Answers - Maths and Science at Al Siraatalsiraatmathsandscience.weebly.com/uploads/1/0/4/6/...5a25%...

Chapter 1

1 a i Q ii TD b i Q ii TDc i ii IND d i Q ii TDe i Q ii TD f i Q ii RDg i Q ii TD h i Q ii TDi i Q ii TD j i Q ii TDk i Q ii TD l i Q ii TDm i Q ii RD n i Q ii TDo i ii IND p i Q ii TDq i ii IND r i Q ii TDs i ii IND t i ii IND

2 a 17.96 b 11.08 c 72.99d 47.86 e 63.93 f 23.81g 804.53 h 500.57 i 821.27j 5810.25 k 1005.00 l 2650.00

3 a, b, d, e, f, h, i, j, k, l, m, n4 c 4.123 g �3.142 o 3.142 p �2.8285

6 a 0.142 857 142 b i 4 ii 4 iii 87 a � 2, b � 5

1 a 2400 b 35 000 c 0.060d 34 e 110 000 f 0.0025g 2.1 h 0.71

2

1BExercise

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1AExerciseAn

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Essential Mathematics VELS Edition Year 9524

Answers

Number Decimal Rational/Irrational

a Rational

b Rational

c 2.000 00 Rational

d 4.472 13 Irrational

e 2.645 75 Irrational

f 5.000 00 Rational

g 4.222 22 Rational

h 2.858 40 Irrational

i 7.000 00 Rational

j �25.000 00 Rational

k 3.141 59 Irrational

l 0.100 00 Rational

m 5.000 00 Rational2132 � 122

10.0919

2�2

�2242 � 72

272

6 � �

1.5#

� 2.6#

242 � 32

242 � 32

116 � 4

(22)2

0.714 28522549

0.6666#24

9

Number 3 sig. fig. 2 sig. fig. 1 sig. fig.4 783 4 780 4 800 5 0008 921 8 920 8 900 9 0007 549 7 550 7 600 8 000

86 321 86 300 86 000 90 00060 407 60 400 60 000 60 00020 005 20 000 20 000 20 000

Number 3 sig. fig. 2 sig. fig. 1 sig. fig.0.123 4 0.123 0.12 0.10.617 8 0.618 0.62 0.60.806 49 0.806 0.81 0.80.080 97 0.081 0 0.081 0.080.034 09 0.034 1 0.034 0.030.000 990 6 0.000 991 0.000 99 0.001

Number 3 sig. fig. 2 sig. fig. 1 sig. fig.24.863 24.9 25 2097.142 97.1 97 100

125.06 125 130 10048.209 48.2 48 50

370.726 371 370 4006070.802 6070 6100 6000

3

4

5 a 3600 b 760 c 4000 d 5200e 0 f 4 g 0.12 h 0.02i 10 j 1600 k 0.08 l 11

6 a 4 b 40 c 10 d 29

0521681766ans_p524-579 6/6/06 4:00 AM Page 524

1 a b c 10 : 7 d 7 : 4

2 a i ii iii 4 : 8 � 1 : 2 iv 8 : 4 � 2 : 1b i ii iii 3 : 1 iv 1 : 2c i ii iii 7 : 5 iv 5 : 4

3 a 1 : 2 b 1 : 5 c 4 : 3 d 3 : 2e 4 : 1 f 5 : 1

4 a 1 : 10 b 1 : 5 c 2 : 3 d 7 : 8e 25 : 4 f 1 : 4 g 1 : 4 h 24 : 5i 4 : 20 : 5 j 4 : 3 : 10 k 5 : 72l 3 : 10 : 40

5 Kristy bought 120 watermelons and 80 mangoes6 Georgia received $3000, Leanne $1200 and

Ma’Ayan $18007 108 litres of water is needed8 Amy made $2400, Belinda $3600, Candice

