1 k r ¼ 15 l k ¼ 11
m p ¼ 2 n r ¼ 10 o y ¼ 15 6 a 528 b 180 c 348 d 372
p x¼2 e 624 f 216 g 312 h 444

Exercise 5-07 Exercise 5-09

1 a w¼7 b x ¼ 18 c m ¼ 16 1 a t ¼ $11 b x ¼ $0.48 c n ¼ 55 d y ¼ 10
d p ¼ 18 e x¼9 f k¼9
g m ¼ 3 h y ¼ 10 i d ¼ 9 2 a B, 299 b A, 1140 mL c A, 39 d D, 53
3 a 4a þ 12 ¼ 240, a ¼ 57
2 a m¼6 b n¼4 c k ¼ 11
b 2l þ 17 þ 17 ¼ 100, l ¼ 33
d c ¼ 16 e x¼9 f x ¼ 9
c 6y – 13 ¼ 95, y ¼ 18
g d¼6 h h ¼ 5 i a¼7
11b
d 2 ¼ 44, b ¼ 8
3 a p ¼ 11 b m ¼ 13 c x ¼ 17 e 7n – 184 ¼ 2000, n ¼ 312
d y ¼ 60 e k ¼ 24 f n ¼ 21 f 200 þ 5x ¼ 750, x ¼ $2750
g d ¼ 18 h y¼9 i m¼4
45 5 391 6A
4 a m ¼ 12 b d ¼ 10 c x ¼ 40
d k ¼ 48 e x ¼ 60 f a ¼ 8 Power plus
g k ¼ 30 h n ¼ 55
1 a 5a – 3b b 4m – 10n c 4j – k þ 4
5a m ¼ 19 b p¼8 c p ¼ 19 d 5b2 e 3x2 – 6x f 5xy þ 2yz þ 4xz
d n ¼ 8 e x ¼ 10 f n¼9
g x¼7 h y ¼ 4 12 i h¼7 2 a 2 b 24 c 10 d 9
j x¼3 k k ¼ 10 l n¼0 e 8 f 4 g 7 h 4

Exercise 5-08 3 a i P ¼ 2l þ 2b or 2(l þ b)

ii A ¼ lb
1a x¼5 b x¼3 c x¼2 b i P ¼ 2 þ y þ x þ y þ 2 þ x or 2ðx þ 2 þ yÞ
d x¼4 e d¼9 f x ¼ 8
¼ 4 þ 2x þ 2y
g x¼2 h x¼1 i x¼4
j x¼3 k x ¼ 1 l x ¼ 2 ii A ¼ x(2 þ y)
c i P¼pþqþr
2D ii A ¼ pq
2
3a x¼7 b x¼8 c x¼3 d i P ¼mþ5þmþ3þn
d x ¼ 11 e x¼2 f x¼2
g x¼3 h x¼5 i x ¼ 5 ¼ 8 þ 2m þ n
j x¼9 k x ¼ 2 l x ¼ 1 ii A ¼ mn þ 12 3 3 3 n ¼ mn þ 3n
2

4D

554 9780170188777
 Answers

e i P ¼xþyþyþxþx Chapter 6
¼ 3x þ 2y
ii 1
SkillCheck
A ¼ x2 þ 3x32
2 1a
¼ x2 þ x
f i P ¼ a þ b þ c þ ðb  dÞ þ ða  cÞ þ d
¼ 2a þ 2b
ii A ¼ ad þ cðb  dÞ
or bc þ dða  cÞ
or ab  ½ða  cÞ 3 ðb  dÞ
b
4 a x b x2 c 0 d 1
e 2x f 0 g x h x2
i 1 j x
2
5 a x ¼ 1 b 3 c n ¼ 2
d r¼9 e d¼0 f z ¼ 2 12

Chapter 5 revision 3 a AB and DC, or AD and BC

b No c 90 d 65
1 a 28 b 118 c 170
d 3100 e 390 f 2800 4 Teacher to check

2 a 198 b 136 c 297 d 156 5 a, b, d

D E
3 n – (n) ¼ 2 3 n
4 a 4x b u5 c y
d 10a e 24abc f 20mw2

5 a 43m3n3k b 63a4b G F
c 93c3c
c DE and FG, DG and EF
6 a 3N b N – 5 or 5 – N c N þ 1
d 13 N 6a

7 a Mþ3 b Bþ5 c 2H – k
8a 7 b 0 c 6 d 60
9 a 109 b 11 c 169 d 94
b
10 a m ¼ 4 b k ¼ 12 c d ¼ 18
11 a w ¼ 35 b e ¼ 12 c p¼3 d x ¼ 12
12 a t ¼ 2 b n¼3 c y¼3
d m ¼ 68 e x¼9 f m ¼ 10

13 a C b N ¼ 59
14 a 5N ¼ 180 b 456 7 Teacher to check

9780170188777 555
 Answers

Exercise 6-01 d

1a reflection b translation
c reflection d rotation
e translation f rotation
g translation h rotation
i reflection j rotation
k reflection l rotation

2a

3a

556 9780170188777
 Answers

d c

e d

4a
o

5 The answer is the same.

b 6 a 270 b 90 c 270 d 180
7 a 1 left, 5 up b 3 down

Exercise 6-02
o
1 a rotation and translation, or two reflections, or
reflection and translation
b rotation and translation
c rotation and reflection

9780170188777 557
 Answers

2a b

b
c

4a
l m

3a
b Translation
5a i rotation, rotation ii 0 rotation
b i reflection, reflection ii rotation
c i rotation, reflection ii reflection

Exercise 6-03
1a b c

558 9780170188777
 Answers

d e f Infinite 3 a and f, order 3

4 Teacher to check
5a i 4 ii Yes, order 4
b i 6 ii Yes, order 6
g h
c i 1 ii No
d i 6 ii Yes, order 6
e i 5 ii Yes, order 5
f i 1 ii No
6 Teacher to check
2 a a, e b c, d, h c f d b
7 Circle
3a 1 b 1 c 0
d 5 e 0 f 3 Mental skills 6
4
D H I MO V X 2 a 330 b 160 c 1600 d 260
e 400 f 290 g 400 h 800
5a 3 b 1 c 1
i 6400 j 16 000 k 300 l 70
d 1 e 1 f 3

6 Teacher to check Exercise 6-05

7a b 1a scalene, right b scalene, right
c scalene, acute d isosceles, obtuse
e isosceles, obtuse f isosceles, acute
g equilateral, acute h isosceles, acute
i isosceles, right j equilateral, acute
k isosceles, acute l scalene, obtuse

2 Teacher to check.
3 No. In an equilateral triangle, all angles are equal.
c d 4 a b
None

c d

e f

8 Teacher to check None

9 Teacher to check
10 Teacher to check
5 Yes, equilateral triangles.
Exercise 6-04 6 No, two obtuse angles can’t be joined to form a
triangle. The sum of the angles in a triangle is equal
1 a Yes, order 4 b Yes, order 2 c No to 180, and two obtuse angles would sum to more
d Yes, order 6 e Yes, order 2 f No than that.
2 H, I, N, O, S, X, Z 7C
9780170188777 559
 Answers

8a 1 b, c Teacher to check Exercise 6-08

9a 3 b, c Teacher to check
1 a rhombus b parallelogram c square
10 a no b yes, order 3 d trapezium e rectangle f kite

11 a x ¼ 42, equal angles of an isosceles triangle 2a b

b y ¼ 7, equal sides of an isosceles triangle
c x ¼ 60, angles in an equilateral triangle equal
60
d l ¼ 4.8, equal sides of an isosceles triangle c d
e a ¼ b ¼ 17.2, equal sides of an equilateral
triangle None
f r ¼ 15, equal angles of an isosceles triangle
12 Teacher to check. e f
None
Exercise 6-06
1a a ¼ 50 b b ¼ 30 c c ¼ 30
3
d d ¼ 60 e e ¼ 124 f f ¼ 50 Number of Order of
g g ¼ 67 h h ¼ 22 i i ¼ 52 axes of rotational
j j ¼ 90 k k ¼ 60 l l ¼ 30 Quadrilateral symmetry symmetry
m m ¼ 65 n n ¼ 139 o q ¼ 158 Square 4 4
p m ¼ 60 q y ¼ 120 r x ¼ 96 Parallelogram 0 2
s x ¼ 50 Trapezium 0 No rotational
symmetry
2 a x ¼ 60 b a ¼ 80 Rhombus 2 2
c a ¼ 40, b ¼ 50, c ¼ 90
Kite 1 No rotational
3A symmetry
Rectangle 2 2

Exercise 6-07 4a square, rectangle

b parallelogram, rhombus, square, rectangle
1a i d ii a and b c parallelogram, rhombus, square, rectangle
b i t ii q and p d trapezium
c i w ii x and z e rhombus, square
f kite, rhombus, square
2a h ¼ 104 b y ¼ 16 g parallelogram, trapezium
c e ¼ 95, d ¼ 85, d b ¼ 116, a ¼ 50 h parallelogram, rhombus, rectangle
e m ¼ 135 f y ¼ 114, x ¼ 66
g e ¼ 67 h h ¼ 29 5 Teacher to check
i m ¼ 90 j x ¼ 70
k p ¼ 130 l w ¼ 88
Exercise 6-09
3B
1a a ¼ 90 b b ¼ 60 c c ¼ 140
4 a m ¼ 112 b a ¼ 94, b ¼ 86 d d ¼ 93 e e ¼ 90 f f ¼ 75
c a ¼ 74, b ¼ 74, c ¼ 38 g g ¼ 45 h i ¼ 130 i j ¼ 75
5 the angle sum of a triangle is 180, angles on a j r ¼ 90 k m ¼ 62 l l ¼ 25
straight line add to 180 m n ¼ 131 n p ¼ 50 o x ¼ 280, y ¼ 80

2D

560 9780170188777
 Answers

3A 7 Shape Properties
4 a 90 b Rectangle Trapezium • One pair of parallel sides
• No axes of symmetry
Kite • Two pairs of adjacent
Exercise 6-10
sides are equal
1 • One pair of opposite
Parallelogram
angles are equal
Trapezium

Rectangle
Rhombus
• Has one axis of symmetry

Square
• Diagonals intersect at

Kite
right angles
Opposite sides are equal ü ü ü ü
Opposite sides are parallel ü ü ü ü Parallelogram • Opposite sides are equal
Opposite angles are equal ü ü ü ü and parallel
All angles are 90 ü ü • Opposite angles are equal
Diagonals are equal ü ü • No axes of symmetry
Number of axes of symmetry 0 0 2 2 4 1
• Diagonals bisect each
Order of rotational symmetry 0 2 2 2 4 0
other
(Note: An isosceles trapezium has line symmetry, Rhombus • All four sides are equal
but other trapeziums do not.) • Opposite sides are
parallel
• Opposite angles are equal
• Has two axes of symmetry
c Pairs of adjacent sides equal, diagonals intersect at • Diagonals bisect at right
right angles. (Other answers possible.)
angles
2 • Diagonals bisect the
Parallelogram

angles of the rhombus

Trapezium

Rectangle
Rhombus

Square

Rectangle • All four angles measure

Kite

90
Diagonals are equal ü ü • Opposite sides are equal
Diagonals bisect each other ü ü ü ü and parallel
Diagonals intersect at right angles ü ü ü • Has two axes of
Diagonals bisect the angles of the ü ü
symmetry
quadrilateral
• Diagonals are equal
3B • Diagonals bisect each
other
4a rectangle, square
b square, rhombus Square • All four sides are equal
c rectangle, square • All four angles measure
d parallelogram, rhombus, rectangle, square 90
e parallelogram • Has four axes of
f rectangle, square, rhombus, kite symmetry
g square • Diagonals are equal and
h square
bisect each other at right
5 cointerior, parallel, 110, 70, angles angles
6 a Yes, a square is a rectangle • Diagonals bisect the
b Yes, a rhombus is a parallelogram. angles of the square

