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ANSWERS

345ISBN 9780170351027 Answers

CHAPTER 1Exercise 1–011 C2 a 9 b 49 c 121 d 196 e 73.96 f 81 g 146.41 h 3.61 i 16 j 262.44 k 64 l 92.163 a 4 b 6 c 8 d 11 e 144 B5 a 4.24 b 5.66 c 9.06 d 12.25 e 14.836 D7 a True b False c False d True e False8 25 m2

9 7 m10 Side = 8 m

Exercise 1–021 A 2 C3 a p2 = q2 + r2 b i2 = m2 + n2

c a2 = b2 + c2 d e2 = d2 + f 2

e x2 = y2 + z2 f r2 = s2 +t2

4 a 132 = 52 + 122, True b 162 = 92 + 122, False c 172 = 82 + 152, True5 a and c

Exercise 1–031

hypotenuse

2 c2 = a2 + b2

c2 = 62 + 82

c2 = 100 c = 100 = 103 a 26 cm b 15 cm c 17 m d 34 m e 5 cm f 2 cm4 a 2.2 cm b 1.4 cm5 a 12.4 cm b 13.4 m c 23.5 m

Exercise 1–041 A 2 B3 202 = b2 + 122

b2 + 122 = 202

b2 = 202 – 122 = 400 – 144 = 256

b = 164 a 24 cm b 24 m c 5 m d 7 cm5 a 13.4 m b 8.5 m c 8.3 m d 11.8 m

Exercise 1–051 A 2 B3 a 8 cm b 288 m c 337 m d 1475 m e 41 m f 2380 cm4 a 9.7 cm b 10.4 m c 19.1 m5 hypotenuse

Exercise 1–061 Substitute given values into Pythagoras’ theorem,

and check if the left-hand side is the same as the value of the right-hand side.

2 B 3 C4 172 = 152 + 82

289 = 225 + 64 289 = 289 Yes, so the triangle is right-angled.5 a 412 ≠ 102 + 402, No b 252 = 202 + 152, Yes c 222 ≠ 152 + 162, No d 22 = 1.62 + 1.22, Yes e 6.12 = 1.12 + 62, Yes f 742 ≠ 82 + 222, No6 b ∠ R d ∠ Q e ∠ Q

Exercise 1–071 three Pythagoras’2 C 3 B4 132 = 52 + 122

169 = 25 + 144 169 = 169, So {5, 12, 13} is a Pythagorean triad.5 a 412 = 92 + 402, Yes b 252 ≠ 72 + 202, No c 202 = 122 + 162, Yes d 522 ≠ 112 + 502, No e 72 ≠ 52 + 62, No f 252 = 72 + 242, Yes g 172 = 82 + 152, Yes h 122 ≠ 42 + 82, No6 {10, 24, 26} and {15, 36, 39}7 a 342 = 162 + 302 b {8, 15, 17}8 {14, 48, 50} and {21, 72, 75}9 a True b True c False10 Teacher to check, Yes.

Exercise 1–081 C 2 6.5 m 3 17 cm4 5 cm 5 2.5 m6 a

95 m

73 m b 61 m

7 2.6 m 8 23 m9 32 – 23 = 9 m 10 13.3 km

Practice test 11 9:08 p.m. 2 608 mm 3 220

4 44 m 5 1

14 6 –2x + 8

7 $24 8 x = 4 9 5 10 $16.5511 a 5.83 b 6.71 c 7.2112 82, 28, 75, 6813 k, k2 = h2 + j2

8 m

ANSWERS

346Developmental Mathematics Book 3 ISBN 9780170351027

14 a c = 61 b r = 25015 a 5.74 cm b 10.32 m16 a 10.7 m b 175.3 m c 23.4 km17 a 342 = 162 + 302, Yes b 2.22 ≠ 1.62 + 0.42, No18 a 32 = 2.42 + 1.82, Yes b 262 ≠ 72 + 242, No19 75.6 cm20 56 cm

CHAPTER 2Exercise 2–011 B2 a 19 b 39 c 37 d 148 e 39 f 44 g 59 h 77 i 108 j 59 k 122 l 1083 b and e, g and j, i and l4 a 82 b 82 c 148 d 1895 a They are the same. b Just add 41 to c’s answer6 a T b F c F d T7 a 2 b 3 c 2 d 3008 C9 a 856 b 1146 c 1125 d 1545 e 658 f 982 g 1859 h 364110 a 120 b 90 c 120 d 80 e 316 f 942 g 674 h 68311 a

3 6 6

8 5 2

4 4 7

b 4 7 7

9 6 3

5 5 8

Exercise 2–021 A2 a 11 b 16 c 14 d 28 e 6 f 52 g 16 h 59 i 224 j 436 k 663 l 8383 a 84 – 9 = 84 – 10 + 1 = 74 + 1 = 75 b 358 – 41 = 358 – 40 – 1 = 318 – 1 = 3174 D5 a 63 b 43 c 47 d 89 e 51 f 87 g 102 h 123 i 408 j 501 k 468 l 4926 6 + 30 + 3 = 397 a 25 b 71 c 38 d 38 e 47 f 37 g 35 h 578 a F b T c T d F9 5070

Exercise 2–031 C 2 B3 a F b T c T d T e F4 a 3 b 7 c 13 d 21 e 25 f 7 g 16 h 121 i 264 j 185 a 0.4 b 1.7 c 0.9 d 1.7 e 3.2 f 0.7 g 2.2 h 3.4 i 12.5 j 2.06 a 0.22 b 1.42 c 5.52 d 11.32 e 126.22 f 0.43 g 3.27 h 0.92 i 7.23 j 1.907 a 0.264 b 1.731 c 5.844 d 11.321 e 126.2328 a $5 b $52 c $27 d 45 e $29 f $10 g $232 h $501 i $227 j $4029 a $5.71 b $12.43 c $32.57 d $4.23 e $218.93 f $110.43 g $1.68 h $502.92 i $22.30 j $43.9010 a $490 b $487 c $486.80 d $486.85

Exercise 2–041 D 2 A3 a 0.03 b 0.26 c 0.53 d 3.364 a 0.2 b 2.2 c 2.9 d 2.85 a 15.98 b 51.05 c 133.368 d 132.58 e 22.14 f 338.9 g 28.814 h 147.63 i 28.3 j 9.48 k 307.037 l 420.36 a 0.3 b 4.1 c 0.9 d 1.2 e 0.06 f 2.22 g 0.3 h 1.86 i 3.8 j 11.6 k 2.1 l 11.797 a $23.50 b $17.30 c $7.75 d $57.40 e $55.22 f $31.01 g $20.65 h 51.188 a $17 b Yes c $17.40 d $2.609 $14.39 10 $4885

Exercise 2–051 B 2 C3 a 30 b 24 c 28 d 18 e 40 f 24 g 63 h 36 I 42 j 30 k 21 l 72 m 48 n 27 o 35 p 16 q 45 r 184 a T b F c T d T e T f F5 a 140 b 506 c 567 d 328 e 350 f 416 g 150 h 1164 i 340 j 570 k 2960 l 6120 m 8100 n 28800 o 41000 p 364000

ANSWERS

347ISBN 9780170351027 Answers

6 a 5, 10, 330 b 25, 100, 42007 a 270 b 1500 c 2600 d 1400 e 540 f 5800 g 3600 h 82 000

Exercise 2–061 B 2 D3 a 260 b 54 c 6800 d 4.5 e 22650 f 154.2 g 38 h 204.154 a F b T c F5 a 1 b 1 c 2 d 36 a 4.5 b 16.8 c 0.14 d 0.0127 a 22.4 b 8.4 c 171 d 259.2 e 8.52 f 18.825 g 0.368 h 0.8722 i 108.18 j 0.0096 k 10.155 l 51.2128 a 16.64 b 1.664 c 1.664 d 0.1664 9 Estimate = $20 × 6 = $120, Answer = $130.8010 Estimate = 9 × 1 = 9 m2, Answer = 7.74 m2

Exercise 2–071 B 2 D3 a 5 b 4 c 4 d 5 e 6 f 7 g 5 h 5 i 11 j 9 k 7 l 8 m 5 n 9 o 5 p 9 q 7 r 44 a F b T c T d T e F f F g T5 a 43 b 39 c 32 d 107 e 23 f 153 g 16 h 14 i 80 j 31 k 52 l 176 a 12 b 54 c 33 d 51 e 24.5 f 2.18 g 2.9 h 3.21 i 0.43 j 0.62 k 0.048 l 0.0367 a 594 b 650 c 316 d 4788 a 4 b Tinsel $1.05 Baubles $0.65 Gift wrap $1.70

Cards $0.90

Exercise 2–081 D 2 C3 a 0.038 b 2.56 c 0.0724 d 78 e 0.1283 f 0.1278 g 0.095 h 0.0254 12.95 a 7.6 b 10.81 c 30.9 d 22.5 e 31.6 f 103.02 g 14.4 h 164.25

6 684.6, )3 684 6228 2

.

.

7 a 4 b 6.2 c 12.06 d 42.6 e 249 f 8.6 g 1184.6 h 1830 i 1.15 j 415 k 260 l 6498 4.641 9 1.19 m 10 $6.28

Exercise 2–091 D 2 C3 a T b F c T

4 a 0 7. b 0 62. c 2 1. d 3 46.

e 5 23. f 0 528. g 7 23. h 12 425.

5 a 3.1875 b 6.52 c 95 13.

d 2.825 e 30 43. f 8 71.

g 11.35 h 9 40571428.

6 a, b, d, g terminating; c, e, f, h recurring7 a Divide 3 by 8 b 0.375 c terminating8 a 0.25 b 0 3. c 0.625 d 0.6 e 0 16. f 0 285714.

g 0 416. h 0.875

9 a 23

b 0 6. c $600

Language activityDECIMAL DILEMMA

Practice test 21 720 2 12000 3 1, 2, 3, 64 x 5 7 6 97 $12 8 d = 14 9 36rv 10 1611 a 38 b 81 c 47112 B13 a 49 b 9714 a 2.68 b 0.92515 a 16.25 b 19.7116 a 960 b 530017 a 4760 b 0.028 c 0.94818 T19 a 44 b 339 c 58620 a 1.642 b 17.15 c 457.521 F22 a 6 12. b 0 48. c 12 412.

23 0 2.