$1200 and Diane $48009 a 60 L: 20 L orange juice, 40 L water

40 L: 16 L orange juice, 24 L waterb 16 : 9

1 a b c d

e 1 f 3 g 2 h 5

2 a b c de f g h

i j k l

3 a 4 b c de f

4 a b c d

e f

5 a b c d

e f6 tonne remains 7 3 tonnes8 tonnes were processed9 a b c a d

e f g hi j k l

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i 30 j 20 k l

m n o 6 p

2 a b c de f g 6 hi 9 j 16 k 18 l 64m n o p 4q r s t

3 a b c 16 de f

4 a b c de f

5 of an hour, or 25 minutes6 7 truckloads are needed7 $ 33 or $33.758 152 students participated9 3 hours is spent serving customers

10 a b c d 1 ef g h i

11 a 1 b c 1 d e a f

1 a 3% b 28% c 60% d 70%e 100% f 124% g 105% h 240%

2 a 0.71 b 0.8 c 2.5 d 0.72e 0.603 75 f 0.2075 g 0.154 h 0.3525

3 a b cd e f gh

4

141400

77500

83400

483800

72100 � 18

25

2 50100 � 21

280100 � 4

571100

1FExercise

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1EExercise

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23a35

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1DExercise

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3

1CExercise An

swers

Answers 525

Percentage Fraction Decimal10% 0.1

50% 0.5

5% 0.05

25% 0.25

20% 0.2

12.5% 0.125

1% 0.01

75% 0.75

15% 0.15

90% 0.9

37.5% 0.375

62.5% 0.625

0.16#

1616.6

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23662

3%

0.3#

13331

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38

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320

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0521681766ans_p524-579 6/6/06 4:00 AM Page 525

5 a 25% b 33.33% c 16%d 200% e 2800% f 25%

6 a $25 b $150 c 60 kg d 71.4 kme 15 apples f 300 m g 200 peopleh 200 cars i $49

7 a 30 minutes b 900 g c 616 gd 40 cm e 160 cents f 4.5 mm

8 a $540 b $600 c $508d $1324 e $120 f $40

9 16.67% 10 8.33% 11 40 kg12 10 students13

14 a i 20% ii 44% b i 10% ii 19%

1 a i $2 ii 20% b i $5 ii 25%c i $16.80 ii 14% d i $2450 ii 175%e i $16 650 ii 111% f i $20.50 ii 0.1%

2

3 166.67% 4 93.75% 5 40%6 $37.50 7 $10018

9 a $200 b $125 c $20d $9.90 e $5250 f $54 000

10 a $3.41 b $1.38 c $1.74 d $2.3211 29.78% 12 42.31%13 a $54.75 b 128.11%

1 $148.75 2 $760.50 3 a $784b $29 700 c $226 550 d $19 360e $476.25 f $9072

4 $613.33 5 $333 333.336 a $2166.70 b 16 m c 30.6 m d $164

e 95 cm f 1.52 m

7 $490 8 $4010 9 $10 85010 $20 588.7511 a i $54 187.50 ii $33 277.90

b 10 years12

1 a $10 b $300 c $67.50 d $265e $900 f $592.59 g $1291.41h $491.89

2 8% pa for 54 months 3 $25604 a $110 b $1300 c $567.25 d $1065

e $8400 f $3042.59 g $23 041.41h $4751.89

5 9 months 6 1 year 4 months7 $2083.33 8 a $14 400 b $2409 10%

10

11 a $60 b $1060 c $63.60 d $1123.60e i $67.42 ii $1191.02 iii $91.02f i $5832 ii $2894.06

Multiple-choice questions1 A 2 B 3 D 4 E 5 E6 E 7 E 8 C 9 B 10 C

Short-answer questions1 a b 3 : 2 2 $125 : $753

13

1IExercise

1HExercise

1GExercise

An

swer

s


Selling Cost price Lossprice ($) ($) ($)