9780170188777 561
 Answers

Power plus b

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

2 a all angles equal 90 b all sides equal

c all sides equal
3 a parallelogram b kite
c rectangle d rectangle
e parallelogram f parallelogram

4 Teacher to check c
5 Teacher to check

Chapter 6 revision
1a

3a

2a

562 9780170188777
 Answers

c 10 a x ¼ 59 b u ¼ 51 c a ¼ 127
d v ¼ 76 e p ¼ 100 f m ¼ 62, n ¼ 56
g y ¼ 100, z ¼ 130

11 a x ¼ 111 b m ¼ 129 c x ¼ 112

d p ¼ 96 e m ¼ 99 f y ¼ 70

12 a square b rhombus c trapezium

d parallelogram e rectangle f kite

13 a

None None

5a b

c
b square 4, rhombus 2, parallelogram 2,
rectangle 2
14 A quadrilateral with all sides equal.
15 a parallelogram b trapezium
16 a y ¼ 70 b x ¼ 81 c m ¼ 26 d y ¼ 61
17 Teacher to check.
6 a Yes, order 2 b Yes, order 5 c No
18 a square, rectangle
7a equilateral, acute-angled
b square, rectangle
b scalene, right-angled
c square, rectangle, parallelogram, rhombus
c isosceles, acute-angled
d square, rectangle, parallelogram, rhombus
d scalene, obtuse-angled
e scalene, acute-angled
f isosceles, right-angled Mixed revision 2
8 a isosceles, acute-angled 1a 5
b 11
c 1
6 15 8
b \F and \H
2 a 25% b 60% c 57.5%
9 a equilateral, acute angled
b scalene, acute angled

9780170188777 563
 Answers

3a b

c
c

4 a 2w b a2 c 4abk d 4p
e m2 f 0 g 8k h 10m 7 a 2 25 b 3 12 c 1 23 d 1 56
5 8a 4 2 5 7
5 b 3 c 8 d 10

9 a 62 b 1800 c 10 d 620
10 a 198 b 192 c 135 d 264
11 a > b < c >
5 1 19
12 a 7 12 b 3 10 c 24

13 a

X
6a

564 9780170188777
 Answers

b 28 a 4x þ 16 ¼ 200, x ¼ 46
b 4p þ 14 ¼ 56, p ¼ 10.5
29 a p ¼ 105 b k ¼ 40 c x ¼ 90
30 a parallelogram, rhombus, rectangle, square
b rectangle, square
c square
d kite

Chapter 7
c SkillCheck

Thousandths
1

Hundredths
Hundreds

Tenths
P

Units
Tens
•
a 1 4 • 8 2
b 6 • 0 1 4
c 9 3 1 • 0 2
d 7 0 • 8
e 0 • 3 7 5
14 a i 5 ii Yes, order 5 f 0 • 1 9
b i 4 ii Yes, order 4
g 8 • 5 9 2
c i 3 ii Yes, order 3
h 7 1 5 • 3

15 75 cm 2 a 4 hundreds b 4 tenths
c 4 hundredths d 4 units
3 7
16 a 10 b 18 c 8 13 e 4 thousandths f 4 tenths
17 a 5 b 19 c 8 3a 9
b 2
c 7
d 6
50 5 20 25
18 a x ¼ 23 b x ¼ 9 c d ¼ 6 d m ¼ 5 4 a 20, 21, 30, 32, 34 b 206, 213, 216, 230, 234
19 a scalene, right-angled 5 a 320 b 57 800 c 325 000
b scalene, acute-angled d 4000 e 40 f 12
c isosceles, acute-angled g 1000 h 810 i 64
d equilateral, acute-angled
6 a 45, 44, 42, 40, 39, 38
20 a m ¼ 60 b x ¼ 50 c k ¼ 65 d m ¼ 60
b 556, 549, 522, 520, 513, 505
21 a 40% b 5% c 12%
7 a 30 b 800 c 9000 d 17 000
22 a $10 b 18 mins
8 Teacher to check
23 a pq b x4 c d7 d 28  b
9 a 553 b 2825 c 717
24 a x ¼ 130 b m ¼ 50 c n ¼ 35 d 258 e 764 f 174
25 a 1 12 b 1
c 4 16 g 3150 h 740 i 319
25

26 a 1
20 b 5%
27 a m ¼ 5 b n ¼ 1.5 c x ¼ 3 d x¼8

9780170188777 565
 Answers

Exercise 7-01
7 2 39 143
2a 10 b 5 c 100 d 250
1a 2 b 3 c 4 d 3 e 3
f 1
g 11
h 41
1000 20 100 125
e 5 f 1 g 6 h 5 3 999 13 1
i 7 i 10 j 1000 k 1000 l 2500
471 321 1001 91
m 10 000 n 1000 o 2000 p 100
2A q 41
r 1 35 s 27 14 t 7
2 1000
500
3a 9.998, 23.89, 43.89, 56.314, 56.324, 80.879, 400
b 0.0586, 0.099, 0.568, 0.586, 1.002, 5.608 3B
c 0.222, 0.89, 0.891, 1.23, 1.814, 7.007 4a 0.9 b 0.15 c 0.79 d 0.6
d 0.005, 0.05, 0.5 e 0.4 f 0.23 g 0.6 h 0.411
e 3.004, 3.044, 3.4, 3.404, 3.441, 3.44, 3.441 i 0.704 j 0.87 k 0.07 l 0.14
f 0.022, 0.2, 0.202, 0.22 m 0.8 n 0.235 o 0.247 p 0.17
4a 4000.99, 1256.3, 570.25, 400.099, 125.63, 0.9899 q 0.368 r 0.9345 s 0.493 t 1.67
b 6.539, 5.639, 5.37, 5.369, 5.367, 3.66, 3.659 u 4.47 v 23.9 w 6.8 x 0.023
c 1.61, 1.601, 1.6, 1.599, 1.509 y 0.45
d 6.6, 6, 0.6, 0.06
e 7.07, 0.77, 0.707, 0.7, 0.07, 0.007
Exercise 7-03
f 0.44, 0.404, 0.4004, 0.044
1 a 12 b 16.933 c 167.317 d 1.3276
5a 0.2 < 0.25 b 0.731 > 0.73
c 0.035 < 0.305 d 0.007 < 0.070 2 a 41.493 b 5.9 c 6.69 d 9.06
e 1.59 > 1.059 f 0.099 < 0.99 3C
g 44.44 > 4.444 h 0.7932 > 0.7239
4 a 81.03 m b 18.97 m
6a
1.6 1.7 1.9 2.0 2.2 2.3 2.4 5 18.6 km
b 3.99 4.11
6 8037.2 kg
3.95 3.98 4.03 4.05 4.07 4.09 4.12
7 a 12.45 s, 12.7 s, 13.5 s, 13.81 s, 14.62 s
c
0.62 0.63 0.65 0.67 0.69 0.71 b 2.17 s
c Yes, 12.7 – 0.3 ¼ 12.4 s, which is faster than
d
8.0 8.02 8.06 8.1 8.12 8.16 8.2 12.45 s.
e 8 a $605.55 b $15.25
0.07 0.11 0.13 0.21 0.23 0.25
f 9A
1.9 2.0 2.1 2.2 2.4 2.6
10 6.23 m
g 4.45 4.55 4.675 4.75
11 a 2.54 b 8.74 c 5.45
4.3 4.4 4.5 4.6 4.7 4.8
d Teacher to check. e Teacher to check.
7 Teacher to check.
Exercise 7-04
8 Teacher to check.
1a 249 b 8.1 c 37 420
d 341.6 e 725 f 2196
Exercise 7-02
g 604.3 h 3.2 i 0.65
7 j 4521.3 k 10 640 l 6304
1a i 10 ii 0.7
5
m 5980 n 84761.2 o 0.592
b i 10 ¼ 12 ii 0.5 p 3620 q 219 400 r 400.75
5
c i 10 ¼ 12 ii 0.5
d i 4
10 ¼ 25 ii 0.4 2C

566 9780170188777
 Answers

3a 4.63 b 5.07 c 1.203 6 a 0.72 b 0.72 c 7.2

d 0.364 e 0.3815 f 5.502 d 72 e 7.2 f 0.72
g 0.01146 h 0.6943 i 0.00428
j 0.67 k 0.02131 l 0.572 7 Teacher to check.
m 0.081 348 n 0.502 o 0.0491
p 0.0004 q 0.0173 r 0.012 53
Exercise 7-06
4 a 1000 b 0.01
c 100 d 10 1a 2 b 1 c 1 d 3
e Teacher to check. f Teacher to check. e 3 f 3 g 4 h 3
i 3 j 4 k 6 l 2
Mental skills 7
2a 12.2 b 7.14 c 18.009
2a 88 b 167 c 314 d 34.2 e 22.5 f 12.6
d 85 e 129 f 121 g 34.75 h 8.032 i 0.9
g $11.60 h $6.75 i $4.70 j 4.8 k 0.012 l 12.6
j $30.05 k $7.10 l $32.90 m 0.32 n 1.95 o 0.48
p 0.072
Exercise 7-05 3 a 14.37 b 46.296 c 525.42
1a Multiplication Estimate Answer 4 $162.45 5 $719.55 6 2.08 m2 7B
0.69 3 18 0.7 3 20 ¼ 14 12.42
6.9 3 180 7 3 200 ¼ 1400 1242
6.9 3 1.8 7 3 2 ¼ 14 12.42
Exercise 7-07
690 3 1.8 700 3 2 ¼ 1400 1242
1a 2.4 b 6.2 c 4.16
d 4.1 e 14.65 f 2.1975
b Multiplication Estimate Answer g 0.008 h 2.6775 i 24.45
10.4 3 42 10 3 40 ¼ 400 436.8 j 3.675 k 0.51875 l 0.106
1.04 3 4.2 134¼4 4.368 m 2.4 n 3.39 o 2.875
104 3 4.2 100 3 4 ¼ 400 436.8 p 64.21 q 11.9 r 13.75
0.104 3 4.2 0.1 3 4 ¼ 0.4 0.4368 s 0.122 t 259.45

c 2 $17.14 3D 4 $28.16
Multiplication Estimate Answer
3.8 3 92 4 3 100 ¼ 400 349.6 5 a 69.6 b 11.6
0.38 3 92 0.4 3 100 ¼ 40 34.96
6 a 24.8 4 8 ¼ 3.1
38 3 0.92 40 3 1 ¼ 40 34.96 b 12.3 4 5 ¼ 2.46
380 3 0.92 400 3 1 ¼ 400 349.6 c Teacher to check

2 a 21.42 b 2.142 c 2142

d 2142 e 214.2 f 21.42
Exercise 7-08

3 a 20.4 b 2.04 c 0.204 1 a More, we are dividing by a number less than 1

d 2.04 e 204 f 20.4 b Teacher to check
c 36
4 a 244.8 b 244.8 c 2.448
2 a more
d 2448 e 2.448 f 24.48
b Teacher to check
5 a 75.6 b 756 c 0.756 c 68
d 0.756 e 0.0756 f 75.6 3 The answer is more than the number.