CHAPTER 3Exercise 3–011 B 2 C3 a 6 b 7 left c 8 left d 4, 2 left4 a 5 b –1 c 2 d 2 e 0 f –1 g –1 h 3 i 3 j 0 k 7 l 95 a 3 b 5 + (–3) c –5 + (–3)6 a 3 b 7 c –9 d –4 e 8 f –7 g –7 h 9 i 1 j 16 k 6 l 217 a 6 b 23 c 6 d 12 e 38 f –24 g 35 h –118 $51 9 13th floor 10 220

Exercise 3–021 C 2 D3 a F b T c F d T

ANSWERS


4 × –2 5 –6 8 –4

3 –6 15 –18 24 –12

–7 14 –35 42 –56 28

–9 18 –45 54 –72 36

10 –20 50 –60 80 –40

5 a –12 b –30 c 21 d –16 e 36 f 27 g –42 h –25 i –72 j 30 k 16 l 42 m 36 n –168 o –100 p –1356 a –8 b –2 c 9 d –8 e 7 f –4 g –8 h –7 i –9 j 30 k –40 l –7 m 8 n –2 o 16 p 207 a 32 b –18 c 12 d 28 $1500

Exercise 3–031 B 2 C3 a × b ÷ c ÷ d ÷ e × f ÷ g × h × i ×4 a 27 b 44 c 129 d 37 e –42 f 85 g –45 h 78 i 805 a –18 b –25 c 142 d 17 e –12 f 326 a 5 b 9 c 122 d 2867 a –36 b 15.6 c –5 d 95.1 e –31 f 27.9 g –236 h 2 i –4.058 $1685

Exercise 3–041 A 2 D 3

54

125

98

85

, , ,

4 a 114

b 312

c 135

d 158

e 213

f 217

g 212

h 129

5 a 32

b 103

c 225

d 158

e 135

f 196

g 179

h 145

6 23 pieces7 a T b F c T d T e F

8 a 25

b 25

c 45

d 34

e 5

12 f

25

g 2132

h 1825

i 12

j 34

9 a 8 pieces b 13

c 29

Exercise 3–051 C 2 B3 a T b F c T d F4 a 40 b 8 c 60 d 400 e 10 mins f 10 m g $80 h 12 L i 80 cm j 600g k 15 h l $450

5 a $640 b 13

6 a $350 b 712

7 a $9000 b $15 000 c 13

8 a 3 ha b 4 ha c 5 ha

Exercise 3–061 C 2 B3 a T b T c F d F e T f F g T h T

4 1170

15

710

67

, , , 5 56

34

38

112

, , ,

6 a < b > c = d < e > f < g < h =

7 Convert fractions to 12ths: 12

612

= , 34

912

= , 13

412

= , 56

1012

= , 712

0 113_ 1

234

56

712

8 Her daughter.

Exercise 3–071 D 2 B

3 a 3 b 8 c 3

128

121112

+ =

d 9 e 4 f 9

124

125

12− =

4 a 56

b 920

c 1115

d 58

e 4940

1940

= f 2928

11

28=

g 345

h 138

158

= i 523

j 1712

5 a 14

b 715

c 38

d 49

e 16

f 524

g 323

h 1

12

i 214

j 31

12

6 a 51320

b 21

24 c 8

940

d 338

e 234

7 a 23

b 13

c 2

ANSWERS

349ISBN 9780170351027 Answers

Exercise 3–081 C 2 D 3

2 13 5

215

××

=

4 a 1

12 b

12

c 340

d 732

e 12

f 1027

g 8 h 16

i 715

j 16

5 23

51

103

313

× = =

6 a 12

b 12

c 178

d 13

e 14

f 178

g 1

18 h 1

12

i 1

20 j

715

7 a 645

b 8716

c 21116

d 11922

e 99

32

8 a 18

b $2100 c $1050

Language activityFRACTION FRENZY

Practice test 31 2.19 2

45

3 15x + 2y

4 24cm2 5 412

6 4.15

7 $6 8 3x2

9 7 6 3 0 –2 –510 12.711 a –2 b –11 c –1412 A13 a 28 b –7 c –10814 B15 a 6 b 60 c –31

16 a 114

b 158

c 2710

17 a 23

b 45

c 13

18 a 30 b $90 c 150 cm19 a T b F c T

20 a 14

15 b

1124

c 234

d 418

21 a 215

b 217

c 938

d 223

22 a 8 b 716

CHAPTER 4Exercise 4–011 C 2 A3 a a + b b a – b c ab d

ab

4 a T b F c F d T5 a 3a – 8 b 12– 2b c 2(m + n) d 3(x–y) e 2n + 7 f w2 – 5 g 3y + w h 2(x+ y) i (mn)2

j 24 – g2 k 120 + 3d l m2 + 2n m 12 – 3b n h + 2j6 a 5a cents b $6q c $15d

d $r3

e $kw f $d

127 a 4g b m + 2n c 2d + 2w

8 a g2 b 12

mh c dw

9 a 2m b m – 4 c 2m + 10 d m + 810 a 4x b 2y c 4x + 2y d x + y

Exercise 4–021 A 2 D3 a F b F c F d T4 a –20 b 19 c 50 d –24 e –3 f 24 g –62 h 1505

3m – n 2m2

4mn 3(2m + n) 6mn2

m = 2, n = 4 2 8 2 24 192

m = –1, n = 3 –6 2

−43 3 –54

m = 5, n = –2 17 50 –10 24 120

m = –1, n = –4 1 2 1 –18 –96

m = 3, n = –2 11 18 –6 12 72

6 a 12.6 b 48 c 45.92 d 90.3 e 13 f 2.47 a y x= −3 1

x –1 0 1 2

y –4 –1 2 5

b y x= −12

x –1 0 1 2

y 13 12 11 10

ANSWERS


c y x= 2 2

x –2 0 2 4

y 8 0 8 32

d yx

= +23

1

x –3 0 3 6

y –1 1 3 5

8 311.6 cm3

Exercise 4–031 B 2 D3 a 3x, 2x b 4a. a c 5w, –2w d 2ab, 3ba e 2ab, 2ba f –6m, 18m4 a F b T c F5 a 3a b 6x c 6w – 3 d 7m e 2y f –2n +7 g –2a h 15m i –3t6 a 4m – 2n – 6m + n = 4m – 6m – 2n + n

= – 2m – n b 8x + 5y – 2y – x = 8x – x + 5y – 2y

= 7x + 3y7 a 7x – y b 6x – 6y c 11m – 3n d 10m – n e 3x + 4y f 9a – 5b g 15r – 8s h –2ab + 6 i –xy – 7y + 78 a 9x + 1 b 24x + 12 c 6x – 69 All the terms are unlike and cannot be added or

subtracted.

Exercise 4–041 D 2 B3 a F b T c T d T4 a 5a × 3b = 5 × 3 × a × b

= 15ab b –6x × 8y = –6 × 8 × x × y

= –48 xy c 5a2 × 2a = 5 × 2 × a2 × a

= 10 a3

d –4mn × (–7m2) = –4 × (–7)× mn × m2 = 28 m3n

5 a 16m b 12xy c –18mn d –20ab e –12cd f 10wv g 27ab h 6x2y i 60mn j 24a2b2 k 12a3 l 15m4

m 6w3 n –20xy3 o –24ab3 p 18x3y2

q –32r4s2 r –72w3 s 21m4 t 24a2b2

6 a 9x2 b 12bh c 27vw

Exercise 4–051 A 2 D3 a F b T c T d F4 a 4a b –3b c 2d d –3ab

e –3bc f –2xy g –4m h 9ac

i −4vx

j –2r k −6xy

l −12w

y

5 a 4 2xy

b 5 3

2

ab

c 45

3

2

mn

6 a 2 4ab b 4x2y c −5 2

3

mn

7 a 3x × 4 b 14a ÷ 7 c –24ab ÷ (–6b)8 a 12 – 12x b 6 + 2a c 8a2

9 a 18 + 12x b 13m c 6a d –18y2

e 6m2 f 24 + 4y g 18m h 0

Exercise 4–061 B 2 C3 a 4(3x – 2) = 4 × 3x + 4 × (–2)

= 12x + (–8) =12x – 8

b –6(2a – 1) = –6 × 2a + (–6) × (–1) = –12a + 6

c a(3a + 2) = a × 3a + a × 2 = 3a2 + 2a

d –2x(3x – 1) = –2x × 3x + (–2x) × (–1) = –6x2 + 2x

4 a 5x + 10 b 3a – 12 c 8a – 4 d 24x + 16 e 24 – 12a f 2a2 – 3a g 3x2 + 4x h 2m2 – 12m i 6w2 + 15w j 12a2 – 24a k –8a – 6 l –40 +15m m –2x + 8 n –3a – 9 o –12w + 485 a Both sides equal 45. b Both sides should still be equal.6 a 3(2y – 1) + 5y = 6y – 3 + 5y

= 11y – 3 b 12 + 4(2m – 1) = 12 + 8m – 4

= 8m + 8 c 2(3x – 4) – 3( x+ 4) = 6x – 8 – 3x – 12

= 3x – 20 d 5(2a – 2) + 7(3a + 1) = 10a – 10 + 21a + 7

= 31a – 37 a 5x – 23 b 3x + 9 c a + 34 d 3x + 10 e 5x – 9 f 4a + 54 g –2x + 32 h x – 37 i –a + 428 14w – 28v – 6v – 15w = – w – 34v

Exercise 4–071 C 2 B3 a The factors of 8 are: 1, 2, 4, 8.

The factors of 20 are: 1, 2, 4, 5, 10, 20. The HCF of 8 and 20 is 4.

b The factors of 16 are: 1, 2, 4, 8, 16. The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40. The HCF of 16 and 40 is 8.

4 a 2 b 3 c 4 d 15 e 2 f 6 g 4 h 9

ANSWERS

351ISBN 9780170351027 Answers

5 Any 4 of or combination of: a 1, 3, 9, a, b, ab b 1, 2, 7, 14, m, n, mn c 1, 2, 4, 8, x, x2 d 1, 2, 3, 4, 6, 12, b, c, bc e 1, 2, 4, m, m2 f 1, 2, 4, 8, 16, b, b2

g 1, 2, 4, 5, 10, 20, a, a2, a3

h 1, 2, 3, 6, m, m2, m3, m4

6 16, xy, 16 × xy = 16xy7 a 4a b 2 c 2 d 3 e 8m f 4a g 2w h 2m i bc j mn k 3s l 6uv8 4bc

Exercise 4–081 D 2 B3 a 3a + 3b = 3(a + b) b 5x – 10y = 5(x – 2y) c 6m + 18n = 6(m + 3n) d 4b2 – 4 = 4(b2 – 1) e 9a + 3b = 3(3a + b) f 15x – 12y = 3(5x – 4y) g 7u + 14v = 7(u + 2v) h 8n2 – 2 = 2(4n2 – 1) 4 a 2(a + 6) b 6(p – 3) c 5(n + 4) d 8(y – 8) e 12(a + 5) f 16(x – 3) g 18(a + 3) h 14(c – 2) i 15(a + 5) j 5(3x – y) k a(a + b) l y(x + z) m n(m + n) n 9(p – 3q) o xy(z – 3)5 a 3a2 + 6ab = 3a(a + 2b) b 15xy – 10y2 = 5y (3x – 2y) c 16mno + 24noq = 8no(2m + 3q) d 48b2 – 16bc = 16b(3b – c) e 27ab + 18bc = 9b(3a + 2c) f 25x2 – 15xy = 5x(5x – 3y)6 a 4p(a – 3q) b 4s(4r + 3t) c 7y(4x – 6y) d 32bc(2a – d) e 8m(m + 6n) f 11b(2b – a) g 18g(2f + g) h x(yz – 7uv) i 7b(2a2 – 3bc) j 9w(6w + uv) k 8t(3r2 – 2v2) l 25mn(3n + 2m)7 7bc(6a2 – 2b + 4a)

Exercise 4–091 C 2 B3 a –5 b –4 c –6 d –5 e –5 f –4x g –6n h –5v4 a –4a – 4b = –4(a + b) b –5x – 10y = –5(x + 2y) c –16m – 8n = –8(2m + n) d –4b2 – 4 = –4(b2+1) e –9a + 3b = –3(3a – b) f –35x – 7y = –7(5x + y) g –7u + 14v = –7(u – 2v) h –8n2 + 2 = –2(4n2 – 1)5 a –2(a + 9) b –6(p + 4) c –4(n + 5) d –7(y + 7)

e –12(a + 5) f –16(x – 2) g –18(a – 2) h –4(c + 7) i –15(a – 5) j –25(x + 2y) k –a(a + c) l –y(x – z) m –n(m – n) n –3(p + 9q) o –xy(z – 5)6 a –3a2 – 6ab = –3a(a + 2b) b –5xy – 20y2 = –5y(x + 4y) c –8mno + 24noq = –8no(m – 3q) d –32b2 – 16bc = –16b(2b + c) e –9ab + 18bc = –9b(a – 2c) f –50x2 – 25xy = –25x(2x + y)7 a –3p(a + 4q) b –4s(2r + 3t) c –7y(x + 6y) d –16bc(a – 2d) e –6m(m – 8n) f –11b(3b + a) g –6g(f – 3g) h –x(yz + 7uv) i –7b(a2 + 3bc) j –3w(2w – 3uv) k –8t(r2 + 2v2) l –15mn(n – 3m)8 –12bc(2a2 + b – 3a)