5.00 10.00 5.0012.00 20.00 8.0010.80 12.00 1.20

118.20 120.00 1.80750 1 500 750

19 475 20 500 1025

Cost price Mark- Selling($) up ($) price ($)30.95 10 40.9599.95 80 179.95

199.95 395.95 595.90799.95 700 1 499.95

18 799 16 700 35 49918 000 8 995 26 995

Decimal Fraction Percentage0.6 60%

0.0325

0.75 75%

1.2 120%

2.0 2 200%

1 210

34

314%13

400

3313%1

30.3

35

Depreciated New TaxYear value purchases deduction2004 $1500 $340 $2212005 $1619 $239 $2232006 $1635 $426 $2472007 $1814 $1186 $3602008 $2640 $105 $329

P ($) r (% pa) Time I ($)a 1 000 10 3 years 300b 10 000 3 2 years 600c 500 4 5 years 100d 5 700 2.5 4.5 years 641.25e 280 4 3 years 33.60f 12 000 3.25 1.25 years 487.50g 7 500 12.60 81 months 6378.75h 9 600 8.95 2 months 143.20

0 0.5

h d a e f c b g

1 1.5 2

0521681766ans_p524-579.qxd 7/3/08 3:44 PM Page 526 ppg WILEY 3:Users:ppg:Desktop:VELS 9:Quark and Pdfs: Aptara (PPG-Quark)

4 $1800 5 a $25 b 16.67%6 $167.20 7 $680

Extended-response questions1 a $231 b $651 c i $63 ii $34.652 a $10 800 b $616.67

c Loan 1 d Loan 1

Chapter 2

1 a i 4 � r ii t � 2 iii B � Gb i 6P ii 10n iii 2D iv 5P � 2D v 10P � 5Dc

2 a 2 � x b ab � y c x � 5 d 3x

e 3x � 2y f 3p g 2x � 4 h

3 a 4x � 10 b (m � n)2 c m2 � n2

d e4 a 5x b c y � 55 a i 2(x � y) ii xy b i 4p ii p2

c i x � y � 5 ii6 a A � 60 m2 b length � x � 12

width � 5 � y c A � (x � 12)(5 � y)7 a b c i ii

1 a 15n b 12y c 20p d 6xye 10pr f 9mn g �14xy h �15mni �12ab j 30ab k �24rs l �30mnm �12pqr n 30mnt o �24vwx

2 a 15n2 b �2m2 c 10s2 d 12a2be �15mn2 f 8ab2 g 6x2y2 h 8a2b2

i �6m2n2 j 2r3s2 k �10n2p3 l �m3n3

3 a 3a b c de f g uv hi j k lm n o

4 a b c d 5xye f 10 g 24 hi j 3b k �3r l

5 a b c �6ab de f g 10y h 3bi 4b j 2xy k 5m l 2rs2

6 a 7a b 9m c 8x d 12xe 2xy f 7mn g x � 5 h 4a � 2i 13xy j 10ab � 4a k 4 � 6b l 3 � a

7 a 5a � 9b b 6x � 5y c 3a � 4d 11x � 3 e 5xy � 4x f 5pq � 7g 4mn � m h 0

8 a ab2 b 7x2y c 3m2n d p2q2

e 6x2y f 9rs2 � 2r2s g �2x2 � 5x

h 2a2 � 3a i 5a2b � 4ab2 j 8rs2 � 10rsk 7m2n2

9 a 4(x � y) b 4(2x � 1) c 2(x � 1)

1 a 3m � 3n b 5a � 10 c 2a � 10d �9x � 27 e �15x � 6 f �4x2 � 4xyg �8gt � 40t h x2 � 2x i d2 � 4d

2 a 2x � 8 b 6x � 14 c 6x � 1d 5x � 1 e 5x � 13 f 2x � 1g �2x � 5 h �5x � 19 i �x � 5j �x � 13 k �2x � 2 l �2x � 6

3 a 5x � 12 b 4n � 8 c 4x � 2d �23x � 6 e �4x � 6 f x � 7g �4x � 18 h �13x � 7

4 a x2 � 5x � 6 b x2 � 7x � 12c x2 � 6x � 5 d x2 � x � 20e x2 � x � 2 f x2 � 4x � 32g x2 � 7x � 12 h x2 � 9x � 10i x2 � 2x � 63 j x2 � 2x � 3k x2 � 3x � 2 l x2 � 7x � 10