9780170188777 567
 Answers

4B Exercise 7-10
5 a 5088 4 8 b 1792 4 7 c 3330 4 9
d 172.5 4 5 e 1292 4 4 f 4950 4 6 1 a 0.4 b 0.5 c 0.8
g 1680 4 7 h 1482.3 4 9 i 6.6 4 3 d 0.7 e 2.6 f 0.3
g 0.9 h 2.9
6 a 8.7 b 36.6 c 4.9 d 203.5
e 30 f 12.6 g 208 h 80 2 a 0.48 b 0.74 c 0.07 d 0.29
i 5.7 j 2041 k 1.064 l 130.2 e 0.31 f 0.66 g 2.10 h 4.00

7 16 8 18 3 a 25.38 b 341.61 c 420.90

d 734.65 e 27.36 f 1314.21
9 a 14 km b 38 min
4 Rounded Rounded
10 a 27.2 4 3.4 ¼ 8 b 12.3 4 5 ¼ 2.46
c Teacher to check Calculator (1 decimal (2 decimal
display place) places)
Exercise 7-09 a 4.063333333 4.1 4.06
b 2.053333333 2.1 2.05
1 Meaning as c 2.202222222 2.2 2.20
Fraction division Decimal d 5.168181818 5.2 5.17
a 3
345 0.6 e 4.2825 4.3 4.28
5
f 1.05416666 1.1 1.05
b 1
142 0.5 g 0.232142857 0.2 0.23
2
c 1
144 0.25 h 3.43125 3.4 3.43
4
i 1.416666667 1.4 1.42
d 4
445 0.8
5 j 7.9586875 8.0 7.96
e 2
245 0.4
5
f 3 5 a 10.3337 b 431.5433 c 1.4450
4 344 0.75
d 3217.6541 e 4.6709 f 0.8889
g 1
145 0.2
5
6a 8 b 40 c 6
h 1
148 0.125
8 d 26 m e 3

2 a 0.4 b 0.375 c 0.75 d 1 7 Teacher to check.

e 0.5 f 0.75 g 0.6 h 0.25
8 Teacher to check.
i 0.625 j 0.875 k 0.5 l 1

3 The fractions are equivalent, for example, 12 ¼ 24 ¼ 48

Exercise 7-11
4 a 4.8 b 23.75 c 12.625
d 6.6 e 57.4 f 19.125 1 $89.06 2 112.9 m 3 $9
g 110.875 h 80.25
47 5 15.8 km 6 26.6 km
: :: : : :
5 a 0.416 b 0:27 c 0.1 d 0.10275 7 258.3 t 85 9 1.4 km
6 a 0.8583333 . . . b 0.0454545 . . . 10 a
Classic Rock

c 0.777 . . . d 0.461538461538 . . .
The Edge

Triple M
WS-FM
NOVA

2DAY
C91.3

Hope

2SER

: : :
ABC

MIX
SBS

7 a 0.1: b 0.1: 6 c 0.8: 3

JJJ

: :
d 0.1: 42857 e 0.6: : f 0.285
: 714:
g 0.2: h 0.4: 28 571 i 0.5: 71 428 90 110
j 0.4: : k 0. 6
: l 0.5: b 2.4 MHz c 0.8 MHz d 4 MHz
m 0.8 57 142 n 0.7 o 0.8
11 a $15.24 b $6.84 c $487.76 d $1234.05
: : : : : : : :
8 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 12 120 sheets

568 9780170188777
 Answers

Power plus 11 a 406.3 b 125.72 c 2345.9

: : : : : : : : d 3.90 e 78 654.06 f 678.431
1 0:14285
: 7;
: 0:28571
: 4;
: 0:428571; 0:571428;
0:714285; 0:857142; the same set of six digits are 12 $340.20 13 $0.72 14 $8.25
repeated in order, but with a different digit starting
each time.
:
2 0:9 ¼ 99 ¼ 1 Chapter 8
3 a 0.0004 b 0.000 008 c 1.331 SkillCheck
d 0.2 e 0.6 f 0.3
1a 1000 b 60 c 1000
4 Queen’s chamber 8.07 d 10 e 1000 f 24
armoury 8.262 g 1000 h 1000 i 1000
throne room 8.79 j 60 k 100 l 1000
banquet hall 9.24
kitchen 9.96 2a 1032 b 94.5 c 400
dungeon 8.16 d 2700 e 90 f 63
g 20 h 43 i 65
5 24.15 j 37.5 k 9.5 l 8.2

6 a 3.7, 24.6 3a metres b centimetres

b 2.3, 5.7, 6 c millimetres d metres
c 5.1, 0.72, 4.5, 18 e metres f metres
g metres h centimetres
Chapter 7 revision i centimetres j millimetres
k seconds
1 a 3.998, 34.89, 34.98, 36.86, 38.141, 340
4 a 32 cm b 36.9 mm c 93 m
b 1.293, 1.239, 1.1015, 1.015, 1.006
2a 1 89 9 111
2 b 100 c 100 d 250
Exercise 8-01
3 a 0.4 b 0.13 c 0.07 d 0.011
4 a 65.355 b 104.49 c 11.315 1a 60 b 1000 c 1000
d 1037.9 e 396.51 f 2.379 d 10 e 24 f 1000
g 1000 h 60 i 1000
5 a 75.4 b 754 c 7540 j 1000 k 1 000 000 l 3600
d 1.39 e 0.139 f 0.0139
2a 640 cm b 4000 kg c 72 h
6 a 319.2 b 31.92 c 319.2 d 2 400 000 L e 900 mm f 12 700 g
d 3.192 e 319.2 f 0.3192 g 480 mins h 5600 mL i 420 mm
j 72 000 mg k 380 000 cm l 16 200 secs
7 a 16.5 b 0.6 c 288.92
d 7.32 e 4.6 f 29.1 3 a 200 b 150 c 50
g 1.3325 h 0.001 i 5.137 d 350 e 25 f 200
g 1 580 000 h 40 000
8 a 381.2 b 12.2 c 0.6875 d 65.2
4a 2 b 3 c 8.5
9 a 25 b 31.8 c 230 d 25.4 d 9.8 e 0.75 f 0.325
: : g 6000 h 18 000
10 a 0.8 b 0.375 c 0.5 d 0.6

9780170188777 569
 Answers

5 a kilo b centi c milli 4 a 102 400 mm2 b 0.1024 m2

6 Teacher to check 5 a 6.5 m2, 114 000 cm2, 25 050 000 mm2
b 54 cm2, 990 mm2, 0.000 032 m2
7a 4500 b 180 c 0.75
d 24 e 12 000 f 520 6 a 87.5 ha b 8 750 000 000 cm2
g 7 h 48 i 8650
j 3 k 0.065 l 960 7B
8 a 8 810 000 m2
8D
b 6.24 (to 2 decimal places)
9 a 120, 330, 800, 35, 7400
9 836 mm2
b 0.12, 0.33, 0.8, 0.035, 7.4
c Teacher to check 10 a 1 000 000
b 100
10 a 2200 b 0.8 c 2.35
c Teacher to check
d 0.36 e 330 f 4.9
g 0.27 h 48 i 10 800
j 16900 k 365 l 7.4 Exercise 8-04

Exercise 8-02 1a 55.8 m2 b 58.6 m2 c 96 cm2

d 324 m2 e 1.44 cm2 f 4 cm2
1 a 24 cm b 44 mm c 90 m d 138 cm g 96 mm2 h 225 m2 i 154 mm2
j 1890 cm2 k 448 m2
2a 46 mm b 44 cm c 118 m
d 39 cm e 246 cm f 2000 mm 2C
g 31.8 km h 26 cm i 208 mm
3a i 25 m2
j 60 mm k 48 m
ii 250 000 cm2
3 a 90 mm b 178 mm c 130 mm d 116 mm iii 25 000 000 mm2
b i 0.513 m2
4 a 44 m b 30 cm c 48 mm ii 5130 cm2
d 40 m e 36 km f 54 mm iii 513 000 mm2

5 a 4 cm b 8 cm c 12.75 cm d 18 cm 4a i 625 mm2 ii 6.25 cm2

b i 1100 mm2 ii 11 cm2
6 Any two numbers that add up to 15
c i 1050 mm2 ii 10.5 cm2
7C d i 2250 mm2 ii 22.5 cm2
5 7 cm
Exercise 8-03
6 a 15 000 000 m2 b 40 000 m2 c 31.36 m2
1 a hectares b m2 c cm2 d 3.51 m2 e 6.29 m2 f 0.25 m2
d m2 e cm2 f mm2 7 $7858.50
2B 8 4.5 m
2 2
3a 1500 mm b 1.5 m 9 a 10.08 m2 b 0.16 m2 c 63
c 6.9 cm2 d 65 000 cm2
e 500 000 mm2 f 120 000 m2 10 Teacher to check
g 1.22 m2 h 12.5 cm2 11 a i 20 m2 ii 20 m2 iii 12.8 m2
i 3200 m2 j 790 mm2 b 80 tiles
k 750 000 mm2 l 245 ha c 3.6 L
m 86.5 m2 n 0.0513 m2
o 4700 cm2 p 0.9 ha

570 9780170188777
 Answers

Mental skills 8A Exercise 8-08

2a 108 b 154 c 166 d 210 1 Prisms are a, c, e, g, h, i, l
e 52 f 82 g 196 h 324
2a i octagon ii octagonal prism
i 91 j 137 k 46 l 69
m 253 n 38 o 24 p 85 b i kite ii kite prism
c i pentagon ii pentagonal prism
Exercise 8-05 d i T-shape or octagon
ii T-prism or octagonal prism
1a 15 cm2 b 16 cm2 c 36 mm2 e i trapezium ii trapezoidal prism
d 18 cm2 e 10 cm2 f 48.59 m2 f i L-shape or hexagon
g 8.82 m2 h 9.01 mm2 i 7.68 cm2 ii L-prism or hexagonal prism
j 45.72 cm2 k 21.76 m2 l 1750 mm2
4a b
2D
3 a 15.6 m2 b 300 mm2 c 7.8 m2
4 20 m 5 3 cm 6 $5.10
7 Any 2 values whose product is 72.
c d e
8 8 cm

Exercise 8-06
1 a 48 cm2 b 136 m2 c 54.4 cm2
d 3 cm2 e 340 mm2 f 84 cm2
g 16.2 m2 h 43.46 cm2 i 16.192 m2
7A B C
2A
3 a 168 000 cm2 b 7 cm2 c 4.5 cm2
d 70 000 cm2 e 0.5456 cm2 f 4.9 cm2
8C
4A
9a i ii
5 Teacher to check