Language activity1 C 2 S 3 G 4 R5 A 6 L 7 B 8 I9 T 10 E 11 NABSTRACT ALGEBRA ANTICS

Practice test 41 150 2 1800 3 3b 4 96 cm3

5 $30 6 $35.15 7 5 8 2 9 9.9 9.909 9.91 9.95 10 27, 24311 a 2a – b b 12xy

c 3(m + n) d 73

ab

12 D13 a –2.4 b 29.2 c 53.814 a 2v – 11w b 13ab – 4b c 16mn – m2

15 a 6ab b –24x3y c 72uv2w16 21xy

17 a –4a b 6x c −ba2

18 a F b T c F19 a 5m – 14 b –3a2 – 7a20 a 9m b 4x c 16mn22 a 6(a – 2b) b 2x(7 – 8y) c 2u(3u – 14v) d 7ab(4b – a)23 a –6(m + 4n) b –8x(3 – 2y) c –15u(u + 3vw) d –8b(6bc + a2)

CHAPTER 5Exercise 5–011 C 2 B3 a P b Q c r d p

ANSWERS


4 a

b

A

C Ba

c

b

Z X

Y

z

y

x

c P

q

Q

R

p

r

5 a c b x c p6 a hypotenuse = 13, opposite = 12, adjacent = 5 b hypotenuse = 10, opposite = 8, adjacent = 6 c hypotenuse = 17, opposite = 15, adjacent = 8 d hypotenuse = q, opposite = r, adjacent = p e hypotenuse = y, opposite = x, adjacent = z f hypotenuse = u, opposite = v, adjacent = w7

r

Q

P

Rp

q

Exercise 5–021 C 2 B

3 sin A =opposite

hypotenuse cos A =

adjacenthypotenuse

tan A =oppositeadjacent

4 a 8

10,

610

and 86

b 610

, 8

10 and

68

5 a i bc

ii rq

b i ac

ii pq

c i ba

ii rp

6 a sin F = 9

15 b cos F =

1215

c tan F = 9

12 d sin D =

1215

e cos D = 9

15 f tan D =

129

7

24

2610

A

B C

Exercise 5–031 tan 60° ≈ 1.73 2 tan 23° ≈ 0.423 tan 71° ≈ 2.90 4 tan 45° = 15 tan 38° ≈ 0.78

Exercise 5–041 C 2 B3 a 1.111 b 0.743 c 0.6694 a 42° The 3 angles of a triangle add up to 180°. b 0.900, 0.669, 0.7435 a 0.866 b 1.732 c 0.707 d 0.643 e 0.990 f 1.036 g 0.891 h 0.934 i 3.732 j 0.9706 a 0.6157 b 2.0503 c 0.1045 d 0.4663 e 0.1219 f 0.3249 g 0.7193 h 1.0000 i 1.0000 j 1.60037 a 0.8 b 0.9 c 5.7 d 0.4 e 0.6 f 0.9 g 3.5 h 0.5 i 0.3 j 0.08 a 39° b 49° c 83° d 73° e 11° f 39° g 44° h 68° i 55°9 a 43° b 58° c 26° d 60° e 58° f 15° g 75° h 27° i 37° j 90° k 44° l 90° m 37° n 0° o 37° p 30° q 45° r 60°10 42°

Exercise 5–051 C 2 C

3 tan 28° = m5

5 ×tan 28° = m m = 2.658547158 m = 2.664 a c = 11.52 b q = 7.55 c x = 5.465 11.626 a a = 3.7 b r = 15.8 c y = 19.77 13.86 m 8 156.9 m

Exercise 5–061 A 2 D3 a F b T c T d F4 a 33° b 71° c 37°5 a 62° b 28° c 80°

ANSWERS

353ISBN 9780170351027 Answers

6 a

R

P

Q5 cm

12 cm

tan P = 5

12, P = 23°

7 67° 8 64°

Exercise 5–071 B 2 A

3 tan 35° = x

15 8. 15.8 tan 35° = x x = 11.0632791 x = 11.1 m (1 DP)4 a 11.49 b 2.07 c 9.37 d 15.65 e 3.40 f 0.84 g 3.56 h 7.595 2.11 m 6 63.377 m

Exercise 5–081 A 2 C 3 c =

°847cos

4 a sin 46° b cos 32° c tan 16°5 a 11.12 m b 5.54 m c 19.53 cm

6 tan 53° = 8 3.d

d = 8 3

53.

tan °

d = 6.254 498 616 d ≈ 6.3 cm7 a 12.66 m b 11.12 m8 No


3 sin R = 711

R = 39.52119636 R = 40° (nearest degree )4 a 32° b 58° c 52°5 a 41° b 60° c 51°

6 a

R

P

Q7 cm

16 cm

cos Q = 716

Q = 64°

b 26°7 21° 8 58°

Language activitytriangles trigonometry label vertices smallcosine adjacent opposite hypotenuse CAHcalculator degrees

Practice test 51 $102 2 –y – 3 3 x = 72 4 60 m

5 116

6 4 7 13.5 8 yes

9 4x2 – 6x 10 12

11 hypotenuse = 10, opposite = 6, adjacent = 812 B13 a 0.391 b 6.314 c 0.58814 a 81° b 51° c 69°15 26.69 cm 16 14.8 cm 17 27°18 a 16.1 cm b 23.2 m19 a 8.5 m b 4.3 m20 a 65° b 75° c 26°21 67°

CHAPTER 6Exercise 6–011 D 2 B

3 a 1

100 b

3100

c 10100

110

= d 15100

320

=

e 20

10015

= f 50

10012

=

g 62100

3150

= h 34

1001750

=

i 60100

35

= j 40

10025

=

k 12100

325

= l 24

100625

=

m 75100

34

= n 82100

4150

=

o 68100

1725

=

4 a 0.7 b 0.9 c 1.4 d 0.18 e 0.35 f 0.06 g 0.24 h 0.96 i 1.08 j 2.43 k 0.08 l 0.075 m 2.2 n 0.04 o 0.44 p 0.12 q 0.125 r 0.145 s 0.125 t 0.0255 a 40% b 30% c 87.5% d 25% e 5% f 80% g 7.5% h 31.25% i 48% j 42.5% k 162.5% l 525% m 135% n 91.7% o 112.5%6 a 2% b 6% c 5% d 9% e 8% f 17% g 13% h 31% i 45% j 47% k 92% l 30% m 70% n 450% o 112.5%

ANSWERS


7 Fraction: 1

10,

14

, 3

10,

25

, 12

, 35

, 34

, 45

, 9

10, 1

Decimal: 0.1, 0.25, 0.3, 0.4, 0.5, 0.6, 0.75, 0.8, 0.9, 1.0 Percentage: 10%, 25%, 30%, 40%, 50%, 60%, 75%,

80%, 90%, 100%

8 a 35

, 0.655, 68.5% b 38

, 0.38, 38.2%

c 0.805, 82.5%, 56


3 a 14

b 18

c 45

d 12

e 13

f 1 g 1

10 h

23

i 34

j 25

4 a 10% of $200 = 1

10200×

= $20

b 75% of 80 cm = 34

80×

= 60 cm5 a 70c b 6 mm c 21c d $1.80 e $32 f 25 km g $105 h $33 i 63 km j $60 k 60c l $30 m 30c n $28 o $2.80 p $720 q 6 years r 36 km6 a $12.50 b 1.62 m c 6 m d 0.2 year e 64.8 cm f 5.85 yr g 4.88 L h 3.6 h i 840 m j $652.80 k 2.375 days l $24007 a 25 200 b 30 8008 225 L 9 $1408

Exercise 6–031 D 2 C

3 a 1230

25

= b 75120

58

=

4 a 25

b 14

c 950

d 15

e 11

250 f

18

g 13

h 3

500 i

18

5 a 40% b 25% c 18% d 20% e 4.4% f 12.5%

g 3313

% h 0.6% i 12.5%

6 a 20, 75 b 27, 3313

7 a 25% b 12.5% c 12.5% d 20% e 5% f 5% g 20% h 2.5% i 8.3% j 25% k 25% l 20%8 a 68% b 90% c 80%, Gina9 35%

10 a 48% b 15

c 32%

Exercise 6–041 D 2 A 3 add, subtract4 a $55 b 910 m c $6250 d $34000 e 4125 kg f 90 t5 a $170 b 2000 m c $48 000 d $250 000 e 240 ha f 4000 kg6 a $338 b $552.50 c $8327 $700 8 $721.60.9 $16 675 10 $115.20, No

Exercise 6–051 D 2 B3 a T b F c F4 a 15% of an amount = $450 1% of the amount = $450 ÷ 15

= $30 100% of the amount = $30 × 100

= $3000 b 60% of an amount = $960 1% of the amount = $960 ÷ 60

= $16 100% of the amount = $16 × 100

= $16005 a $1600 b $400 c $800 d 2000 m e 2000L f 30 m g 8 h h $20 000 i 3000 kg6 440 7 $6000 8 35009 a $1148.95 b Find 28.6% of it. It should be the tax paid.10 a $160 b $96

Exercise 6–061 A 2 B3

Cost price Selling price Profit or loss

$12.00 $15.00 $3.00 profit

$25.00 $30.00 $5.00 profit

$60.00 $20.00 $40.00 loss

$250.00 $200.00 $50.00 loss

$735.00 $780.00 $45.00 profit

$1590.90 $1470.10 $120.80 loss

$424.75 $450.50 $25.75 profit

$6550.80 $6250.35 $300.45 loss

ANSWERS

355ISBN 9780170351027 Answers

4 a $5 b 3313

% c 25%

5 a $50 500 b 9%6 a 37.5% b 27.27%7 $66.70 8 $5359 a $15.80, $173.80 b $4.50, $49.50 c $8.40, $92.40 d $12, $132 e $3.60, 39.60 f $2.80, $30.80 g $5.20, $57.20 h $2.60, $28.6010 a $104.28 b $29.70 c $55.44 d $79.20 e $23.76 f $18.48 g 34.32 h $17.16

Exercise 6–071 D 2 A3 a $250 b $25004 a P = $450, R = 5 % = 0.05 as a decimal,

N = 2 years I = PRN

= 450 × 0.05 × 2 = $ 45

5 a $60 b $180 c $162.50 d $502.50 e $558.90 f $599.696 P = $2500, R = 9 % = 0.09 as a decimal

p.a. = 0.0075 as a decimal per month, N = 8 months I = PRN

= 2500 × 0.0075 × 8 = $ 150

7 a $45 b $180 c $4080 d $200 e $3000 f $8828 a $910 b $23109 4 years 10 1.1%

Practice test 61 $6 2 6xy 3 168 4 8

5 412

6 7, 6, 3, 0, –2, –5

7 4.15 8 129 –12x – 30 10 5h 45 min

11 a 325

, 0.12 b 710

, 0.7 c 1320

, 0.65

12 C 13 D14 a 6m b 3 h c 48L

15 a 1315

b 15

c 1

400

16 a 8623

% b 20% c 0.25%

17 $300 18 $750 19 $1009.7320 a $300 b 31.6%21 $28 146.8022 a $90 b $23823 5%

CHAPTER 7Exercise 7–011 D 2 C3 a 5 ×5 × 5 b 5 c 34 a 34 b 25 c 72 d 83

e x5 f 52 × a3 g 32 × 63 h wv3

i 53 × a2 j m2n3 k 42u2v l 15mn5 a 37 b 58 c 211 d 63

e m7 f x5 g p7 h n11

6 a 3 × 4 × m3 × m2 b 5 × (–3) w4 × w7

= 12m5 = –15w11

7 a 10n7 b 24a7 c 60n7 d 48w8

e –12v7 f –63n7 g 45a7 h –64a7

i –72c10 j 48a7b4 k –32m7n6 l 24a7c5

8 a F b T c F d T9 No, 129610 a 576 b 324 c 1125 d 2048 e 1600 f 1764 g –2000 h 288