5 a 15x2 � 41x � 14 b 6x2 � 7x � 2c 10x2 � 11x � 3 d 6x2 � 17x � 14e 21x2 � 29x � 10 f 6x2 � x � 2g 10x2 � 4x � 14 h 6x2 � 5x � 6i 9x2 � 18x � 7 j 12x2 � 25x � 12k 15x2 � 11x � 2 l 6x2 � 25x � 14

6 a 2x � 2 b 2x2 � 3x c 9x2 � 6x � 1d 4x e 3x f 12x � x2

7 a P � 2(x + 3y + 5) b A � 3y(x + 5)c P � 2(7x + 5)

A � 6x(x + 5)d P � 80 cm

A � 300 m2

8 a 2x2 � 2x � 2 b �6x2 � 9x � 21c �10 � 5x � 5x2 d 3x2 � 9x � 6e �2x2 � 6x � 4 f �2x2 � 5x � 3

9 a x3 � 3x2 � 3x � 1 b �2x3 � x2 � 2x � 1

1 a 2b b 6s c 4a d 2 e 4 f 1g 3x h 3r i 2x j 2x k 4x l 4ab

2 a 6(x � 1) b 2(x � 1) c 3(x � 1)d 7(a � 1) e 4(2a � b) f 4(a � b)g 2(2a � 5) h 6(a � b) i 3(1 � 2x)j 4(2 � a) k 3(1 � 3x) l 2(2 � b)m x(x � 2) n y(y � 5) o y(y � 2)p x(1 � x) q 2a(a � 1) r 9b(1 � b)s 3a(a � 2) t 2m(2 � 3m) u 3c(2 � 3c)v 12a(1 � 2a) w 15x(1 � 3x) x 16y(x � 2)

3 a �4(2x � 1) b �3(2x � 1) c �5(2x � y)d �7(d � 2e) e �4(2x � 3) f �2(3x � 4)

2DExercise

2CExercise

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7w2

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3m2

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2ab

3d

12b

2a

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3rs8

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x2

2ab3�a

3

2BExercise

Pn � 0.5P

10 � 0.5Pn

P10

5x2

500n

a � 1a1x � y

x � y

5

500C

2AExercise

An

swers

Answers 527

0521681766ans_p524-579.qxd 7/14/08 2:00 PM Page 527 Techbooks[PPG-Quark]

g �5(2x � 3y) h �2(2d � 7e) i �3x(2x � 3)j �4x(2x � 3) k �2y(7y � 3) l �3d(d � 2)m �3x(1 � 4x) n �3p(2 � 5p)o �5r(2 � r) p �7d(1 � 2d)

4 a (x � 3)(2 � x) b (x � 1)(4 � x)c (m � 3)(5 � m) d (x � 8)(2 � x)e (w � 4)(6 � w) f (x � 1)(3 � x)g (a � 4)(2 � a) h (x � 1)(b � x)i (3a � 2)(a � 4) j (6a � 3)(a � 5)k (4y � 1)(y � 1) l (3 � 2x)(5 � x)

5 a 5(a � 5) b 5(x � 3) c 2(3a � 7)d x(x � 4) e y(y � 9) f a(a � 3)g (p � 4)(p � 3) h (x � 5)(x � 2)i (m � 4)(m � 1) j (2x � 1)(x � 1)k xy(x � 4 � y) l (2 � 5a)(a � 7)m (x � 2)(x � 4) n (y � 2)(y � 3)o (y � 3)(y)

6 a 63 b 84 c �20d �70 e 69 f 189

7 a 2(x � 2) b 2(x � 3) c 10(x � 2)d 2(x � 5) e 3(x � 1) f 3(x � 4)