Exercise 8-07
b i ii iii
2 2 2 2
1 a 152 cm b 372 cm c 60 cm d 11 cm
2 a 11 250 cm2 b 500 cm2 c 1300 cm2
3D
4 a 140 cm2 b 67.5 km2 c 48 mm2 c i ii
d 220 m2 e 150 cm2 f 1020 mm2

5 a 30 cm2 b 100 cm2 c 204 mm2

d 135 cm2 e 55 cm2 f 22 m2
iii iv
g 128 mm2 h 372 cm2

6 42.8 m2 7 60 m2 8 282 tiles

9780170188777 571
 Answers

d i ii Exercise 8-10
1 a 225 cm3 b 1071 cm3 c 576 cm3
d 2295 cm3 e 27 cm3 f 39.6 m3
g 40 500 cm3 h 144.72 m3
e i ii iii
2 Length Breadth Height Volume
a 50 cm 50 cm 50 cm 125 000 cm3
b 5 cm 10 cm 18 cm 900 cm3
c 4m 2.5 m 1.4 m 14 m3
d 24 mm 16 mm 11 mm 4224 mm3

f i ii iii
3 6 23 mm
4 a 2268 cm3 b 2 268 000 mm3
5 a 62 cm3 b 6400 cm3 c 498 m3
d 126 mm3 e 23 552 m3 f 23 500 cm3
10 D g 28 700 mm3

6 a 733 720 cm3 b 0.73 372 m3

Mental skills 8B 7 6m
2a 56 b 108 c 64 8 a 200 cm3 b 5.625 cm3 c 5000 cm3
d 420 e 344 f 128 d 3 000 000 cm3 e 600 000 cm3
g 224 h 264 i 46
j 68 k 140 l 108 9 Teacher to check
m 78 n 39 o 32 10 B 11 5 m
p 19
Exercise 8-11
Exercise 8-09
1 a mL b ML c L
1 a cm3 b cm3 c m3 d m3 d mL e L f kL
e mm3 3
f m (Other answers possible.) (Other answers possible.)
2D 2a 7 b 2700 c 3500
3a 3000 mm 3
b 5 000 000 cm 3 d 10 e 5.2 f 1 400 000
c 2600 mm3 d 4 cm3 g 0.42 h 8900 i 6200
e 7 200 000 cm3 f 66 cm3 j 1.75 k 5000 l 9
g 1 000 000 000 mm3 h 0.0023 m3 m 2 500 000 n 0.52 o 0.023
i 126 m3 j 3.45 cm3
3A
k 25 000 000 000 mm3 l 0.000 078 m3
m 0.063 m3 n 0.0014 cm3 4a D b G c J d H
o 0.005 m3 e I f A g F h E
i C j B
4 0.306 m3
58
5a E b G c F d C
e A f B g D 6 a 54 L b 27

6 2 520 000 mm2 7 38 000 000 cm3 7 gigalitre

8 a 0.2 mL b 12 mL
c 2160 mL or 2.16 L d 17 280 mL or 17.28 L

572 9780170188777
 Answers

10 a i ii iii
9 6 14 h
10 a 2700 cm3 b 2700 mL
3
11 a 48m b 48 000 L
12 a 72 000 cm3 b i ii iii
b 72 L

Power plus 11 a 20 000 b 500 000 c 7.5 d 0.00 023

3 3
1a P ¼ 47 cm A ¼ 82.5 cm 12 a 80 m b 320 cm c 672 mm3
b P ¼ 46 cm A ¼ 52.5 m d 360 m3 e 3000 cm3 f 870 m3
c P ¼ 78 cm A ¼ 203 cm
d P ¼ 277 mm A ¼ 2250 mm 13 a 80 000 L b 0.32 L c 0.000 672 L
d 360 000 L e 3L f 870 000 L
2 a and b Teacher to check.
c 15 cm 3 15 cm 14 2 3 1015 ¼ 2 000 000 000 000 000 L
3 l ¼ w ¼ 4cm
4 a 66 m b 11 L c 3, $137.85 d 15 m Chapter 9
2 2
5 a 45 m b 13.5 m c $10.80 SkillCheck
Chapter 8 revision 1 a 3 b 0 c 3 d 5
1a 4h b 42 g c 0.125 kL 2a A 10 B 2 C 1 D 3
d 3.2 km e 8300 mL f 9040 mm b A 10 B 4 C 8 D 14 E 17
g 0.0035 t h 900 mins i 54000 s c A 22 B 15 C 2 D 11 E 20 F 26
j 7.15 m k 4 200 000 mL l 17 kg d A 56 B 24 C 8 D 6 E 30 F 56
e A 60 B 50 C 35 D 15 E 6
2 a 52 m b 36 mm c 64 cm d 88 mm F 19 G 41
2 2
3 a 91 000 cm b 250 mm c 17.5 m2 3a
d 0.24 m2 e 2.4 cm2 f 8 600 000 mm2 –3 –2 –1 0 1 2 3 4 5 6 7 8 9

b
1 2 3 4 5 6 7
4 a 16 m2 b 24 cm2 c 162 m2 –6 –5 –4 –3 –2 –1 0

c
5 a 360 mm2 b 112 mm2 c 5.2 cm2 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4
d 187 km2 d
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7
6 a 120 m2 b 828 cm2 c 68 mm2
7 a 9 cm2 b 34 m2 c 84 m2
d 12.5 mm2 e 196 m2 f 128.2 mm2 Exercise 9-01
8 6L 1 a E3 b C3 c C4
9a b c d F4 and G4 e F3 and G3 f C3

Prism 2 a swimming pool b primary school

Not a prism c park d pond
Not a prism
e car park f tennis courts
d e f
3 a A13 b G6 c N25 d U16
Prism 4 19
Prism Not a prism

9780170188777 573
 Answers

5 Back rows 6b y
16
6 a No b No c No d Yes 15
14
7 Teacher to check 13
12
8 a Wavy vertical line or column 11
b Horizontal line or row 10
9
9 a St John’s oval b The Square 8
c Women’s Tennis Centre d Main Quad 7
e Biochemistry and Microbiology 6
5
10 a N14, N15, O14 or O15 b M27 4
c H2 or H3 d H19 or H20 3
2
Exercise 9-02 1
0 1 2 3 4 5 6 7 8 9 10 11 x
1 A(1, 4) B(2, 2) C(3, 1) D(3, 4) E(4, 3)
F(5, 2) G(6, 5) c an ostrich

2 M(0, 2) P(1, 1) A(2, 0) B(2, 3) N(3, 1)

J(3, 3) E(4, 0) U(5, 2)
Exercise 9-03
3 a cube 1 A(4, 3) B(2, 2) C(0, 2)
D(2, 3) E(2, 1) F(1, 1)
6 G(2, 3) H(0, 3) I(4, 3)
5 J(2, 1) K(3, 0) L(4, 0)
4 M(0, 2) N(0, 3) O(0, 0)
P(2, 0) Q(1, 0) R(3, 2)
3
S(2, 2) T(3, 1) U(1, 2)
2
V(4, 1) W(4, 3) X(4, 1)
1 Y(1, 4) Z(1, 3)
0
1 2 3 4 5 6 2
Q 6
4 a NUMBER b PLANE c WATER N 5 L
d METRE e NURSE f UMPIRE C 4
B 3
5b y
15 2 M
14
13 1 A
12 I H
11 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
10 –1
9
D –2 E
8
7 –3
6
5 K –4 G
4
–5 F P
3
2 J –6
1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 x

c a shark 3 a A, M b B, C, N, Q c D, K, J
d F, G, P e E, I, H, L

4 a 4th b 3rd c 2nd

574 9780170188777
 Answers

y y
2
5 þ þ a 2
b 2

 þ 1 1

  –3 –2 –1 0
–1
1 2 3 x –3 –2 –1 0
–1
1 2 3 4 x
þ  –2 –2

y
6 a, b y

y c 2
d 2
D 3 1 1

–3 –2 –1 0 1 2 3 x –3 –2 –1 0 1 2 3 4 x
C2 –1 –1

–2 –2

1 A –3

F
0 x
–3 –2 –1 1 2 3 All points lie on a horizontal line.
–1 B
3
–2 E
y
4
–3
3
2
c They lie in a straight line. 1
d Teacher to check.
–2 –1 0 1 2 3 4 x
7 a, b –1
y All lie on x-axis
10
9
8
7
6 4 y y
1 1
5 a b
4 –2 –1 0 1 2 3 x –2 –1 0 1 2 3 x
3 –1 –1

2 –2 –2

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
c y
d y
–1
x
–2 3 3
–3
2 2
–4
1 1
–5

–6 –1 0 x x
1 2 3 –2 –1 0 1 2 3
–7 –1 –1

–8 –2 –2
–9
–3 –3
–10

c a bicycle All points lie on a vertical line.

5 a
y
b y
3 2
Exercise 9-04 2 1
1
1a (0, 2), (2, 3), (4, 4), (7, 9) –2 –1 0
–1
1 2 3 x
b (2, 1), (1, 3), (2, 4), (5, 2) –2 –1 0
–1
1 2 3 x
–2

c (0, 2), (1, 5), (2, 8) –3

d (4, 1), (2, 3), (1, 0), (5, 2) –4

9780170188777 575
 Answers

y
5 Mental skills 9
y 4
c 3
d 3 2 a 720 b 486 c 825 d 128
2 2 e 560 f 216 g 189 h 432
1 1 i 560 j 616 k 135 l 675
–4 –3 –2 –1 0 1 2 3 4x –3 –2 –1 0 1 2 x
–1 –1 Exercise 9-05
–2 –2

–3
1a y
10
A
6 a They are collinear
b They increase by the same amount A' 5
F
F'
7B B
B' E
x
–10 –5 5 10
8 a y
b
y
9 8 E' D
8 6 –5
D'
7 4
6 2
–10
5
–4 –3 –2 –1 0 1 2 3 4 x
4 –2

3 –4
–6
b A(2, 6) fi A0 (8, 4)
2
1 –8
B(1, 2) fi B0 (7, 0)
C(2, 2) fi C 0 (8, 4)
–3 –2 –1 0 3 x
–1
1 2
D(2, 0) fi D0 (8, 2)
c y E(4, 0) fi E0 (10, 2)
2 F(4, 4) fi F 0 (10, 2)
1
G(2, 4) fi G0 (8, 2)
–2 –1 0
–1
1 2 3 4 5 6 x The x-coordinate of each vertex decreases by 6
–2 while the y-coordinate decreases by 2.
–3
2 y
10
The dots in parts a and b lie on a curve, not in a
straight line. The dots form a zig-zag line in part c.
5
A
9 There is a rough pattern; as the age of the tree
C
increases, the height increases at a steady rate A
10 x
y –10 –5 C 5
26
24 B
–5
22
20
B
18
–10
16
14
12
A(1, 3), B(1, 3), C(3, 2)
10
8
3 Translated 5 units left, 4 units down
6
4
2