Exercise 7–021 C 2 A3 a 28–3 =25 b x9 – 3 = x6 c 126– 3 =123

4 a 23 b 45 c 37 d 35

e d5 f m g x4 h m3

5 a 3n4 b 4a8 c 3n d 2w10

e –3v4 f –7n5 g 5a3 h –4a7

i –4c j 8a4b3 k –4m3n l 8a4c3

6 a F b F c T d T

7 No, 102427

8 a 202.27 b 157464 c 38.04 d 32768

Exercise 7–031 C 2 B3 a 53 × 2 = 56 b x4 × 3 = x12

4 a 215 b 68 c 312 d 518

e 740 f x12 g n18 h m16

i w20 j a18 k 915 l x8

m 524 n q24 o p56

5 a F b T c T6 a 4x6 b 27a12 c 25n12 d 64m24

e 343c15 f 32w40 g 216b12 h 81t8

i –32a30 j 64w24 k –27c21 l 64q54

7 a T b F c F

8 a a20

32 b

m4

9 c

912w

d 25

12m

e x24

64 f

w21

8− g

6424c

h 81

24n9 a T b T

10 a 81

16

24x b

mn

24

12 c 7298 15a

d ab

40

60

ANSWERS


Exercise 7–041 B 2 C3 a T b F c F d T4 a 1 b 1 c 1 d 1 e 1 f 1 g 1 h 2 i 1 j 6 k 1 l 6

5 a 143 b

15w c

43n

6 a 132 b

124 c

14

d 152 e

134 f

172

7 a 1 b 1

243 c

116

d 16

e 1 f 1

1288 a F b T c F d F e F f T

9 a 3

4x b

65a c

47m d

23w

e 1

3 2x f

14 3n

g 2

3 4x h

35 6a

i 3

2 5u j

56w

10 a 112

b 89

c 134

d −710

e 12

Exercise 7–051 B 2 C3 a F b T c F d T4 a 42 b 33 c 7–5 d 5–4

e w f c3 g x–7 h a–5

5 a 66 b 7–2 c 56 d 2–1

e x–2 f c9 g w–1 h a–3

6 a 28 b 36 c 49 d 58

e 3–4 f 2–12 g 4–6 h 1 i x9 j a12 k w48 l p24

m a−6 n x−14 o 1 p x12

7 a 6 9x b 4 2a c 16 12m d 12 3a e 5 8m f 16 10a g 81 12x− h 2 4w−

i −32 6 5a b j −3 11m n k −40 12w l −7 6xy8 a T b T c F d F e T f F g T h F

Exercise 7–061 D 2 B3 a 23 600 b 587 000 c 81 600 d 3570 e 4 230 000 f 45 600 g 32 500 000 h 428 000 i 408 000 j 12 100 000 k 60 300 000 l 2 100 000

4 a 0.035 b 0.0038 c 0.83 d 2.4 e 0.0031 f 0.072 g 0.000 91 h 0.70 i 4.8 j 0.051 k 56 l 0.715 a 70 000 b 69 000 c 68 7006 0.0997 a 57 464 b 57 4608 0.36

Exercise 7–071 D 2 A3 a 3.3 × 104 b 6 × 105

c 2.8 × 103 d 8.24 × 105

e 9.02 × 107 f 2.6 × 108

4 a 1.2 × 104 b 4.56 ×105

c 1.2 ×108 d 4.5 ×107

e 6.803 ×106 f 3.45 ×107

g 8 ×1010 h 5.2 ×108

5 a 72 000 b 824 000 c 410 000 000 d 603 e 1 980 000 f 37286 a 50 000 b 3800 c 1 680 000 d 24 500 000 e 4000 f 92 g 300 400 000 h 1 090 000 0007 a 7 × 104 2.8 × 106 6.11 × 106 2.006 × 107

b 2.006 × 107 6.11 × 106 2.8 × 106 7 × 104

8 a 4.568 21 × 105 b 6.8 × 104

c 2.29 × 107 d 1.52 × 108

9 a 1.23 × 103 b 1.44 ×104

c 7.392 ×103 d 9.49 × 106

e 2.52 × 104

10 1 × 106 or 1.0485 76 × 106

Exercise 7–081 C 2 A3 a 5 × 10–3 b 1.2 × 10–3

c 6.83 × 10–4 d 7 × 10–5

e 4.2 × 10–5 f 1.8 × 10–7

4 a 9 × 10–3 b 1.2 × 10–4

c 9.72 ×10–5 d 4 ×10–7

e 5 ×10–2 f 7.508 × 10–4

g 7.214 × 10–4 h 8 × 10–4

5 a 0.008 b 0.000 624 c 0.005 01 d 0.000 000 72 e 0.942 f 0.000 028 346 a 0.012 b 0.0035 c 0.000 06 d 0.000 482 e 0.9 f 0.000 007 6 g 0.000 010 82 h 0.000 000 004 067 a 6.1 × 10–4 5 × 10–5 1.8 × 10–5 3.129 × 10–7

b 3.129 × 10–7 1.8 × 10–5 5 × 10–5 6.1 × 10–4

8 a 8 × 10–5 b 7 × 10–3 c 4.8 × 10–6

d 1.5 × 10–3 e 1 × 10–12

ANSWERS

357ISBN 9780170351027 Answers

9 1 micrometre = 1 × 10–6 metre (one-millionth) 1 nanometre = 1 × 10–9 metre (one-billionth)

Exercise 7–091 B 2 C3 a 1800 b 2 400 000 c 7 000 000 000 d 2 00 560 000 e 0.42 f 8.9 g 50 000 000 h 0.030 094 a 3.2 × 1013 b 2.44 × 1015

c 6.83 × 102 or 683 d 5.17 × 106

e 5.25 × 105 f 7.54 × 10–6

g 3.07 × 1010 h 1.38 × 10–3 or 0.001 38 i 3.59 × 10–7 j 1.11 × 1019

5 a 2.2 × 104 b 4.5 × 109

c 1.3 × 1015 d 6.3 × 1021

e 2.0 × 1020 f 2.7 × 10–12

g 1.9 × 1014 h 3.3 × 10–15

6 a 4.2 × 104 b 5.6 × 104

c 8 × 103 d 8.6 × 104

e 5.7 × 105 f 8.9 × 103

g 7.3 × 10–2 h 3.5 × 10–1

7 a 1.156 × 109 b 3.144 × 1017

c 2.073 × 103 d 1.817 × 103

8 a Venus by 1476 times b Jupiter by 3 times c Neptune by 17.25 times d Uranus by 1.3 times e Mercury, Mars, Uranus, Venus, Earth,

Neptune, Saturn, Jupiter

Language activityAn impatient index

Practice test 71 $51 2 14 3 –14

5 12

6 30% 7 7:25 pm

8 3pq(9p – 5q) 9 82.69 10 14

11 a a13 b 311 c 12x9 d 15n7

12 a 5n8 b 6x12 c 4x4

13 a 220 b m18 c 81x12 d 215

5n14 a 1 b 1 c 5

15 a 1

72 b 4

3a c

12 4x

16 a −10 3 3a b b 4 3 3m n c 36 6a17 a 522 000 b 6 040 000 c 0.00209

18 a 3.872 × 105 b 6.72 × 106

c 1.9 × 1010

19 a 1.86 × 10–2 b 4.05 × 10–4

c 4 × 10–9

20 8 × 10–4 3.8 × 106 6.2 × 109

21 a 1.8942 × 105 b 9.39 × 1019

CHAPTER 8Exercise 8–011 D 2 C3 a ∠BAC b ∠YXZ c ∠PQR d ∠DEF e ∠ABC f ∠EDF4 a 33° b 91° c 230° d 90° e 152° f 300°5 a acute b obtuse c reflex d right e obtuse f reflex6 a

b

c

d

e

f

ANSWERS


7 a

B C

A

42°

b

B A

C

103°

c

Z Y

X

85°

d

E F

P

225°

e

P Q

R161°

f

V U

W

300°

8 a acute b reflex c obtuse d right e reflex f obtuse g acute h straight i reflex j revolution9 Sample answers a angle between 2 walls b path around a roundabout c angle when a door is wide open d angle when a page is open in a book e angle between your fingers f angle from north to east anticlockwise

Exercise 8–021 C 2 A3 a 50° b 15° c 45° d 56° e 37°4 a 120° b 145° c 35° d 74° e 124°5 a

b

c

d

e

30°

60°

6 a x + 5 8 = 90 (complementary angles) x = 90 – 58 x = 32

b n = 42 (vertically opposite angles) m + 42 = 180 (supplementary angles)

m = 180 – 42 m = 138

7 a a = 70 complementary angles b b = 52 complementary angles c x = 130 supplementary angles d y = 48 supplementary angles e m = 30 angles at a point f n = 123 angles at a point g s = 78 vertically opposite angles h t = 26 vertically opposite angles i x =134 supplementary angles

ANSWERS

359ISBN 9780170351027 Answers

j y = 38 angles at a point k a = 171 vertically opposite angles l b = 57 complementary angles8 Other answers possible.

Exercise 8–031 C 2 D3

*

*

4

*

*

5

*

The other pair of co-interior angles are on the other side of the transversal and in between the parallel lines.

6 a alternate angles b corresponding angles c co-interior angles7 a a = 70 alternate angles b b = 110 corresponding angles c c = 50 co-interior angles d x = 115 corresponding angles e y = 112 co-interior angles f d = 121 alternate angles g e = 125 alternate angles h x = 82 alternate angles i y = 115 corresponding angles j d = 47 co-interior angles k x = 120 corresponding angles, y = 60

supplementary angles, z = 60 corresponding angles

l a = 88 alternate angles, b = 92 supplementary angles, c = 92 alternate angles

8 a No alternate angles are not equal. b Yes, corresponding angles are equal. c No, co-interior angles are not supplementary.