8 a �4(x � 3), 4(3 � x)b �3(x � 3), 3(3 � x)c �8(n � 1), 8(1 � n)d �3(b � 1), 3(1 � b)e �5m(1 � m), 5m(m � 1)f �7x(1 � x), 7x(x � 1)g �5x(1 � x), 5x(�1 � x)h �2y(2 � 11y), 2y(11y � 2)i �4n(2 � 3n), 4n(3n � 2)j �4(2y � 5), 4(5 � 2y)k �5(3mn � 2), 5(2 � 3mn)l �13(x � 2), 13(2 � x)

1 a (a � 2)(a � 3) b (a � 4)(a � 2)c (x � 3)(x � 7) d (a � 1)(2a � 4)e (b � 4)(3 � a) f (x � 3)(x � 3)

2 a (a � 2)(x � 4) b (x � 3)(4 � a)c (m � 4)(2 � n) d (x � 1)(y � 3a)e (x � y)(2 � a) f (n � 5)(m � 1)g (5 � q)(p � 2) h (n � 3)(3m � 6)i (a � 2b)(5x � 1) j (y � 3)(x � 4)

3 a (p � 4)(11 � q) b (n � 1)(p � 9)c (a � 2)(3 � b) d (4y � 1)(3 � 2x)e (2x � 1)((3 � m) f (x � 5)(11 � a)g (x � 3)(5 � a) h (y � 3a)(x � 1)i (x � y)(2 � a) j (y � 3)(x � 4)k (b � y)(a � x) l (5x � y)(2 � b)

4 a (x � 3)(x � 2) b (x � 5)(x � 2)c (x � 4)(x � 3) d (y � 4)(y � 6)e (y � 3)(y � 5) f (y � 4)(y � 2)g (x � 2)(5x � 2) h (x � 3)(3x � 4)i (x � 2)(7x � 2) j ((y � 2)(7y � 21)k (y � 3)(2y � 5) l (y � 3)(3y � 4)

5 a (b � 4)(3 � a) b (x � 2)(5 � y)c (p � 3)(2 � r) d (3x � 4)(1 � 2y)e (3r � 10)(2 � 5s) f (a � 1)(b � 1)g (3x � 4)(1 � 2y) h (5p � 8)(3 � r)i (8x � 4)(2 � y) j (5p � 8)(3 � r)k (3s � 10)(2 � 5r) l (7p � 4)(3 � 2r)

6 a (x � 6)(x � 9) b (a � c)(a � 4b)c (a � 3b)(a � 3c) d (3x � 2)(x � 5)e (2x � 3)(x � 4) f (3x � 2)(2x � 5)g (x � 3)(x � 2) h (5p � 15)(p � 1)i (x � 1)(x � 2)

7 a (11 � q)(p � 4) b (a � 2)(4 � b)c (6y � 1)(z � 2) d (b2 � 5)(a2 � 2)e (1 � y)(1 � x) f (a � 2)(b � 2)g (2y2 � 1)(x � 4) h (4a2 � 2)(b � 3)i (x � 4)(x � 2)

8 a (x � 3)(x � 4) b (x � 10)(x � 1)c (x � 8)(x � 2) d (x � 5)(x � 3)e (x � 6)(x � 2) f (x � 4)(x � 3)g (x � 3)(x � 2) h (x � 6)(x � 2)i (x � a)(x � b)

1 a (x � 2)(x � 1) b (x � 3)(x � 1)c (x � 4)(x � 1) d (x � 5)(x � 1)e (x � 7)(x � 1) f (x � 11)(x � 1)g (x � 6)(x � 2) h (x � 10)(x � 1)i (x � 5)(x � 3) j (x � 7)(x � 2)k (x � 8)(x � 2) l (x � 3)(x � 4)

2 a (x � 3)(x � 1) b (x � 2)(x � 1)c (x � 5)(x � 1) d (x � 7)(x � 1)e (x � 5)(x � 3) f (x � 2)(x � 9)g (x � 3)(x � 4) h (x � 2)(x � 6)i (x � 1)(x � 12)