0 2 4 6 8 10 12 14 16 18 20 22 24 26 x

576 9780170188777
 Answers

4a y 7 a Rotation 90 clockwise about K(2, 2)

10 b (2, 3)
S T
8a y
5 V U 10

X W
x 5
–10 –5 X' W' 5 10 E D
F C
–5 x
V' –10 –5
U' 5 10
S' T'
–10 –5 H A

b S(2, 8) fi S0 (2, 8) –10

T(8, 8) fi T0 (8, 8)
U(8, 6) fi U0 (8, 6) b A(6, 5) fi A0 (6, 5)
V(4, 6) fi V0 (4, 6) The x-coordinate changes sign but the
W(4, 1) fi W0 (4, 1) y-coordinate does not change.
X(2, 1) fi X0 (2, 1) 9 a Reflection across the x-axis b (3, 7)
The x-coordinate of each vertex does not change
while the y-coordinate changes sign. 10 a Rotation 90 clockwise about S(3, 3)
b R(3, 4) fi R0 (4, 3)
5a y
10
The x-coordinate of R becomes the y-coordinate
of R0 and the y-coordinate of R changes sign and
becomes the x-coordinate of R0 .
S T
5
11 y

Q R 10
P'
–10 –5
O x
P 5 10
R' Q' 5

–5

T' S'
–10 –5
x
5 10
–10

b O(0, 0) fi O0 (0, 0) –5

P(4, 0) fi P0 (4, 0)
Q(4, 2) fi Q0 (4, 2)
R(2, 2) fi R0 (2, 2) –10

S(2, 7) fi S0 (2, 7)

T(0, 7) fi T 0 (0, 7) 12 Translated 10 units right.
The x- and y-coordinate of each vertex changes D: (10, 0) fi (0, 0)
sign. The x-coordinate of D increased by 10 while the
y-coordinate did not change.
6 a Reflection across the x-axis
b D(5, 8) fi D0 (5, 8)
The x-coordinate does not change but the
y-coordinate changes sign.

9780170188777 577
 Answers

Power plus Chapter 9 revision

1b y 1 a student centre b Pi stadium
12 c main campus d library
11
10
9
2 a D5 or E5 b B6 or B7 c E8 to I8
8
7
3 B
6
6 F
5 5
4 4
D
3 A
3
2
2
E
1
–7 –6 –5 –4 –3 –2 – 1 2 3 4 5 6 7 x 1
1 C
–2 0
–3 1 2 3 4 5 6
–4
–5
–6 4 A(2, 0) B(3, 2) C(0, 4)
–7 D(2, 1) E(1, 3) F(1, 1)
–8 G(4, 1) H(4, 3) I(0, 5)
J(3, 0) K(3, 4)
d a cat
5 a 3rd
2a x y b Any coordinates of the form (0, n), where n is a
0 2 number
1 3 c 4th
3 5 d Any coordinates of the form (a, b), where a
6 8 and b are positive numbers
8 10 e (0, 0)
y¼xþ2 6a y
b x y 6
1 0 5
4 3 4
7 6 3
8 7 2
10 9 1
y¼x1
–3 –2 –1 0 1 2 3 x
c x y –1

0 8 –2

2 6
4 4 b star
6 2
7a y
8 0
y ¼ 8  x or x þ y ¼ 8 2

d 1
x y
1 5
–2 –1 0 1 2 x
0 3 –1
2 1
–2
3 3
4 5 –3
y ¼ 3  2x or 2x þ y ¼ 3
578 9780170188777
 Answers

b y b P(5, 2) fi P0 (1, 1)

3 Q(3, 7) fi Q0 (1, 6)
2 R(5, 5) fi R0 (1, 4)
1 S(7, 7) fi S 0 (3, 6)
The x-coordinate of each vertex increases by 4
–2 –1 0
–1
1 2 3 x units and the y-coordinate increases by one unit.
11 a Rotated 180 about point S. Or 2 reflections
b V(5, 4) fi V 0 (5, 4)
8a y The x- and y-coordinates of V both changed
5 (0, 5) sign when transformed to V 0 .
4 (1, 4)
3
(2, 3) Chapter 10
2 SkillCheck
1
(5,0)
1a 5 b 1.5 c 2
–1 0 1 2 3 4 5 x
–1 d 1 e 3
(Teacher to check scale diagrams.)
Collinear, decreasing by the same amount 2 a 50 b 34.5
b y 3 a Cola, Orange, Lime, Lemonade
5 (2, 5) b 5 c 23
4 4 a 11, 22, 24, 28, 31 b 13, 15, 16, 17, 18, 21
3 (1, 3)
5 a 18, 17, 11, 6, 5 b 31, 23, 17, 14, 8, 5, 2
2
(0, 1)
1 Exercise 10-01
(5,0)
–1 0 1 2 3 4 5 x
–1 1 a 10 cars
(–1, –1) b 5 cars. It is difficult to represent the whole range
Collinear, increasing by same amount of values accurately.
c 8:00–10:00 a.m.
9 a Reflected across the y-axis. d 6:00–8:00 a.m.
b F(4, 3) fi (4, 3); the x-coordinate changes e 6:00–8:00 a.m., 5; 8:00–10:00 a.m., 40; 10:00
sign while the y-coordinate does not change. a.m.–12:00 noon, 10; 12:00 noon–2:00 p.m., 20;
10 a y 2:00–4:00 p.m., 35; 4:00–6:00 p.m., 15
5 f i 8:00–10:00 a.m. dropping children at school,
going to work
ii 6:00–8:00 a.m. not many people around yet,
a few going to work
–10 –5 P' 5 10 x iii 2:00–4:00 p.m. parents picking up children.
P
2 a Sydney b Darwin
–
R R' 5 Q' c 200 000 people d 2.1 million or 2 100 000
S'
S Q
e Adelaide f 20 times

–10 3 a i 99% ii 88% iii 88%

b Dishwasher c Mobile phones
d About 15% e Teacher to check.

9780170188777 579
 Answers

4 a 1 unit ¼ 10% b 45% c 2006 3a Profit

5
d i 3 and 4 ii 5 and over

Millions of dollars
e 3 and 4 f True 4
3
5 a Within 5 km of home
44 2
b 100 ¼ 11
25
75
c 100 ¼ 34
1
d Fewer accidents occur. Most travelling is
done close to home. 0
6 3 2010 2012 2014
e 100 ¼ 50 f True 2011 2013 2015
Year
g Teacher to check
b Profit
4
6 a 100 mm

Millions of dollars
28 7
b Meet community needs, 100 ¼ 25
21
c 100
d Meet community needs, decrease cost, save 3
natural resources, reduce pollution, and others.
e Teacher to check
7 a dog b goldfish 2
3 1 4 2 2010 2012 2014
c i 30 ¼ 10 ii 30 ¼ 15 2011 2013 2015
Year
d 360 e 96 f No
g Dog 27, Bird 12, Cat 24, Guinea pig 18, c Graph in part b because it is much steeper.
Goldfish 9 4 a Australian weekly wages are four times bigger
8a i 70 cm ii 120 cm than Malvolia’s.
b No scale on vertical axis, use of pictures instead
b i 4 ii 11
of columns.
c 0 and 1, babies grow quickly
c Columns
d 6 and 7, children’s growth slows down Average weekly wages
e 3 years 1400
f 10 years, growth slows down 1200
g
Average weekly

i fairly flat ii possibly horizontal 1000

wages ($)

h Teacher to check.
800

Exercise 10-02 600

400
1 a 20 000 boxes 200
b It has a correct even scale for the sales axis
c It is difficult to see where the graph starts, it Malvolia Australia
exaggerates the amount of difference. 5 No scale on the horizontal population axis.
d Bigger pictures/diagrams can appear larger 6 a The scale does not begin at 0, the scale is not
than the actual amount and exaggerate any even: increasing by 50, then 25.
difference. b Firefighter salaries
1400
2 a 120 beats/min b 20 beats/min 1200
c Heart rate scale does not begin at 0
1000
d Heart rate and exercise
Per week ($)

800
150 600
Heartbeat rate
(beats/min)

120 400
90 200
60
SA WA Vic ACT Tas NSW
30
State
1 2 3 4 7 Teacher to check
Minutes of exercise
580 9780170188777
 Answers

Exercise 10-03 Exercise 10-04

1a 1D
2a
0 1 2 3 4 5 6 7 8 9 Stem Leaf
No. of goals kicked per game 7 6
b 8 c 0 to 5 d 22 8 1 6 8
9 5 7 8
2 a 18 b 16 c 18 to 26 10 1 5 5
d 25 e No f 22 11 2 2 4 7
12 4
3 a 37 b 31 to 40 c 23
d 23 to 40 e 49 b 76, 124 c 8 d 101
4 a Accidents on motorway each day 3 a 64 b 37 c 99
d 64 to 154 e 9 f 60 to 110

4a Stem Leaf
13 7
0 1 2 3 4 5
Number of accidents 14 0 1 3 5
15 3 4 5 7 7 7 8 9
b 0 c 1.3 d 5, it’s unusually large
16 2 2 3 6 6 8
5B 17 0 1 5 5 7

b 137 cm, 177 cm c 5 d 157 cm

e 158 cm, 159 cm f 14 g 20.8%

Mental skills 10
2a 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 °C

b 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 mL

c 500 504 508 512 516 520 524 528 532 536 540 544 548 552 556 560 564 568 572 576 580 584 588 592 g

d 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 min

e 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 L

f 200 220 240 260 280 300 320340 360 380 400 420 440 460 480 500 520540 560 580 600 620640 660 680 700 kg

g
120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360 375 390 405 420 seconds

h
100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625 650 675 700 725 mL

Exercise 10-05 3 a green b They are not numbers

4 Teacher to check
1 a 30.25 b 32
5 a 7.6 b 6.1
2a i 2.56 ii 3 c Mean, takes into account all scores.
b i 4.43 ii 2
c 6 a The last score. b Arteri
i 64.22 ii all values unique
c Phuong 16.44, Arteri 25.33
d i 45.17 ii 45.1
d Arteri family with a higher last score has the
e i 5.78 ii 3, 5 higher mean.
9780170188777 581
 Answers

7A 4a 8 Huxley quiz marks

8 a 74% b 79%
0 1 2 3 4 5 6 7 8 9 10
9 Teacher to check 10 2550
Marks

8 Crancher quiz marks

Exercise 10-06
1a i 22 ii 5
b i 4.9 ii 2.1 0 1 2 3 4 5 6 7 8 9 10
Marks
c i 5 ii 5
b 5 c 7 d 9 e Mean ¼ 6.5
2a The 4th score f 8 Crancher, greater proportion of higher marks
b Carozza 12, Binns 12 5 a 48 b 101 c 105, 112 d 100.73
c Carozza 40, Binns 40
d No effect 6 a 67 b 51 c 67 d 67.8
3a i 7 ii 6
b i 37.5 ii 10 Exercise 10-08
c i 12 ii 5
1a Group A: mean ¼ 6.1, median ¼ 6
4C 5C 6 Teacher to check Group B: mean ¼ 6.1, median ¼ 6
b
7 a $696 500 b $1 202 000
c $767 273 d $625 000
e Median, not affected by outlier 3 4 5 6 7 8 9 10
price ($1 800 000) Assignment marks for Group A