Exercise 8–041 C 2 A3 a

b

60°

60° 60°

c

d

e

f

4 a equilateral b isosceles c scalene d isosceles e isosceles5 a acute-angled b acute-angled c right-angled d acute-angled e obtuse-angled

ANSWERS


6 a right-angled b acute-angled c obtuse-angled d obtuse-angled e right-angled7 a scalene b scalene c scalene d scalene e isosceles8

Type of triangle

Number of equal sides

Number of equal angles

Scalene 0 0

Isosceles 2 2

Equilateral 3 3

9 a Yes b Yes c Yes

10 a

b

c

d

Exercise 8–051 D 2 B3 a isosceles, acute, x and y b equilateral, acute, m, n and o c isosceles, right-angled, v and w4 a i g ii d and f b i q ii p and s5 a 52 + 65 + x = 180 (angle sum of triangle)

x = 180 – 52 – 65 x = 63

b n = 72 + 46 (exterior angle of triangle) n = 118

6 a a = 80, angle sum of triangle b y = 22, angle sum of triangle c e = 60, angle sum of triangle

d b = 35, angle sum of triangle e d = 105, exterior angle of a triangle f f = 134, angle sum of triangle g c = 112, exterior angle of a triangle h p = 145, angle sum of triangle i g = 65, exterior angle of a triangle j x = 81, angle sum of triangle k q = 50, exterior angle of a triangle l h = 45, angle sum of triangle

Exercise 8–061 B, C2 a

b

3 a

b

c

d

4 Teacher to check. 5 Teacher to check.6 a kite b trapezium c rhombus d rectangle e square f parallelogram g trapezium h rhombus i rectangle j kite

ANSWERS

361ISBN 9780170351027 Answers

Exercise 8–071 B 2 A3

Quadrilateral Sides Angles Diagonals

Parallelogram Opposite sides equal and parallel

Opposite angles equal

Diagonals bisect each other

Trapezium One pair of parallel sides

All angles different

Diagonals different

Rhombus All sides equalOpposite sides parallel

Opposite angles equal

Diagonals bisect each other at right anglesDiagonals bisect the vertex angles

Rectangle Opposite sides equal and parallel

All angles are 90°

Diagonals are equal and bisect each other

Square All sides equalOpposite sides are parallel

All angles are 90°

Diagonals are equal and bisect each other at right anglesDiagonals bisect the vertex angles

4 x + 12 5 = 180 (co-interior angles on parallel lines) x = 180 – 125 x = 55

5 n + 126 + 90 + 78 = 360 (angle sum of quadrilateral) n = 360 – 126 – 90 – 78

n = 666 a x = 28 angle sum of quadrilateral b p = 90 angle of a rectangle c n = 133 angle sum of quadrilateral d x = 124 cointerior angles on parallel lines e v = 115 opposite angles of parallelogram f n = 90 angle sum of quadrilateral g e = 45 diagonals bisect the angles of a square h n = 96 co-interior angles on parallel lines i x = 72 corresponding angles on parallel lines

Exercise 8–081 R 2 C3 a translation b rotation c reflection d translation4 a Yes b Yes5 a No b The size of the angles.6 Matching sides: AB and RP, AC and RQ, BC and PQ Matching angles: ∠A and ∠R, ∠B and ∠P,

∠C and ∠Q7 Congruent shapes are men, rotation.

Exercise 8–091 A 2 D3 a LM = RS, LN = RT, MN = ST b RST c SSS4 A and C5 a ≡ABC LMN b AAS6 B, C and D7 ≡ABC IHG RHS, ≡PQR EFD SSS ≡WXY MON SAS8 Teacher to check.

Language activityWHEN FINDING ANGLESIN QUADRILATERALS AND TRIANGLESREMEMBER ANGLE SUMAND THE ANSWER WILL COME.

Practice test 81 $168 2

k2

3 $20 4 64 cm3

5 10 6 725

7 5 : 2 8 14x + 4

9 38 10 6h 40min11 A 12 C13 a x = 58 vertically opposite angles b n = 18 complementary angles14

15 x = 4816 a scalene b isosceles17 a obtuse-angled b right-angled18 a x = 28, isosceles triangle b n = 71, exterior angle of a triangle19 a parallelogram b trapezium20 a x = 45, angle sum of a quadrilateral b m = 74, opposite angles of a parallelogram21 EDF 22 AAS

ANSWERS


CHAPTER 9Exercise 9–011 B 2 D3 a x = 3 b m = 1 c p = 3 d a = 5 e q = 1 f x = 7 g y = 15 h m = 11 i p = 11 j q = 15 k x = 5 l y = 4 m a = 4 n y = 2 o m = 2 p x = 20 q a = 12 r m = 12 s y = 14 t a = 244 a 4 b add c divide 5 d multiply 45 a x = 2 b y = 7 c x = 10 d y = 16 e m = 2 f x = 13 g a = 6 h b = 9 i y = 9 j x = 8 k p = 3 l n = 3 m x = 11 n b = 3 o t = 4 p x = 27 q t = 22 r n = 10 s p = 16 t q = 32

6 a m = –4 b x = –5 c e = 247

d v = –20

e w = −118

f x = –21 g s = –80 h n = –21

Exercise 9–021 D 2 C3 Various answers such as: a x + 6 = 10 b 3x = 12 c 2x – 5 = 34 a 5a – 3 + 3 = 17 + 3

5a = 2055

205

a=

a = 4

b 2x + 6 – 6 = 14 – 62x = 822

82

x=

x = 45 a x = 3 b a = 2 c b = 4 d m = 4 e b = –2 f a = 4 g x = 5 h a = 7 i b = 8 j y = 4 k m = 5 l n = 96 Teacher to check.

7 a x = 223

b n = 345

c a = –2

d x = 213

e s = −114

f y = −113

g r = 8 h w = −545

i x = 29

j n = –33 k u = –26 l x = –548 a T b F c T d F

Exercise 9–031 C 2 A3 a 3x – 4 b 5a + 6 c 8 – 2x4 a 2x + 9 b 3a – 4 c x + 55 a x = 13 b a = –5 c x = 16 a 2w + 16 = w – 8 2w + 16 – w = w – 8 – w

w + 16 = –8 w + 16 – 16 = –8 – 16

w = –24

b 4x – 15 = 2x + 17 4x – 15 – 2x = 2x + 17 – 2x

2x – 15 = 17 2x – 15 + 15 = 17 + 15

2x = 32x = 16

7 a a = 12 b w = 9 c b = –8 d m = –10 e a = 6 f x = 13 g a = 3 h b = –7 i x = 6 j w = 2 k x = 10 l r = –5 m a = 2 n b = 7 o a = –3

8 a x = 2 b n = 114

c x = −30

d d = 223

e m = 617

f w= –3

g x = −17

h n = 613

i x = −18

Exercise 9–041 B 2 D3 a F b F c T d T4 a 3(w – 4) = 15 3w – 12 = 15 3w – 12 + 12 = 15 + 12

3w = 27w = 9

b –2(a + 4) = 12 –2a – 8 = 12 –2a – 8 + 8 = 12 + 8

–2a = 20a = –10

5 a x = 7 b a = –2 c b = 4 d x = 1 e a = 2 f b = 12 g m = 1 h a = 10 i v = 11 j z = 3 k a = –15 l w = 126 Teacher to check.

7 a x = 2 b a = 2 c b = 123

d y = 5

e a = 2 f b = –1 g x = 2 h w = 2

i a = −313

j n = −725

k x = −1

12 l m = 2

38

8 Teacher to check.9 Various answers such as: 4(x + 2) = 20,

–6(2x – 4) = –1210 Various answers such as: 5(x + 8) = 30,

4(3x + 13) = 28

Exercise 9–051 B 2 C3 a T b F c F d T4 a x = ±6 b x = ±9 c a = ±10 d n = ±1

e x = ± 7 f x = ± 11

g w = ± 14 h b = ± 22

i x = ±7 j x = ± 38

k a = ± 106 l n = ± 19

ANSWERS

363ISBN 9780170351027 Answers

m a = ±12 n x = ± 68 o m = ± 42 p No solution q x = ±16 r No solution s a = ±100 t p = ± 1115 e x = ±2 6. f x = ±3 3. g w = ±3 7. h b = ±4 7. j x = ±6 2. k a = ±10 3. l n = ±4 4. n x = ±8 2. o m = ±6 5. t p = ±10 5.6 a T b F c F d T e F f F7 a x = ±13 49. b n = ±20 76. c w = ±4 32. d b = ±4 65. e u = ±63 25.8 b n = ± 28 c w = ± 54 e u = ± 100 000 g x = ± 212

Exercise 9–061 D2 a n + 6 = 8 b x – 4 = 18

c 8w = 24 d m6

14=

3 a n = 2 b x = 22 c w = 3 d m = 844 n = 20 5 p = 9 6 60 7 58 7 9 s = 8 10 n = 3 11 n = 612 Amy is 16 and Sophie is 48 years old.13 Harry is 4 and Fatima is 8 years old.14 2 15 28 16 14

Language activityTHEY BOTH HAVE TWO EQUAL SIDES

Practice test 9Part A1 $924 2 –x + 5y 3 0.09054 32 cm2 5 0.002 6 4.95 × 105

7 87.4% 8 29.3 9 10 00010 2l + 2w or 2(l + w)

Part B11 a x = 5 b n = 10 c x = 612 C 13 B

14 a x = –4 b c = −12

c x = –20

15 a x = 12 b a = –14 c n = –5

16 a x = 4 b a = –1 c x = 12

17 Teacher to check. Examples are: 2x – 12 = –16 and 6(x + 4) = 12

18 a x = ±7 b x = ± 1319 n ≈ ±7 81.20 3x + 12 = 33, x = 7 21 x = 622 Michael is 64, Sunny is 16.

CHAPTER 10Exercise 10–011 C 2 A3 a $388.80 b $746.70 c $591.81 d $913.314 a $777.60 b $1493.40 c $1183.62 d $1826.625 a i $4160 ii $1920 iii $960 b i $5980 ii $2760 iii $1380 c i $9000 ii $4153.85 iii $2076.926 a $37 887.20 b $46 504.80 c $59 441.467 a Georgia b $36.928 a $899.08 b $1227.27 c $984.23 d $1344.149 a $3120 b $3992.95 c $3735.33 d $4439.8510 Jack 11 $57 890 12 $2734.62

Exercise 10–021 C 2 D3 a $117 b $210.604 a $156 b $280.805 Normal wage = $23.60 × 35 = $ 826 Overtime = $23.60 × 1.5 × 4 + $23.60 × 2 × 1.5

= $212.40 Total wage = $826 + $212.40

= $1038.406 $565.90 7 $644.88 8 $20169 $1728.60 10 $1654.43

Exercise 10–031 A 2 B3 a $2887.50 b $1360.80 c $1306 d $1387.504 a $990 b $877.50 c $923.52 d $778.725 a $7020 b $6570 c $4454.13 d $68256 $395.50 7 $14 7508 $586.35 9 $372010 a 560 b $840

Exercise 10–041 B 2 B3 a T b F c T4 4 weeks wage = $725.50 × 4 = $2902 Annual leave loading = 17.5% × 2902 = $507.85 Total holiday pay = $2902 + $507.85 = $3409.855 a $297.50 b $1997.506 a $882 b $3528 c $617.40 d $4145.40

ANSWERS


7 a $5538.46 b $969.23 c $6507.698 $36 170.559 a $1110.58 b $7456.73 c $4759.6210 a $2486.25 b $446.25 c $5482.50

Exercise 10–051 B 2 C3 a $0 b $7400.50 c $2766.40 d $18 287 e $66 2294 a $109 420, $28 432.40 b $22.6%5 a $6149 b $12 516 c $10 980 d $9289.606 a $36 351, $3448.69 b $68 984, $13 966.80 c $144 020, $41 234.40 d $68 960, $13959

Exercise 10–061 C2 B3 a $450 b $304.50 c $89 d $88 e $672 f $1700 g $340 h $3384 $279.805 a $574 b $390.326 a $41 704 b $413.507

Name: Ali Mc Phee Date: 20/07/15 to 24/7/15

Hourly rate: $21.60 Gross Pay: $680.40

Hours worked: 31.5 Tax: $166.70

Tax rate: 24.5% Net Pay: $513.70

8 a $1925 b $435 c $13909 a $760.20 b 39.0%

Practice test 101 $4.60 2 –6a –18 3 1.5% 4 30 cm2

5 $22 6 6 7 0.175 8 269 11, 13, 17 or 19 10 8h 15min11 C 12 B 13 A14 a $890.40 b $861.1015 $15875 16 $987.84 17 $124 77518 a $370.02 b $2484.42 19 a $1017.69 b $6833.07 Note: a bonus is not included in

holiday pay or loading.20 a $10 683 b $3742.0421 a $352 b $169022 a $272/week b $843/fortnight

CHAPTER 11Exercise 11–011 D 2 D3 a quantitative discrete b quantitative continuous c categorical d quantitative discrete e categorical f quantitative continuous g quantitative discrete h categorical i quantitative continuous j categorical4 a D b D c C d C e D f C g D h D i D j C5 a T b T c F d F6 Teacher to check. 7 Teacher to check.