3 a (x � 3)(x � 1) b (x � 1)(x � 1) � (x � 1)2

c (x � 5)(x � 1) d (x � 2)(x � 2) � (x � 2)2

e (x � 7)(x � 1) f (x � 5)(x � 2)g (x � 3)(x � 2) h (x � 6)(x � 2)i (x � 4)(x � 2)

4 a (x � 5)(x � 1) b (x � 7)(x � 1)c (x � 3)(x � 1) d (x � 5)(x � 2)e (x � 7)(x � 3) f (x � 7)(x � 2)g (x � 6)(x � 2) h (x � 4)(x � 3)i (x � 12)(x � 1)

5 a 2(x � 3)(x � 1) b 2(x � 10)(x � 1)c 3(x � 4)(x � 2)d 4(x � 1)(x � 1) � 4(x � 1)2

e 5(x � 4)(x � 2) f 2(x � 2)(x � 3)g 2(x � 5)(x � 2) h 6(x � 6)(x � 1)i 2(x � 9)(x � 2) j 3(x � 4)(x � 3)k 2(x � 10)(x � 3) l 3(x � 6)(x � 5)

6 a 6x b 6x, 10x c x, 4x, 11xd x, 4x, 11x e 9x, 11x, 19x f 9x, 11x, 19xg 0x, 6x, 15x h 0x, 24x

2FExercise

2EExercise

An

swer

s


0521681766ans_p524-579 6/6/06 4:01 AM 28

8 a (2x � 1)(2x � 3) b (3x � 1)(2x � 5)c (3x � 1)(2x � 7) d (4x � 3)(x � 5)e (4x � 1)(3x � 1) f (8x � 7)(2x � 5)

1 a x2 � 1 b x2 � 16 c x2 � 36d x2 � 9 e x2 � 49 f x2 � 121g x2 � 64 h x2 � 25 i x2 � 81j 25 � x2 k 4 � x2 l 144 � x2

2 a 25x2 � 4 b 9x2 � 16 c 16x2 � 16d 49x2 � 9y2 e 81x2 � 25y2 f 121x2 � 1y2

g 16x2 � 4y2 h 36x2 � 64y2 i 36x2 � 25y2

j 49x2 � 25y2 k 4x2 � 25y2 l 49x2 � 9y2

3 a (x � 3)(x � 3) b (a � 4)(a � 4)c (x � 1)(x � 1) d (x � 6)(x � 6)e (x � 5)(x � 5) f (x � 7)(x � 7)g (b � 9)(b � 9) h (x � y)(x � y)i (m � n)(m � n) j (1 � a)(1 � a)k (3 � x)(3 � x) l (5 � b)(5 � b)m (2 � c)(2 � c) n (6 � b)(6 � b)o (10 � x)(10 � x) p (x � 20)(x � 20)

4 a (4x � 5)(4x � 5) b (2x � 3)(2x � 3)c (7x � 2)(7x � 2)d (2m � 10)(2m � 10) � 4(m � 5)(m � 5)e (11a � 2)(11a � 2) f (10b � 1)(10b � 1)g (4 � 3y)(4 � 3y) h (3 � 8a)(3 � 8a)i (2 � 3y)(2 � 3y) j (4x � 3)(4x � 3)k (5x � 6y)(5x � 6y) l (2a � 3b)(2a � 3b)m (2a � 4b)(2a � 4b) � 4(a � 2b)(a � 2b)n (6u � 2w)(6u � 2w) � 4(3u � w)(3u � w)o (5m � 7n)(5m � 7n) p (2m � 5n)(2m � 5n)

5 a 3(x � 6)(x � 6) b 5(x � 1)(x � 1)c 5(x � 2)(x � 2) d 4(a � 3)(a � 3)e 2(7 � x)(7 � x) f 7(3 � m)(3 � m)g 7(xy � 1)(xy � 1) h 7(2 � ab)(2 � ab)i 3(1 � xy)(1 � xy)

6 a (x � 2)(x � 12) b (x � 5)(x � 1)c (x � 3)(x � 13) d (x � 4)(x � 2)e (x � 6)(x � 8) f (x � 7)(x � 1)g (3 � x)(1 � x) h (11 � x)(7 � x)i (3 � x)(13 � x)