8 6, 7, 8 or 9
3 4 5 6 7 8 9 10
9 a Alf 75.9, Mike 75.7 b Mike Assignment marks for Group B
c Alf 2, Mike 6 d Mike, lower average Group B marks are more spread out (from 3 to
e Alf, smaller range f Alf 76, Mike 75.5 10 and spread evenly) than Group A (clustered
around 5 to 7)
Exercise 10-07 c 4
1a i 4 ii 11 iii 10 iv 9.8 2 a 25
b i 4 ii 24 iii 22 iv 22.3 b Dynamo: mean ¼ 37.16, median ¼ 37,
c i 6 ii 36 iii 37 iv 37.6 range ¼ 42
d i EnergyPlus: mean ¼ 28.88, median ¼ 29,
0.3 ii 1.8 iii 1.8 iv 1.8
range ¼ 28
2a i 39 ii 33 iii 33 iv 30.1 c, d Teacher to check
b i 26 ii 94 iii 88 iv 86.3 3a Penrith Hurstville
c i 40 ii 131 iii 124.5 iv 121.45 8 7 6 5 3 3 4 4 5
d i 44 ii 17 iii 17 iv 22.1 8 8 6 0 4 3 5
6 6 5 4 5 5
3 Maximum daily temperature in Cowra
6 6 6 6 6 6 8
1 7 1 1 5 8
10 11 12 13 14 15 16 17 18 19
6 1 1 8 1 3 3 6
Temperature (°C) 6 9 4 6

a 11.5C b 10C c 12.6C d 9C b Hurstville: mean ¼ 66.5, mode ¼ 66,

median ¼ 69.5, range ¼ 62

582 9780170188777
 Answers

Penrith: mean ¼ 56.45, mode ¼ 48, 66, 81, Chapter 10 revision

median ¼ 54.5, range ¼ 63
c Hurstville, scores are clustered in the 60s, 70s 1 a 0–4 years b 13.5%
and 80s, it has a higher median and mean c It covers more years than each of the other
d 96, mean and range groups.
4a 2 a 26% b Anglican, Other Christian
7 Murray 7 Winton c There would have been almost no Buddhist,
9 2 6 9 9 Muslim or Other.
8 8 8 7 5 2 1 1 1 3 1 1 2 3 5 6 9
9 8 8 7 7 7 6 5 4 3 2 0 4 0 1 4 5 5 6 7 7 8 8 3 a Snowy Mountains b Uluru
c 21 to 25 d True
0 5
4a January and February
b 50 c 26 d in the 30s and 40s b January and February
e 29 to 50, 26 to 48. c October
f 7 Murray: mean ¼ 40.7, median ¼ 42, d January and February
7 Winton: mean ¼ 38.6, median ¼ 39.5
g Teacher to check 5 a Profit scale does not begin at 0.
h No outliers b Sales have increased greatly

5 a 25 c Company profits
4
b Cougars: mean ¼ 65.24, median ¼ 66, 3.5
Profit ($ millions)

mode ¼ 46, 58, 61, 66, 68, 86, 92, range ¼ 49 3

Tigers: mean ¼ 71.56, median ¼ 70, 2.5
mode ¼ 53, 70, 87, 89, range ¼ 50 2
1.5
c,d Teacher to check
1
6a Maria Stacey 0.5
0
9 1 2008 2009 2010 2011 2012 2013
5 2 0 4 5 9 9 Year
9 8 7 5 2 0 3 0 0 5 5 7 7
6 a 18 8
6 5 1 4 4 b 28 c 3 d 15
3 5 7 a 31
b Stem Leaf
b Maria: mean ¼ 36.7, median ¼ 37.5, 7 1 5 6 8 9 9
mode ¼ no mode, range ¼ 34 8 0 0 0 2 2 2 3 4 4 5 8 8
Stacey: mean ¼ 31.3, median ¼ 30, 9 0 0 0 0 2 2 4 5 6 8 8
mode ¼ 29, 30, 35, 37, range ¼ 24 10 4 5
c Stacey, smaller range d Maria e Maria c 90 kg d 71 kg
8a i 4 ii 4
Power plus b i 8.78 ii 6
c i 3.5 ii 1
16
9a i 4 ii 4
2 a 74.16 b 77.16
c It also went up by 3 marks b i 10 ii 6
d It changes the mean by the amount added or c i 3.5 ii 7
subtracted
10 a i 4 ii 4.5 iii 6 iv 4.25
3 92% b i 35 ii 60 iii 66 iv 57.36
4 a 40 b, c Teacher to check
5 Yes, the other two sisters earn a total of $6700
per week

9780170188777 583
 Answers

11 a Boys Girls 4a 2g b 2000 kg c 8 weeks

7 0 1 8 d 6500 mL e 72 hours f 4000 g
9 8 2 8 9 g 1.5 kg h 3L i 8 min
8 0 3 5 7 9 j 2.5 t k 9500 mg l 12 kg
0 4 8
8 5 0 5 1 2 3 5 9 5
6 2 6 0 6 9
5 4 3 3 2 7 3 5 6
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
8 5 8 3
3 9 4
a Between 10 and 13 b 22
b 94, girl 6
Stem Leaf
c Girls: mean ¼ 55, median ¼ 54, mode ¼ 66,
0 4 5 6 9
range ¼ 76
1 0 1 3 4 5 5 6 7 8 9
Boys: mean ¼ 55.8, median ¼ 60, mode ¼ 73,
2 1 2 4 8
range ¼ 83
d Overall the boys performed better than the girls
7 a 9.44 b 3.1 c 9.05
with a higher median and mode.
d 21.89 e 5.407 f 5.283
e The girls seem to be more consistent, clustered
from 50 to 80, whereas the boys are evenly 8 a 4.34 b 1.263 c 0.07
spread across the whole range.
9 a 10.023 b 83.6 c 13.44
Mixed revision 3 10 a 24 mm b 160 cm c 30 cm d 56 cm

1 y 11 a 32 mm2 b 1600 cm2

7 E c 30 cm2 d 121 cm2
6
12 101.6 cm
4 13 a 60 cm2 b 880 mm2
A
B 2 14
4
F 3
–4 –2 0 2 4 x 2
–2 1
D
–4 –3 –2 –1 0 1 2 3 4
–4 C –1
–2
–3

2 0.5 0.75 1.3 1.6 2.25 2.9 –4

0 1 2 3

3 a The cost axis does not begin at 0. 15 a 0.2 b 0.375

b :
30 16 0:5
25
Cost ($)

20 17 a 0.8 b 12.06 c $9.82 d 3.8

15
10 18 a 8.7C b 0.25 m or 25 cm c $3.20
5
19 a 45 m3 b 330 cm3 c 11 880 mm3
New USA Australia
Zealand 20 a 7.5 kL b 7.5 m3
Country
21 a 26 928 mL b 26.928 L

584 9780170188777
 Answers

22 a i 31 ii 30 6 teacher to check 7C
b i 3.529 ii 3.3, 3.5 8a 7 1 12 3
20 b 5 c 25 d 50
23 a i 30 ii 6 9a 5
b 1
c 6
¼ 35
6 4 10
b i 3.5 ii 0.6
Exercise 11-01
24 a i 4 ii 2 iii 2 iv 2
b i 15 ii 21 iii 21 iv 20.56 1a {red, blue}, 2
25 a 4 cm b 32 cm b {red, green, blue, yellow}, 4
c {red, blue}, 2
26 a y d {red, white}, 2
9
8 e {red, black, white, green}, 4
7 f {orange, yellow, green}, 3
6
5 2 a 2, equally likely b 3, not equally likely
4 c 26, not equally likely d 2, equally likely
3 e 10, equally likely f 2, not equally likely
A B B' A'
2
1 3 a {1, 3, 5} b {a, e, i, o, u}
C C'
–8 –7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 6 7 8 x
c {5, 6, 7, 8, 9} d {March, May}
–1
e {Adelaide, Brisbane, Hobart,
–2
E D– D' E' Melbourne, Perth, Sydney}
3
–4 f Grade 1, Grade 2, Grade 3, Grade 4,
–5 Grade 5, Grade 6
–6
4a 7
–7
–8 b No, some coloured regions are bigger than
–9 others.
c pink d green
b A(5, 2) fi A0 (5, 2)
B(1, 2) fi B0 (1, 2) 5 a 20 b {$2, $1, 50c, 20c, 10c}
C(0, 0) fi C0 (0, 0) c No d 20c
D(1, 2) fi D0 (1, 2) 6a 52 b Yes c 13
E(5, 2) fi E0 (5, 2) d 26 e 4 f 2
When reflected in the y-axis, the x-coordinate of g 1 h 20 i 12
each vertex changes sign while the y-coordinate j 2
stays the same.
7D
8 a {A, B, C} b No, there are more As
Chapter 11 c A
SkillCheck 9a 3 b {5, 6, 7, 8} c 6
d {black, red} e red likely
1a impossible b likely f {hearts, spades, clubs, diamonds}
c even chance d impossible g clubs
e likely f unlikely
g certain h even chance Exercise 11-02
i likely or certain j teacher to check
2 a 15 b 4
c 9
d 3 1 a heads, tails b 2
9 10 16
c 12 d 50%
3 a 0.875 b 0.6 c 0.26 d 0.7
1 1
4 a 60% b 31% c 75% d 5% 2a 6 b 2 c 0
5 1
5 a teacher to check b teacher to check d 6 e 2 f 1
c more d more 3 a 50% b 25% c 50%
e teacher to check f more d 20% e 40% f 37.5%

9780170188777 585
 Answers

1
4a 10 b 0.15 c 55% 8 a 25% b 30% c 100%
d 75% e 0.35 f 65% d 0% e 40% f 20%
5D
9a F b D c E
1 1 2 1
6a 26 b 26 c 26 ¼ 13 d C e G f A
5 21 10 5
d 26 e 26 f 26 ¼ 13 2 1 4
10 a 15 b 15 c 15
7 a pink b yellow c black 11 5
d purple, blue, pink d 15 e 15 ¼ 13 f O

8 a blue b green c white 11 Teacher to check

3
9a 10 b 0.3 c 40% Exercise 11-04
2
d 5 e 0.4 f 20%
2
1a 10 ¼ 15
5
10 7 b 16, the expected value is higher than the
11 Teacher to check observed value
11
6 3 c
12 800 ¼ 400 80

2a i 0.16 ii 0.16 iii 0.54

13 Teacher to check
iv 0.24 v 0.1 vi 0.32
26
14 a 52 ¼ 12 b 13
52 ¼ 14 c 1
52 b i 8 ii 4 iii 2
d 4
¼ 1
e 16
¼ 4
f 6 3
¼ 26 iv 6, 7 v 10 vi 10
52 13 52 13 52
2 1 4 1
g 52 ¼ 26 h 52 ¼ 13 3 a Teacher to check b Teacher to check
15 a 1 b 5 c 12 d 25 e Teacher to check
c 9 d Teacher to check f Experimental probability would get closer to 12
16 C 4B
17 Teacher to check 18 Teacher to check 5a Teacher to check b Teacher to check
4
:: c i 16, 8 ii 16, 8 iii 12, 25 iv 56, 41
19 a 0.64 b 36 11 % or 36:36%
c 2 d Teacher to check e Teacher to check
f The experimental probability would get closer
20 a 0, Teacher to check b 1, Teacher to check to the theoretical probability