Exercise 11–021 C 2 B3 a sample b census c sample d sample e census f sample g census h sample4 a random b biased c biased d biased5 a 807 b 3 : 2 c 306 Teacher to check.7 Teacher to check.

Exercise 11–031 D 2 C3 adding dividing number often popular

no higher lower4 a 3.6 b 9 c 4 d 11.3 e 15.5 f 34.5 g 4.3 h 12.4 i 336.1 j 66.55 a 3 b no mode c 2 d 12 e 15 and 17 f no mode g 2.6 h 21.5, 5.7, 11.1 i 131 j no mode6 a $27.57 b $50 c $23.83 d The outlier made the mean higher than most

amounts of pocket money. 7 a 40.27 b 18 c higher d 42.5 e Yes, 428 a No mode b $793 906.25 c Yes, $1 220 500 d Increase

Exercise 11–041 A 2 B3 highest lowest lowest highest middle

scores even average middle

ANSWERS

365ISBN 9780170351027 Answers

4 a 6 b 5.5 c 13 d 24 e 55.55 a 7 b 7 c 8 d 8 e 386 Red: median = 49.05, range = 8.9 Yellow: median = 47.35, range = 15.8 Green: median = 52.15, range = 13.97 a Yellow b Green8 a range = 4, median = 2 b range = 12, median = 14 c range = 6, median = 1 d range = 4, median = 3 e range = 4, median = 100 f range = 4, median = 10.5 g range = 8, median = 6.5 h range = 5, median = 31 i range = 5, median = 3.5 j range = 5, median = 39 range = 3, median = 7 10 mode = 71, range = 8, median = 73.5, mean = 73.7511 The mode, as it is the lowest statistic, compared

to the mean and median.

Exercise 11–051 D 2 B3 horizontal dots score hundreds leaf4 a

876543

b

987654

c

9 10 11 12 13 14

d

22 23 24 25 26

e

50 51 52 53 54 55 56 57 58 59 60

5 a i 3 ii 8 iii 7 b i 4 ii 9 iii 8 c i 9 ii 14 iii 11 d i 22 ii 26 iii 24 e i 50 ii 60 iii 586

180 200 220 240250260 280

a $280 b $250 c $720 d $240 e A cluster from $220 to $250, no outliers.

7 a Stem Leaf1234

2 3 56 7 82 5 3 9

b Stem Leaf5678

2 97 93 4 5 2 6 6

c Stem Leaf34567

6 82 4 56 8 9 42

d Stem Leaf6789

0 5 62 2 92 31 5

e Stem Leaf1213141516

3 94 7 85 5 0 60

8 Range = 35, median = 75.5, mean = 76.5

9 a Stem Leaf3456789

4 6 7 95 5 52 5 6 2 2 4 62 2 2 2 3 4

8

b Range = 64 and mode = 72 c 58.6190 ... × $18 ≈ $1055 d 62 e Yes, from 60 to 70s. f Yes, 98

Exercise 11–061 D2 C

ANSWERS


3 a Score Tally Frequency

47 |||| 4

48 |||| || 7

49 |||| ||| 8

50 |||| |||| |||| 14

51 |||| || 7

52 |||| || 7

53 ||| 3

|

|

|

| |

|

|

b Range = 6, mode = 50

4 a Score (000s) Tally Frequency fx

21 ||| 3 63

22 || 2 44

23 |||| |||| 10 230

24 || 2 48

25 || 2 50

26 |||| 5 130

27 || 2 54

28 ||| 3 84

29 | 1 29

Totals 30 732

| |

|

b range = 8000 km c mean = 24 400

5 a Score Tally Frequency fx

2 | 1 2

3 ||| 3 9

4 || 2 8

5 || 2 10

6 |||| 5 30

7 |||| |||| || 12 84

8 || 2 16

9 ||| 3 27

Totals 30 186

|

| |

b range = 7 c mode, mode = 7 d mean = 6.2

6 a

Score Tally FrequencyCumulative frequency fx

0 |||| 5 5 0

1 |||| 5 10 5

2 |||| |||| |||| |||| 20 30 40

3 |||| |||| ||| 13 43 39

4 |||| 5 48 20

5 || 2 50 10

Totals 50 114

|

|| | | || ||

b mode = 2 c mean = 2.28 d median = 27 a Cumulative frequency: 3, 9, 18, 22, 25 fx: 0, 6, 18, 12, 12, 48 i 4 ii 2 iii 2 iv 1.92 b Cumulative frequency: 4, 13, 25, 32, 37, 40 fx: 48, 117, 168, 105, 80, 51, 569 i 5 ii 14 iii 14 iv 14.238

Score FrequencyCumulative frequency fx

0 2 2 0

1 3 5 3

2 5 10 10

3 5 15 15

4 9 24 36

5 3 27 15

6 1 28 6

7 1 29 7

8 1 30 8

Totals 30 100

a 8 b 4 c 3.5 d mean = 3.333.. × $45 = $150

Exercise 11–071 column joined line column2 a

16 18 20 22 24 26Score

Competition points8

7

Freq

uen

cy

6

5

4

3

2

1

0

b 20,mode c 24

ANSWERS

367ISBN 9780170351027 Answers

3 a

1 2 3Number of parcel deliveries

Parcel deliveries

4 5

9

8

7

Freq

uen

cy 6

5

4

3

2

1

0

b range = 4 mode = 3 c The mode is the most common number of

parcels delivered. d mean = 2.554 a 8

7

654

3

210

1 2 3Number on die

Throw of a die

4 5 6 7

Freq

uen

cy

b 4 c 4 d 1 e 5, which is the difference between the highest

and lowest number on the die f 53.3%5 a

Mark Frequency

72 3

73 3

74 6

75 2

76 3

77 0

78 3

b

Marks

Science test marks

72 73 74 75 76 77 78

7

Freq

uen

cy

6543210

c Range = 6, mode = 74 d mean = 74.55 e 40%

Exercise 11–081 B 2 Teacher to check 3 C4 centre left right right left two5 a i positively skewed ii clustered at 4-5, no outliers b i negatively skewed ii clustered at 13-15, 1 outlier to the left c i positively skewed ii clustered at 120-130 stems, 1 outlier 168 d i bimodal ii clusters at peaks 7 and 10, no outliers6 a negatively skewed b mode = 38, range = 29 c mean = 28.5 d median = 29 e In the 30s7 mode = 38, range = 21, mean = 29.8 and

median = 30 so it affects the range the most.

Language activityS T A T I S T I C S FT C R

R A N G E M O D EM E D I A N R QA E U

M E A N ED A T A P NL O CE T A L L YA V E R A G E Y

G F GR P OA N A L Y S I S NP OH I S T O G R A M

ANSWERS


Practice test 11Part A 1 $25.50 2

25 2ba

3 11

12 4 x = 60

5 –7 6 x = 2212

7 Several answers such as 2, 11, 7, 8. Teacher to check.

8 isosceles triangle 9 29 10 710

Part B11 B 12 C 13 A14 a sample b census15 mode = 37, outlier = 7816 a mean = 41.8 b Yes, it makes it higher in this case.17 range = 4.7, outlier = 2.718 a 5.85 b It will have little effect on the median.19 a

353025201510

b Stem Leaf123

0 5 5 50 0 0 5 50 5

20 a 28 b 27.45 c 27.521

Score Frequency

3 8

4 12

5 5

6 5

22 a negatively skewed b positively skewed

CHAPTER 12Exercise 12–011 C2 B3 a mm b km c m d cm e cm f cm g kL h g i h j mL k t l s4 a 3 mm b 850 km c 3 m d 15 cm e 12 cm f 170 cm g 25 kL h 50 g i 8 hours j 250 mL k 5 t l 50 sec

5

Millimetres Centimetres Metres Kilometres

4000 400 4 0.004

65 000 6500 65 0.065

786 000 78 600 786 0.786

95 000 000 9 500 000 95 000 95

85 400 8540 85.4 0.0854

7900 790 7.9 0.0079

654 000 65 400 654 0.654

6 a 4 b 2.5 c 2.5 d 6500 e 210 f 7850 g 7000 h 114 i 9600 j 0.025 k 3.5 l 6800

7 a 1

1000 b 1 000 000 c 1000

d 1

100 e

11000000

f 1 000 000 000 (one billion)8 a 1000 b 1 000 c 1000 d 2.75 MB e 1600 MB f terabyte (TB)

Exercise 12–021 B2 D3 a 1 mm b 1°C c 1 min d 100 g e 1 cm f 1° g 5 km/h h 250 g

i 10 mL j 1 kL k 14

tank

4 a ±0.5 mm b ±0.5 °C c ±0.5 min or ±30 s d ±50 g e ±0.5 cm or ±5 mm f ±0.5° g ±2.5 km/h h ±125 g i ±5 mL j ±0.5 kL or 500 L

k ±18

tank

5 a i ±0.5 kg ii 74.5 to 75.5 kg b i ±5 mL ii 275 to 285 mL c i ±10 m ii 210 to 230 m d i ±25 g ii 425 to 475 g e i ±0.05 cm ii 2.55 to 2.65 cm f i ±2.5 mm ii 52.5 to 57.5 mm g i ±25 mg ii 2725 to 2775 mg h i ±0.005 s ii 11.235 to 11.245 s

Exercise 12–031 B 2 A3 a 34 cm b 25.4 m c 33.7 cm4 Rectangle: P = 26 cm Square: P = 48 mm Equilateral triangle: P = 12.6 cm Rhombus: P = 33.6 m Parallelogram: P = 26 cm Kite: P = 18.6 cm

ANSWERS

369ISBN 9780170351027 Answers

5 a 58.92 cm b 42.26 cm c 44 cm d 108 cm e 44 cm f 236 cm6 a 300 m b 30 c $315

Exercise 12–041 A 2 B3 a 18.8 cm b 25.1 mm c 17.6 m4 a 21.1 cm b 123.4 mm c 27.8 m5 a i 20.57 m ii 4 8π +( ) m b i 14.28 cm ii 2 8π +( ) cm6 a 41.1 cm b 7.1 m c 13.4 m d 12.1 cm e 57.6 m f 24.3 m g 31.7 m h 21.4 cm i 27.7 m7 a 11.8 m b $354

Exercise 12–051 C 2 B3 a 0210 b 1748 c 0439 d 1852 e 1200 f 0755 g 0046 h 21254 a 5 a.m. b 9 p.m. c 6:55 a.m. d 6:48 p.m. e 8:50 a.m. f 11:39 a.m. g 10:56 p.m. h 12:54 a.m.5 a 3 h b 9 h c 6 h d 7 h e 12 min f 6 min g 7 min h 19 min6 a 5 h 48 min b 3 h 6 min c 20 h 58 min7 a 17 min 30 s b 3 min 40 s c 8 min 41 s8 a 17 h 25 min b 9 h 9 min c 13 h 35 min d 13 h 19 min e 10 h 21 min f 18 h 21 min9 5 h 55 min 10 6:51 p.m. 11 16 h 31 min

Exercise 12–061 D 2 B3 a 6:03, 2 h 1 min b 5:28, 2 h 37 min c 7:00, 2 h 7 min d 6:05, 1 h 36 min e 7:18, 1 h 7 min4 7:30 from Gosford5 a 7:36 b 1 h 5 min c 19 min6 a 8:40 a.m. b 7 h 40 min c 7:30 p.m.