7 a i 8 � 2x ii (8 � 2x)2 iii 16x(8 � x)b i 49 ii 15

1 a x2 � 2x � 1 b x2 � 4x � 4c x2 � 8x � 16 d x2 � 10x � 25e x2 � 14x � 49 f x2 � 20x � 100g x2 � 6x � 9 h x2 � 18x � 81i x2 � 2x � 1 j x2 � 12x � 36k x2 � 6x � 9 l x2 � 20x � 100m x2 � 10x � 25 n x2 � 14x � 49o x2 � 18x � 81 p x2 � 8x � 16

2 a 4x2 � 4x � 1 b 4x2 � 12x � 9c 9x2 � 12x � 4 d 9x2 � 6x � 1e 16x2 � 16x � 4 f 25x2 � 30x � 9g 49x2 � 42x � 9 h 16x2 � 24x � 9i 4x2 � 4x � 1 j 16x2 � 8x � 1k 9x2 � 12x � 4 l 4x2 � 28x � 49m 9x2 � 12x � 4y2 n 25x2 � 40x � 16y2

o 49x2 � 42x � 9y2 p 25x2 � 30x � 9y2

q 81x2 � 72x � 16 r 4x2 � 20x � 25s 16x2 � 16x � 4 t 49x2 � 42x � 9

3 a 4 � 4x � x2 b 25 � 10x � x2

c 1 � 2x � x2 d 16 � 8x � x2

e 121 � 22x � x2 f 81 � 18x � x2

g 144 � 24x � x2 h 100 � 20x � x2

i 49 � 28x � 4x2 j 4 � 12x � 9x2

k 25 � 20x � 4x2 l 9 � 24x � 16x2

4 a x2 � 2x � 6 b x2 � 4x � 9c x2 � 6x � 4 d 2x2 � 6x � 5e 4x2 � 13x � 11 f 2x2 � 18

5 a (x � 4)2 b (x � 7)2 c (x � 9)2

d (x � 3)2 e (x � 5)2 f (x � 1)2

6 a (x � 8)2 b (x � 2)2 c (x � 15)2

d (x � 6)2 e (x � 4)2 f (x � 3)2

7 a (4x � 1)2 b (2x � 1)2 c (3x � 1)2

d (2x � 3)2 e (3x � 4)2 f (2x � 5)2

g (3x � 2)2 h (2x � 3)2 i (7x � 2)2

8 a (x � y)2 b (x � y)2 c (v � w)2

d (p � q)2 e (v � w)2 f (q � r)2

9 a (x � 4)2

b i 81 sq. units ii 196 sq. units iii 576 sq. units10 a i 2x � 10 ii 4x2 � 40x � 100

iii 4x2 � 40xb 4x (x � 10)

1 a b c d

e f g h

i j k

l

2 a b c

d e f g

h i j

k l

3 a b

c d

e f

g h�7p � 6

6�4x � 53

45

�4p � 20

96�

�p � 5

24�3m � 68

40

x � 3930

7w � 710

�7(w � 1)