Exercise 11-03 6 a Yes b Teacher to check

c 13.75% d 11
1 5
1a 6 b 0 c 6 7 140
¼ 14
250 25
3 1 2 1
d 6 ¼ 2 e 1 f 6 ¼ 3

1 2
Mental skills 11
2a 10 b 10 ¼ 15 c 0 d 6
10 ¼ 35
3a 7
b 7
c 0 2a $35.85 b $39.80 c $35.75
12 12
2 d $34.80 e $42.85 f $69.80
d 12 ¼ 16 e 3
12 ¼ 14 f 1
g $57.80 h $53.65 i $59.90
4a 1
b 1
c 0 j $133.70
4 4

5a C b A c E Exercise 11-05
d H e D f G
g B h F 1a The sex of a new baby is male
6a 4
¼ 2
b 3
¼ 1
c 0 b No rain tomorrow
18 9 18 6
11 15 5 12 c Winning or drawing a soccer match
d e ¼ f ¼ 23
18 18 6 18 d Being right-handed
7 a 0.604 b 0.012 c 0.988 d 0 e Being 18 years or under

586 9780170188777
 Answers

f Choosing a card that is not hearts from a deck of hot dog, lemonade, ice cream
playing cards pizza, cola, cake
g A traffic light showing red or amber pizza, cola, ice cream
h A train arriving on time or early pizza, lemonade, cake
1 2 pizza, lemonade, ice cream
2a 6 b 6 ¼ 13 c 3
6 ¼ 12
hamburger, cola, cake
5 4
d 6 e 6 ¼ 23 f 3
6 ¼ 12 hamburger, cola, ice cream
1 999 hamburger, lemonade, cake
3a b
1000 1000 hamburger, lemonade, ice cream
4a 15 3
¼ 26 b 23
c 0 12
130 26 1 8
90 9 55 b 12 c 12 ¼ 23 d 12 6
¼ 12
d 1 e 130 ¼ 13 f 130 ¼ 11
26

5a 12
13 b 45% c 0.93 Chapter 11 revision
6 a 0.7 b 0.3 1 a pass, fail b G, PG, M, MA15þ, R
c 15 red, 6 white, 9 blue d 0 c Katrina, Biljana d train, bus
2
7a 12 ¼ 16 b 5
6 2a 5 b sections are not of equal size
8a 3
b 2
¼ 1
c 1
d 0 c 5 d 1 e 4
4 4 2 2
1 3
9C 3a 6 b 6 ¼ 12 c 4
6 ¼ 23
210 21 895
10 a draw b 8% 4a 1040 ¼ 104 b 1040 ¼ 179
208
685
11 a D c 1040 ¼ 137
208 d 0
6
12 a 10
11 b 7
11 c 9
11 d 8
11
5a 14 ¼ 37 b 3
14 c 0 d 1

13 15% 14 0.8 6A 7C
1
Power plus 8a 2
b 40, the observed frequency is lower than the
1a expected frequency
c 24 3
80 ¼ 10
þ 1 2 3 4 5 6
1 2 3 4 5 6 7 9 a Choosing a card that is not a queen from a deck
2 3 4 5 6 7 8 of cards, 48 12
52 ¼ 13
3 4 5 6 7 8 9 b Rolling a number that is not a multiple of 3 on a
4 5 6 7 8 9 10 die, 46 ¼ 23
5 6 7 8 9 10 11 c Buying a ticket that does not win out of 550
6 7 8 9 10 11 12 tickets sold, 549
550
7
10 15
b 11
c There are more ways of obtaining some sums
than others
Chapter 12
1 3 1
d 7 e 2 f 36 g 36 ¼ 12 h 5, 9 SkillCheck
2 a HHH, HHT, HTH, HTT, TTT, TTH, THT,
1a 2 b 3.6 c 18 000
THH
d 5 e 65 f 8
b i 18 ii 38 iii 38
1 7 4
g 7.5 h 8150 i 85
iv 8 v 8 vi 8 ¼ 12
3 a hot dog, cola, cake 2a 6 b 12 c 4
hot dog, cola, ice cream
3 a 21 b 20 c 2
hot dog, lemonade, cake
1 4 1
4a 4 b 5 c 4

9780170188777 587
 Answers

5D
Exercise 12-01
6 a 48 : 28 ¼ 12 : 7 b 20 : 35 ¼ 4 : 7
c 35 : 28 ¼ 5 : 4 d 20 : 48 ¼ 5 : 12
1 a 5:7 b 3:5 c 7:9
e 28 : 35 ¼ 4 : 5 f 48 : 131
d 7 : 13 e 5:3
7A
2a b 1:4
8 a i 72 : 1440 ¼ 1 : 20
ii 816 : 624 ¼ 17 : 13
iii 816 : 72 ¼ 34 : 3
b Teachers: students ¼ 1 : 20 > 1 : 25 so schools
has enough teachers
9 Australia 3 : 250, Pakistan 1 : 40

3 Teacher to check 10 14 : 11

4 Fewer students for each teacher 11 a 1625 mL b 375 : 1625 ¼ 3 : 13

c 375 : 2000 ¼ 3 : 16
5 a 8 : 13 b 3:8 c 13 : 1 d 1 : 25
12 7P
6 a 39 : 23 b 23 : 100
c 38 : 39 d 23 : 28 Exercise 12-03
7a 13 : 25 b 17 : 100 c 5 : 12
1 80 2 152 cm 3 20 cm 4 28
d 150 : 1 e 500 : 43 f 350 : 83
g 3000 : 1421 h 27 : 40 i 59 : 180 5 245 6 480 kg 7 C
j 180 : 7 k 9 : 49 l 7700 : 17
8 8 kg 9 72 10 20.4 t
8D 11 a Ali $90, Felicity $63
9 a 1 : 25 b 1:2 c 1:4 b $225
d 11 : 9 e 1:1 f 2:1 12 72 cm 13 A
Exercise 12-02 14 a 5 mL b 60 mL
15 175 m
1a 12 b 10 c 9
d 20 e 32 f 84 16 25 kg cement, 100 kg sand
g 30 h 75 i 5
j 5 k 4 l 30 17 600 g
m 2 n 40 o 5 18 Sonya $220, Xanthe $275
2D
Exercise 12-04
3a 1 : 10 b 1:2 c 2:5
d 5:7 e 3:2 f 7:3 1a words/min b beats/min
g 10 : 1 h 5 : 11 i 1:1 c cents/min or cents/s d $/kg
j 5 : 12 k 4:1 l 1 : 12 e $/week f L/min
m 2:3:5 n 3:4:6 o 3:1:4 g $/kg h people/year
p 3:2:8:4 i $/kL
4a 80 : 200 ¼ 2 : 5 b 300 : 1200 ¼ 1 : 4 2a 60 km/h b $6.60/h
c 6 : 28 ¼ 3 : 14 d 45 : 120 ¼ 3 : 8 c 12.5 m/s d $16/L or 1.6 c/mL
e 1:3 f 24 : 15 ¼ 8 : 5 e 19 goals/game f $19.20/kg
g 15 : 48 ¼ 5 : 16 h 20 : 1000 ¼ 1 : 50 g 18 min/question h 60 words/min
i 4000 : 350 ¼ 80 : 7 j 250 : 3000 ¼ 1 : 12 i 1.8 children/family j 9.8 m/s
k 9:5 l 20 : 1 k 150 revolutions/s l 4.5 runs/over
m 30 : 2 ¼ 15 : 1 n 3 : 20 m $0.05/g or 5 c/g n 0.12 L /km or 120 ml/km
o 1800 : 450 ¼ 4 : 1 o 20 sheep/h p 14 containers/day
588 9780170188777
 Answers

3B
18 a 794.4 h (¼ 33.1 days) b 444 13 h ( 18.3 days)
4a It costs $1.40 for every kilogram of mass c 158.88 h (¼ 6.62 days) d 46.7 h ( 1.9 days)
b An average of 60 sheep in each hectare of land
e 39.72 h (¼1.655 days) f 3.64 h
c An average of 920 toys produced each day
d 230 L pumped out every hour
Exercise 12-07
5 147 c/L 6 45 cm/year
7 71 calls/month 8 1800 hectares/month 1 a 10 a.m. b 6 km c 1.5 h
d 4 km/h e 2h f 12 km
Mental skills 12A g 2 p.m., 4 km h 6h

2a 160 b 70 c 240 2a 20 km/h b 11 a.m., 40 km

d 900 e 2600 f 900 c 1:30 p.m. d 2.5 h
g 2200 h 300 i 180 e 26 km/h f 25 km
j 400 k 1100 l 210 g 130 km
m 700 n 1800 o 390 h 11:30 a.m. – 12:30 p.m., graph is steeper
p 770
3a 240 km b 180 km c 11:45 a.m.
Exercise 12-05 d 40 km/h e 10 a.m., 160 km
f Sam, finishes journey earlier
1 a $0.90/razor b $0.53/egg g Before 11 a.m., graph less steep h B
c $0.56/pack d $0.05/teabag 4a B b A c C
e $0.01/g f $0.03/g
5 Caitlin travelled 30 km in the first hour, then 20 km
2 a Block Ices b Medium salad in the second hour. She stopped for an hour, trav-
c Party pack d 3L elled another 30 km in one hour, stopped for 12 an
e 280 g f Mega DVDs hour, then travelled another 20 km in one hour.
3 a Bullworths b GIA 6a
c Baldy d Bullworths

4 a 375 g b 2L c 735 g d 115 g

300
5A
6 a Large b Large c Large 250
d Large e Small
Distance from home

200
Exercise 12-06
150
1 1100 words 2 $893 3 420 4 3680 km
5 a 360 mL b 2520 mL 100

66 7 500 m 8 48 km
50
9 975 10 A
11 a 17C b 29C c 12 noon 9 10 11 12 1 2 3 4 5 6 7 8 9 10
Time
12 a 608 km b 5 hours
13 a 12 b 600 c 70 b 300 km c 1 p.m.
d When he is returning home at 100 km/h from
14 34 L 15 $3980 16 4.8 7 p.m. to 10 p.m.
17 a $13.50 b 2.2 kg e 3 hours f 13 h g 100 km

9780170188777 589
 Answers

Exercise 12-08 4 a 1717 b 2206 c 0245 d 0421

5 a 8:55 a.m., 1:55 p.m. b 5:55 p.m., 11:15 p.m.
1 a 1h b 21 h c 5h c 12:45 a.m. d 7:50 a.m.
d 4h e 9h f 11 h e 7:45 p.m.