Exercise 12–071 D 2 B3 a 12 midday b 4:00 a.m. c 2:30 p.m. d 6:00 p.m. e 3:00 a.m. f 7:00 p.m.4 a 10:00 a.m. b 11:00 a.m. c 5:00 a.m. d 6:00 p.m. e 6:00 p.m. f 8:00 p.m.5 6:20 a.m. Friday 6 2:30 p.m.7 a 11:30 a.m. b 11:30 a.m. c 9:30 a.m. d 11:00 a.m.8 a 10 p.m. b 9:30 p.m. c 10 p.m. d 10 p.m.9 4:30 p.m. 10 4:00 a.m. to 8:15 a.m.11 3 p.m. 12 12:30 a.m.

Practice test 121 7:35 p.m. 2 7 : 4 3

181

4 x d r2 2 2= + 5 5 2 3xy x y( )− 6 7w

7 x = 525

8 12x – 60

9 68%, 23

, 0.65, 0.6 10 23

11 C 12 D 13 ±125 g14 a 46.2 cm b 25.5 cm15 56.2 m16 a 28.3 cm b 20.1 m17 50.6 cm18 a 12 h 40 min b 6h 28 min19 a 22 h b 9 h20 a 6:40 a.m. b 1 h 33 min21 a 5:50 p.m. Saturday b 3:15 p.m.

CHAPTER 13Exercise 13–011 C 2 B3 a 25 m2 b 10.08 cm2 c 9.01 cm2

d 10.24 m2 e 4 m2 f 18 cm2

g 48 m2 h 31.5 cm2 i 20 m2

j 24 cm2 k 24 cm2 l 36 m2

m 16.56 cm2 n 65.92 cm2

4 a 80 m2 b 48 cm2

c 103.32 m2 d 57.12 cm2

e 22 m2 f 74.39 mm2

Exercise 13–021 B 2 A3 a 254.47 cm2 b 50.27 m2 c 113.10 mm2

4 a 314 m2

5 a 25.1 m2 b 7.1 m2 c 56.5 cm2

d 28.3 m2 e 190.1 m2 f 254.5 m2

6 10.187 a 76.97 m2 b 33.18 m2 c 63.2 cm2

d 31.49 m2 e 50.3 cm2 f 36.9 m2

8 $445.919 a 628.3 mm2

b i 25132 mm2 ii 32000 mm2 iii 6868 mm2

Exercise 13–031 C 2 A3 a 160 cm2 b 2.16 mm2 c 2.5 m2

d 0.05 cm2 e 96.76 cm2 f 70.29 m2

4 a 76 cm2 b 187 cm2 c 52.08 cm2

d 76.1 cm2

5 a 16.16 m2 b 32 c $147.20

ANSWERS


Exercise 13–041 A 2 C3 a 96 cm2 b 190 cm2 c 136 cm2

4 a 7m

7m

294 m2

b

470 cm2

5 cm

15 cm

8 cm

5 cm

8 cm

5 a 278 cm2 b 460 cm2 c 224 m2

d 292 m2 e 200.88 cm2 f 121.5 m2

6 a 86.64 mm2 b No c 101.08 mm2

Exercise 13–051 D 2 D3 a

5 cm2 cm

6 cm 5 cm

SA = 56 cm24 cm

b 10 cm6 cm

3 cm

8 cm

SA = 120 cm2

4 a 240 cm2 b 108 m2 c 576 cm2

d 1000 m2 e 94.68 cm2 f 220.08 m2

5 240 cm2

Exercise 13–061 B 2 B3 a 6 cm

4 cm

b 376.99 cm2

5 a 327.2 m2 b 414.3 cm2 c 263.9 m2

d 39.6 m2 e 174.9 cm2 f 329.9 cm 2

g 485.2 m2

6 a 332.51 m2 b 14 cans c $896

Exercise 13–071 C 2 C3 a 20 b 450 000 c 72.5 d 655 e 2.56 f 5.7 4 a b

c

5 a 480 cm3 b 108 m3 c 123.2 m3

d 61.1 m3 e 960 cm3 f 1200 cm3

g 1632 cm3 h 2033.6 cm3

6 a 640 cm3 b 640 mL c 0.64 L7 a 99 m3 b 99 000 L

Exercise 13–081 A 2 B3 a 785.4 cm3 b 274.9 mm3 c 1017.9 m3

d 196 349.5 cm3 e 2481.9 cm3 f 247.9 cm3

4 a 327.1 cm3 b 327.1 mL5 1357 mm3

6 a 117.81 m3 b 117 810 L7 4241 cm3

Language activityTHEY ARE BOTH A SUM OF FACES.

Practice test 131 26 2 –6ab – 6ab2 3 24

4 y = 122 5 623

6 x = 1 7 y-axis

8 –65 9 1

42 10 $800

11 a 16.38 cm2 b 91.98 m2

12 B 13 A14 a 29.04 cm2 b 33.01 cm2

15 a 27.5 m2 b 6.825 m2

16 58.88 cm2

17 a 73.5 cm2 b 108.08 m2

18

4 cm

5 cm

12 cm

6 cm

5 cm

SA = 216 cm2

19 a 640.9 cm2 b 134.2 m2

20 a 183.75 cm3 b 48.5 m3

21 a 108.875 m3 b 108 875 L

ANSWERS

371ISBN 9780170351027 Answers

CHAPTER 14Exercise 14–011 C 2 B3 a y = 2x

x 0 1 2 3

y 0 2 4 6

b y = x – 1

x 10 8 6 4

y 5 4 3 2

c y = x ÷ 2

x 4 3 2 1

y 3 2 1 0

d y = x + 3

x 0 1 2 3 4

y 3 4 5 6 7

e y = 3x

x 1 2 3 4

y 3 6 9 12

f y = x – 3

x 7 6 5 4 0 –1

y 4 3 2 1 –3 –4

g y = 2 + x

x 0 1 2 3 4

y 2 3 4 5 6

h y = x ÷ 3

x 12 9 6 3 0 –3 –6

y 4 3 2 1 0 –1 –2

i y = 2x + 1

x 1 2 3 4

y 3 5 7 9

j y = 3x – 1

x 4 3 2 1 0 –1 –2 –3

y 11 8 5 2 –1 –4 –7 –10

4 a d = 5c + 1

c –1 0 1

d –4 1 6

b h = 2g – 3

g 1 2 3

h –1 1 3

c q = 6 + 2p

p –1 0 1

q 4 6 8

d t = 12 – 4s

s 1 2 3

t 8 4 0

e n = 3 – 2m

m –2 0 2

n 7 3 –1

f y = 5x– 6

x 1 3 5

y –1 9 19

Exercise 14–021 3rd 2 C3 a A (3, –2) B (–2, –1) C (–4, 0) D (–3, 3) E (4, 1) F (0, –2) b A 4th quadrant B 3rd quadrant C x-axis D 2nd quadrant E 1st quadrant F y-axis4 a y

xL

MF

S D

K

V N E

G

CJ

T I

H

B A R

Q

P

3

21

–11 2 3–3 –2 –1

–2–3

45

–4–5

–4–5 4 5

b i a rectangle ii a triangle iii a parallelogram5 The Sydney Harbour Bridge

Exercise 14–031 B2 a y

x

A

B

C

D

E4

2

10 2–2 –1

10

3

b y

x

B

C

A

D

E4

10 2–2–2

–4

–1

20

ANSWERS


c y

xE

D

E

B

A

–1–1 1 2–2

–2

–3

–4

–5

00

d y

xC

AB

DE

2

10 2–2–1

–2

–1

10

e y

xC

A

B

D

E

4

10 2–2–2

–4

–1

20

f y

x

A

B

C

D

E

–1–2

–4

00

2

4

6

8

1 2 3–2–3

g y

x

A

B

C

D

E

–1–10

01

2

3

4

1 2 3–2–3

5

6

7

–4

h y

x

A

B

C

D

E

–1–1 1 2 3–2–3

–2

–3

–4

–5

00

–6

i y

x

4

10 2 3–2–2

–4

–6

–1

20

A

B

C

D

E

j y

x

A

B

C

D

E

–1–2

–4

00

2

4

6

8

1 2 3–2–3

3 They form a straight line.

4 a y = x + 3

x –1 0 1 2

y 2 3 4 5

y

x

A

B

C

D

–1 00

1

2

3

4

1 2 3

5

ANSWERS

373ISBN 9780170351027 Answers

b y = 6 – x

x –1 0 1 2

y 7 6 5 4

y

x

AB

CD

–1 00

2

4

6

8

1 2 3–2

c y =2x + 1

x –2 0 1 2

y –3 1 3 5

y

x

A

B

C

D

–1 00

2

4

6

1 2–2

–4

–2

d y = 4x – 3

x –1 1 0 2

y –7 1 –3 5

y

x

A

C

B

D

–1 002

4

6

1 2–2

–4

–6

e y = –3 + x

x –1 0 1 2

y –4 –3 –2 –1

y

x–1

–1 1 2

–2

–3

–4

00

1

A

B

C

D

f y = 12 – 5x

x 1 0 3 2

y 7 12 –3 2

y

x–1 00

2

4

6

8

1 2 3

10

12

–2

B

A

D

C

Exercise 14–041 C2 values table points line3 a x-intercept = 2, y-intercept = –2 b x-intercept = 4, y-intercept = –2 c x-intercept = 1, y-intercept = 2 d x-intercept = 4, y-intercept = 14 a y = 2x

x 0 1 2

y 0 2 4

y

x–1 00

1

2

3

4

1 2 3–1

A

B

C

x-intercept = 0, y-intercept = 0

ANSWERS


e y = 6 – 2x

x 0 1 2

y 6 4 2

y

x–1 00

1

2

3

4

1 2 3

5

6

4

A

B

C

x-intercept = 3, y-intercept = 6f y = 4 – 2x

x 0 1 2

y 4 2 0

y

x00

1

2

3

4

1 2 3

A

B

C

x-intercept = 2, y-intercept = 4g y = –3x + 6

x 0 1 2

y 6 3 0

y

x00

1

2

3

4

1 2 3

5

6

–1

A

B

C

x-intercept = 2, y-intercept = 6

ANSWERS

375ISBN 9780170351027 Answers

h y = –4x – 1

x 0 1 2

y –1 –5 –9

y

x

C

B

A–2

–1 1 2 3

–4

–6

–8

00

x-intercept = −14

, y-intercept = –1

Exercise 14–051 C 2 B3 y-value lies false lie4 a, d and e.5 y

00 1 2

C

A

E

D

B

x

2

4

6

–2 –1–2

–4

–6

–8

6 a and b.7 a No Yes b No Yes c No Yes d No No e No Yes f Yes No g Yes No h No No

Exercise 14–061 B 2 A3 a F b T c T d F4 a x = –4, x = –1, x = 3 b y = 4, y = 1, y = –25 y

x

3

2

1

00

1–3 –2 –1

4

42 3

c : × = 2d : × = 3a : × = –2

b : × = 0

6 y

x

2

10

–10 1 2 3–2 –1

–2

–3

3d : y = 2

c : y = 0

b : y = –1

a : y = –3

7 a y = 3 b x = –2 c y = 2 d x = 28 a y

x

2

10

–10 1 2 3

b : y = –1–2

3

4 5

a : x = 3

A (3,–1)

Exercise 14–071 C 2 B3 y = 4x –2 graphs x-value4 a i (2, 4) ii 3x – 2 = 4 iii x = 2 b i (–3, –2) ii 2x + 4 = –2 iii x = –35 a x = 3 b x = 5 c x = –1

y

x

4

8

6

20

0–2

1 2 3 4 5 6–3 –2 –1

–4

a : y = 2x – 3c : y = 7

b : y = 3

d : y = –5

ANSWERS


6 a x = 1 b x = 2 c x = –2

y

x

4

8

10

6

20

0–2

1 2 3–2 –1

–4

–6

a : y = 4x + 2

d : y = –6

b : y = 6

c : y = 10

7 a x = –1 b x = 2 c x = 5

y

x

4

8

10

6

20

0–2

1 2 3–2 –1

–4

b : y = 10

c : y = 4

d : y = –2

a : y = –2x + 8

4 5

Language activity1 PLANE BRAIN2 NUMBER SLUMBER3 POINT JOINT4 DOT PLOT5 RIGHT HEIGHT6 DOWN TOWN

Practice test 141 $22.30 2 7.05 3 9.51 × 10–3

4 24 cm2 5 5

12 6 $153 7 420

8 8.625 9 192.460 10 3011 a

x 6 4 2

y 1 –1 –3

b x 4 3 2

y 8 5 2

12 C 13 B

14

–4

–2–1 0 1 2 3–2–3–4

02

4B

EA

C

D

6

15

1

1 2 30–1–1

–2

–2

–3

0

2

3

4

5

D

C

B

A

E

16 a x-intercept = 1, y-intercept = –1 b x-intercept = 4, y-intercept = 217 a and b

y

x–1–10

01

2

3

4

1 2 3

5

4 5 6 7 8

b : y = –x + 6

a : y = 3x – 1

18 c lies on the line19 y

x

3

2

1

00

1–3 –2 –1

4

5

–14 5 62 3

c : x = 2

d : y = 0

a : x = –1

b : y = 4

ANSWERS

377ISBN 9780170351027 Answers

20 a y = 2x – 5 and y = 3 b y

x

2

43

10

0–1 1 2 3 4 5 6–3 –2 –1

a : y = 2x – 5

A (4, 3)b : y = 3

Solution is x = 4

CHAPTER 15Exercise 15–011 B 2 D3 a even chance b impossible c likely d even chance e certain f even chance g likely h impossible i unlikely j unlikely4 a {head, tail} b {hearts, diamonds, clubs, spades} c {red, amber, green} d {14, 16, 18, 20, 22} e {$5, $10, $20, $50, $100} f {HH, HT, TH, TT}5 a Yes b No c Yes d No e Yes f yes

6 a 16

b 16

c 23

d 12

e 12

f 12

7 a i 37

ii 47

b 1

8 a 29

b 13

c 49

d 79

e 23

f 59

9 a 14

b 14

c 1

13

d 1

13 e

152

f 1

13

Exercise 15–021 B 2 C3 a Not getting a 3 b Choosing a yellow sock c Getting a tail d Not coming 2nd e Not choosing a heart f Not picking a winner4 event one

5 a 16

b 56

c 13

d 23

6 a 13

b 23

c 5

18

d 1318

e 718

f 1118

7 0.2 8 35%

9 a 99

100 b 200

Exercise 15–031

1330

2 A

3 a probability event frequency frequencies 1

4 a

Number of heads Frequency Relative frequency

0 161680

15

=

1 424280

2140

=

2 222280

1140

=

Total 80 1

b 2140

c 168 d 15

e 1

5 a Score Frequency Relative frequency

1 1818120

320

=

2 2323

120

3 1616120

215

=

4 2424

12015

=

5 2222120

1160

=

6 1717120

Total 120 1

b 15

c 120 d 41

120 e 1

Exercise 15–041 D 2 B3 a 70 b i 23 ii 8 iii 43 iv 4 v 39 c No

ANSWERS


4 a 58 b i 34 ii 18 iii 0 iv 6 v 52 c Yes5

Dogs

14

6

87

Cats

a 7 b 14 c 6

6 a 1655

b 755

c 4455

45

= d 4855

7 a

Eels

22

4

630

Knights

b i 2262

1131

= ii 6

62331

= iii 5262

2631

=

iv 3062

1531

=


Female Male Total

Blue Eyes 8 10 18

Not Blue Eyes 18 12 30

Total 26 22 48

a 18 b 12 c 848

16

= d 2248

1124

=

4 Girls Boys Total

Football 12 18 30

Not Football 11 9 20

Total 23 27 50

a 30 b 9 c 1250

625

= d 1850

925

=

5 a Cake Not Cake Total

Lollies 9 22 31

Not Lollies 15 4 19

Total 24 26 50

b i 950

ii 3750

6 a

Swimming Not Swimming Total

Running 32 28 60

Not Running 14 16 30

Total 46 44 90

b i 1490

745

= ii 3290

1645

=

Exercise 15–061 C 2 D

3 a 3

10 b

710

c 3

10

d 4

1025

= e 610

35

=

4 a 4

30215

= b 630

15

= c 1330

d 2330

5 a i 36200

950

= ii 0.18

b i 14

ii 0.25

c No d It should become closer to the theoretical

probability.6 a Incorrect, as 3 takes up 2 sections out of 6 on

the spinner.

b 26

13

=

7 a i 24 ii 62

b i 3877

ii 6

778

Girls Boys Total

Dancing 23 12 35

Not Dancing 8 18 26

Total 31 30 61

a 2361

b 1261

ANSWERS

379ISBN 9780170351027 Answers

Language activity1 CHANCE 2 CERTAIN3 IMPOSSIBLE 4 UNLIKELY5 EVENT 6 OUTCOME7 PROBABILITY 8 THEORETICAL9 EQUALLY LIKELY 10 SAMPLE SPACE

Practice test 151 $42.50 2 21 3 –6 4 28.8 m2

5 8 2y xy k( )− 6 2 146. 7 a horizontal line

8 py

2

24 9 12.4 10 5:55 a.m.

11 A 12 B 13 D

14 a 16

b 56

15 a

Number of heads Frequency Relative Frequency

0 8840

15

=

1 232340

2 9940

Total 40 1

b 2340

c 57 times d 15

16 a 58 b 11 c 42 d 3158

17

Sheep

26

16

2817

Cows

18 Smartphone No smartphone Total

Tablet 12 11 23

No tablet 31 4 35

Total 43 15 58

19 Male Female Total

Licence 24 18 42

No Licence 5 3 8

Total 29 21 50

a 42 b 5 c 1850

925

=

20 a 0.26 b 0.25 c Yes.

CHAPTER 16Exercise 16–011 B 2 D3 a 15 b 12 c 12 d 72 e 20 f 6 g 2 h 8 i 4 j 9 k 20 : 32 l 9 : 154 a 1 : 2 b 1 : 3 c 1 : 3 d 5 : 1 e 1 : 4 f 1 : 3 g 1 : 4 h 6 : 1 i 4 : 1 j 1 : 8 k 1 : 6 l 1 : 3 m 3 : 8 n 2 : 3 o 8 : 9 p 3 : 4 q 9 : 20 r 1 : 125 s 20 : 3 t 15 : 15 a 1 : 2 b 1 : 100 c 1 : 25 d 1 : 4 e 6 : 7 f 1 : 4 g 1 : 6 h 3 : 100 i 10 : 1 j 49 : 60 k 1 : 6 l 1 : 2 m 1 : 2 n 7 : 24 o 2 : 15 p 1 : 4 q 1 : 12 r 1 : 10 s 3 : 2 t 25 : 2

Exercise 16–021 A 2 B3 a 1 : 3 b 1 : 6 c 3: 14 a 12 : 25 b 6 : 25 c 25 : 65 $164, $369 6 45 7 358 $42 500 9 480 kg 10 7811 104 12 $539 13 15 cups

14 a 28 b 12

Exercise 16–031 B 2 D3 a 120 cm b 280 cm c 260 cm4 a 9 cm b 120 cm c 5.7 cm d 34 720 cm = 347.2 m5 a 3 cm b 4.5 cm6 a A rectangle 12 cm long and 6.5 cm wide. b Singles court is 12 cm long and 6.3 cm wide. c 120 m long and 63 m wide.7 a 1 : 500 b 1 : 400 c 2 : 500 000 d 1 : 408 a 16.75 m b 5.5 m9 6.8 m10 a 1.2 km b 1.4 km c 1.1 km d 1.4 km e 2.0 km

ANSWERS


Exercise 16–041 B 2 D3

Ratio

Total number of parts

Total amount One part Ratio

3 : 1 3 + 1 = 4 64 64 ÷ 4 = 16 48 : 16

2 : 3 5 75 15 30 : 45

1 : 5 6 600 100 100 : 500

3 : 5 8 720 90 270 : 450

4 : 5 9 1800 200 800 : 1000

7 : 6 13 3900 300 2100 : 1800

4 Asha $10, Juno $155 Nathan $2700, Tom $45006 a $480 b $1607 $24 000 : $32 000 : $40 0008 Tara $56 250, Gemma $93 7509 3 matches 10 $227.2011 280 : 420 : 560 12 True

Exercise 16–051 D 2 A3 a 30 b 50 c 1.84 d 10 e 12.10 f 300 g 20 h 1400 i 232 j 234 8 km/L5 a $166/day b $140/day c The motel in b.6 $23/h 7 $66/h 8 28 beats / min9 55.7 km/h 10 680 words in 8 min.

Exercise 16–061 D 2 A

3 a $h

b $550 c 13 h

4 a 96 words/min b words

minutes c 42 mins d 28805 a $5214 b $28 0006 a $8.58 b 816 g7 $1164.45 8 104 minutes9 11.25 L/100km 10 12 L/100 km11 a 550 minutes b 22 mins/car c 7 hours 20 mins


Distance Time Speed

120 km 3 h 40 km/h

650 km 5 h 130 km/h

1250 km 25 h 50 km/h

680 m 10 s 68 m/s

4860 m 80 s 60.75 m/s

4 55 km/h 5 70 km/h6 a 16 km b 2 h c 8 km/h7

Distance Time Speed

450 km 9 h 50 km/h

1600 m 80 s 20 m/s

472.5 km 4.5 h 105 km/h

8 a 75 km/h b 300 km c 5.5 h9 a 165 km b 165 km/h c 2750 m d 45.8 m/s10 a 1 km b 1000 m c 16.7 m/s11 a 240 km b 240 km/h c 4000 m d 66.7 m/s

Language activity1 ROUND ABOUT Ratio is 1 : 12 TIME TABLE Ratio is 4 : 53 PIECE WORK Ratio is 5 : 44 BREAK AGE Ratio is 5 : 35 OVER ALL Ratio is 4 : 36 ANY WHERE Ratio is 3 : 57 SUN SET Ratio is 1 : 18 MOON LIGHT Ratio is 4 : 59 RATTLE SNAKE Ratio is 6 : 510 SEA SHORE Ratio is 3 : 511 TEXT BOOK Ratio is 1 : 112 HONEY SUCKLE Ratio is 5 : 613 MATCH BOX Ratio is 5 : 314 SUN GLASSES Ratio is 3 : 715 TYPE WRITER Ratio is 2 : 316 CHEESE BURGER Ratio is 1 : 117 WAVE LENGTH Ratio is 2 : 3

Practice test 161 2025 2 3 : 4 3

164

4 x2 2 28 15= + 5 5 4 3xy x y( )+6 11, 13. 17, 19 7 $22 8 –6a – 18

9 45

, 0.803, 0.85, 86% 10 13

11 D 12 B 13 B14 a 520 mL b 1.56 L15 a 900 cm b 42 cm16 Lachlan $5000, Courtney $20 00017 Ruben $36 000 John $27 000 Tim $48 00018 a $40/h b 60 c/apple c 62 words/min19 a $6.51 b 849 g20 a 198 km b 13 h 20 min

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