2 a 22 min b 8 min c 8 min

d 2 h 16 min e 16 min f 4 h 21 min Exercise 12-10
3 a 30 b 30 c 72 d 104 1A
e 168 f 42 g 4 h 8
2a 1 h 5 min b 1 h 50 min c 5 h 44 min
i 12 j 5 k 2.5 l 4
d 3 h 53 min e 5 h 45 min f 11 h 38 min
4 a 3600 b 86 400 c 604 800 g 2 h 25 min h 43 min i 1 h 47 min
j 4 h 8 min k 7 h 39 min l 13 h 25 min
5 a 5 h 40 min b 3 h 6 min c 3 h 47 min
d 6 h 45 min e 4 h 22 min f 10 h 4 min 3 a 3h b 10 h c 14 h 40 min
d 4 h 15 min e 5 h 15 min f 8 h 45 min
6 No. A 13-year-old is 410 248 800 seconds old, g 7 h 5 min h 5 h 30 min i 8 h 40 min
which is under 1 000 000 000 (a billion) seconds. j 8 h 10 min k 5 h 55 min l 8 h 40 min
7 a 6 min 12 s b 9 min 5 s c 3 min 58 s
4 a 8:00 p.m. b 7:00 p.m. c 7:43 p.m.
d 7 min 2 s e 8 min 20 s f 8 min 44 s
d 1:17 p.m. e 2:08 p.m. f 1:32 p.m.
8a 6 h 47 min b 13 h 7 min c 4 h 25 min g 2:14 a.m. h 4:15 p.m. i 6:17 a.m.
d 3 h 25 min e 7h f 7 h 14 min j 3:25 p.m.
g 4 h 13 min h 3 h 28 min i 10 h 3 min
5 Joe 12:43 p.m., Anna 1:14 p.m., Ken 1:19 p.m.,
j 9 h 51 min k 51 min l 49 min
Pathena 1:21 p.m., Mike 1:31 p.m., Gail 2:02 p.m.
Mental skills 12B 6 4 h 45 min 7 6 h 25 min
8 a 2:15 p.m. b 2:30 a.m. c 2:35 p.m.
2a 18 b 34 c 46
d 11:25 a.m. e 7:55 a.m. f 6:15 p.m.
d 66 e 26 f 16
g 8 h 44 i 12 9 a 4 years 2 months b 4 years 6 months
j 40 k 28 l 40
m 18 n 8 o 36 10 a 6 years 1 month 6 days
p 140 b 15 years 5 months 25 days
11 2 h 15 min 12 2 p.m.
Exercise 12-09
13 1 year 4 months 14 17 years 8 months
1a 8:45 a.m. b 1:20 p.m. c 5:50 p.m.
15 $155 16 14 years 0 months 11 days
d 12:17 a.m. e 9:05 p.m. f 6:32 p.m.
g 11:15 a.m. h 2:38 a.m. i 2:40 p.m.
j 3:20 a.m. k 4:55 p.m. l 11:31 p.m. Exercise 12-11
m 1:08 a.m. n 10:45 a.m. o 8:00 p.m.
p 6:43 a.m. 1 a 7h b 6 h 30 min c 3:20 p.m.
d 4 h 11 min e 13 min
2a 1835 b 0805 c 1144 d 2320
f 1 h, 1 h 15 min, Liverpool-Sydney trip occurs at
e 0251 f 1230 g 1538 h 0711
the start of peak traffic period
i 0908 j 2154 k 0042 l 1939
m 0159 n 2218 o 0846 p 1723

3 a 11:23 a.m. b 5:54 p.m. c 1:24 p.m.

d 10:03 a.m. e 11:17 p.m.

590 9780170188777
 Answers

2a 9:35 a.m., 1 h 25 min 6 a 3000 voters/politician b 200 sheep/ha

b TH114 (10:40 a.m.) c $0.80/ticket d 270 stitches/ball
c 25 min d 9:25 a.m.
7 a Chow b Dairy Farm
e TH038, 10:05 a.m.
3 a 7:27 a.m. 8 a $503.50 b 24.1 L c 7.5 ha
b The 5:08 train takes 3 h 4 min and the 9 a 20 km b 3
8:17 train takes 2 h 37 min. c 2:30 p.m. d 2:30 p.m. – 3:30 p.m.
c 46 min e 2.5 km/h
d Teacher to check
e Goulburn 11:12 a.m., Bundanoon 11:47 a.m., 10 a 10 h b 3h c 4h
Moss Vale 12:00 noon, Bowral 12:06 p.m.,
Mittagong 12:11 p.m., Campbelltown 1:07 p.m., 11 a 5 h 16 min b 3 h 28 min
Strathfield 1:37 p.m., Sydney 1:49 p.m. 12 a 10 h 5 min b 4 h 42 min
4 a 12:34, 1 h 4 min b 1:14 c 12:45 c 2 h 9 min d 29 min
d 5, the first bus finishes its run at 11:50, ready to
start the 6th run at 12:00 13 a 1:48 a.m. b 6:24 a.m.
e 10:33 City cathedral, 11:00 Museum, 12:30 City c 3:50 p.m. d 12:30 p.m.
square, 1:12 Town Hall, 2:28 Hall of Fame
14 a 1410 b 0533 c 0019 d 1350
(other answers possible)
f 1:30, 1:38, 1:45, 1:54, 2:05, 2:15, 2:30, 2:42, 15 a 4 h 20 min b 7 h 35 min
2:49, 3:00, 3:08, 3:20. c 6 h 55 min d 6 h 30 min
e 30 min f 8 h 55 min
Power plus
16 14 years 2 months 13 days
1 Teacher to check 17 a 3 h 19 min b 9:05 a.m.
2 a 4:7 b 13 : 8 c 10 : 1
d 7 : 20 e 8:3 f 6:5
Mixed revision 4
3 Kobe is right (38 : 66 vs 36 : 66)
1 a {1, 2, 3, 4, 5, 6}
4 271 374 b {red, blue, green, yellow}
5 a 710 km2 b 54 913 080 400 2 a 3:5 b 3:2 c 5:2
6 a 166 23 min b 8.64 h 3 a 25 km/h b $4/m
c 500 revolutions/min d 300 cans/day
Chapter 12 revision 4 a 5 h 25 min b 1 h 10 min
c 11 h 41 min d 7 h 5 min
1 a 8 : 16 ¼ 1 : 2 b 12 : 24 ¼ 1 : 2
5 a 0825 b 1645
2 a 38 : 17 b 17 : 55
6 a 9:15 p.m. b 4:30 a.m.
3 a 12 b 10 c 9 : 12
4a 4:7 b 1:3 c 1:6 7 a 1:3 b 8:3 c 1:3
d 5:9 e 3:1:4 f 1 : 5 : 20 d 40 : 3 e 1 : 12 f 2:5:7
g 2:1 h 10 : 1 i 5:1 8a 1
b 2
2 3
j 1 : 20 k 1:3 l 1:5
m 1:2 n 4:7 o 48 : 5 9 a 50 3
b 5

5 a 100 b $45 000 10 20

9780170188777 591
 Answers

11 a 3 7 17 {red, amber, green}

10 b 10

12 a 40 km/h b 440 km 18 a 2 b 16 c 4 d 25
9 5 3
13 50 h 19 a 10 b 12 c 8 d 1 12
14 a 6 km b 1 p.m. for 1.5 h 20 a (2, 1) b (1, 0) c (2, 3)
c 26 km d 10:30 a.m. and 4 p.m.
e first hour 21

15 2 L
0 1 2 3 4 5

General revision 22 a 2.7 b 2.5 c 2 d 5

23 a \ACD and \CFE (other answers possible)
1 a Sum of digits ¼ 1 þ 9 ¼ 5 ¼ 15, which is b \ACD and \BCF (other answers possible)
divisible by 3. So 195 is divisible by 3 c AH
b 65
24 a 105 b 75 c 75
2 85
1
25 4
3 a 121 b 7 c 1000
26 a Teacher to check b 1
4 a 60 b 360 c 405 d 192
27 a 1 : 5 b 4:3 c 1:4
5 2x þ 8
28 a b
6 a 3x b 5m2 c 7k
2
d 6y e 10  kn f 2p þ 4

7 a 7200 b 0.425 c 4
d 0.24 e 50 f 6700

8 a 42 mm b 40 cm c 16 cm
c
9 1810 10 6 h 35 min 11 470
12 a 70 b 150 c 25
13 5, 3, 2, 4, 6, 11
29 y
14 a 2 b 12 c 13 d 56
5
e 120 f 100 g 9 h 2
4 S
15 T 3
2 R
1

–2 –1 1 2 3 4 x
–1

30 3, 11
31 a 1, 3, 9, 27 b 9
16 a 0.5 b 50%

592 9780170188777
 Answers

32 a 240 49
10 × 24 45°

5 × 2 × 4 × 6

5 × 2 × 2×2×2 ×3 90° 45°

Other factor trees possible.
b 240 ¼ 24 3 3 3 5 50 8:45 p.m.
33
Appendix 1 Calculator skills

Exercise A-01
Trapezium
1a 5068 b 14.5 c 45
34 a d 5.724 e 3.5 f 26.9
g 23 h 1.68 i 160
j 29.48 k 8.084 l 12.42

2 a $19.15 b 85 cents
b 2 c 2
3 $1875.50 4 7542 kg 5 2.4 m
7 1 3
35 a 20 b 10 c 250 6 $11.25 7 23 trees 8 75.2 km/h
36 a 1.7 b 0.7 c 1.0 9 $85.74 10 13 buses
37 a False b True c False 11 a $41.20 b $1318.40
38 a b ¼ 7 b r¼7 c n¼4 d p¼6 12 53.4
39 7
40 a 30 cm2 b 95 cm2 Exercise A-02
41 168 m3 1a 7 b 9 c 12
42 a $9 b 16 m c 200 mL d 8 e 15 f 15
d $20 e 4 kg g 75 h 5 i 5
j 7 k 96 l 45
43 a 73% b 75% c 60% d 47% m 25 n 24 o 96
p 14 q 16 r 15
44 a 15 b 36 c 64 d 35 s 36 t 10
45 a 3
5 b 60
Exercise A-03
46 a $44.70 b 33.6 L
1a 196 b 529 c 216
47 a 29.67 b 3.07 c 5.314 d 1.728 e 26.3169 f 10 201
:
48 a 0.625 b 0.55 c 0.16 g 4.1616 h 6859 i 26
j 148 k 9 l 42

9780170188777 593
 Answers

7 1 1
2 a 4.9 b 10.0 c 4.7 d 4.6 5a 20 b 2 25 c 1000
73 3 13
3 a 16 b 156 c 6 d 10 d 200 e 1 50 f 40

17 1 1 4
6a 20 b 1 14 c 15 d 21
Exercise A-04 e 1 13 f 5
g 1 17 h 35
24 30 96

1a 5
b 8
c 5 i 1 34 j 19 15 k 6 13
20 l 8 13
24
8 17 8
d 8
e 21
f 1 m 12 34 n 7 o 4
27 p 19 19
60
9 25 4

7a 1 3
2a 15
b 47
c 43
8 b 4
8 9 4
:
3 a 2 29 b 8 45 c 2 14 c 15 45 or 15.8 d 1
6 or 0:16

4 a 0.5 b 0.8 c 0.875 8 a 6 34 hours b 33 34 hours

:
d 0.36 e 0.17 f 0.5

594 9780170188777