10

x � 3930

7x � 1110

8y63

�11n35

�14m24 � �7m

1241w44

5x12

13x35

61y40

�8m21

�20p63

25x50 � x

215a28

17x20

�4c96 � �c

24

�m72

22p120 � 11p

603y10

w56

13y22

2b9

a6

x8

14x45

6x15

8x15

2IExercise

2HExercise

2GExercise

An

swers

Answers 529


An

swer

s


i

4 a

b

c d

e f

5 a b c

d e f

g h i

j k l

1 a b c d

e f

2 a b x � 4 c x � 1

d

3 a x � 1 b c d 2 e x � 2

f g h

4 a b x � 1 c

d e

f

5 a x � 1 b x � 5 c x � 3d x � 3 e x � 2 f x � 3

6 a x � 10 b x � 7 c x � 5d x � 20 e x � 6 f x � 9

7 a x � 3 b x � 5 c x � 9d x � 6 e x � 10 f x � 7

8 a (x � 2)(x � 5) b

c d

e f

Multiple-choice questions1 E 2 D 3 A 4 D 5 B6 E 7 D 8 E 9 D 10 D

Short-answer questions1 a 2x � 4 b 6 � y2 a �a � 3b b 2b2 � 4a2

3 a 4m � 4n b �6x � 12 c 6x2 � 2xd 1 � 2x e 7x � 10 f x2 � x � 6

4 a 7(x � 1) b 4(2x � 3y) c �9x(1 � 3x)5 a (a � 2)(2 � x) b (y � 9)(x � 1)

c (2m � p)(6n � 1)

6 a b c

7 a b c

8 a x2 � 9 b 16 � x2 c 49x2 � 49 a (x � 4)(x � 4) b (3a � 4b)(3a � 4b)

c (x � 1)(x � 7) d 3(x � 2)(x � 6)10 a x2 � 4x � 4 b 9x2 � 24xy � 16y2

c x2 � 6x � 11 d 2x2 � 6x � 1711 a (x � 2)2 b (a � 4b)2 c (4x � y)2

12 a (x � 3)(x � 2) b (x � 5)(x � 1)c 2(x � 5)(x � 2)

13 a b c d

14 a 2(x � 1) b c

d

Extended-response questions1 a 20 points b 6g � 2 c 6g � b2 a 6 cm2 b (3 � x) cm c (2 � x) cm

d (3 � x)(2 � x) � 6 � 5x � x2

e 56 cm

Chapter 3

1 a 50 mm b 280 cm c 52.1 cmd 0.837 m e 4600 m f 2.17 km

2 a 200 mm2 b 5 cm2 c 21 000 cm2

d 21 m2 e 1000 m2 f 3.2 km2

3 a 3000 mm3 b 2 cm3 c 8 700 000 cm3

d 0.0059 m3 e 10 000 m3

f 0.000 021 7 km3

4 a 50.5 mm b 0.35 mm3 c 1000 cm2

d 0.000 531 m3 e 20 m f 3.33 cm2

g 2 000 000 m2 h 15 000 mm3 i 150 cm3

j 50 m k 0.02 km2 l 90 000 000 m3

5 a 8000 mm b 110 m c 1 cmd 15 000 000 000 cm2 e 5 mm2 f 0.075 m2

3AExercise

(x � 1)(x � 6)

x � 3

4x � 5x

x � 22(x � 1)

5024 � 2 1

12

59x � 821

11x7

2x15

2x3

x � 42

12

20x � 4448

�5x � 11

12m2

9x20

x � 43 � x

3x � 12 � 15x

(x � 3)(x � 5)

(x � 5)(x � 2)

�(x � 3)(x � 4)

(x � 4)2

x � 2(x � 3)(x � 4)

1(x � 7)(x � 2)

2(x � 2)2

3(x � 4)2

1(x � 3)(x � 4)

x(x � 1)

x � 4

2(x � 2)

x � 2

53 � 12

332 � 11

2

2(2x � 5)

5

23

3x � 44

x � 42(x � 5)

x � 12

x � 23

2(x � 3)

3

x � 1213

23

2JExercise

2x2 � 3x � 64x

5x � 2312x

296x

9 � 5x

12x

7x � 512x

7x � 1110x

1115y

120a

�52x

4a � 105a

35x � 27

4 � 3x

2x

16x � 1824

�8x � 9

1222 � 4x

21

3x16

49x � 5698

�7x � 8

14

�3x � 4818

��x � 16

6

10x � 3648

�5x � 18

24

4p � 32

32�

p � 8

8

0521681766ans_p524-579 6/6/06 4:01 AM Page 530

An

swers

Answers 531

g 1 000 000 mm3 h 0.0001 m3

i 250 000 000 000 cm3

6 825 cm and 2.25 cm 7 500 000 m2

8 500 000 cm3 9 0.175 km2

10 a 5.4 m3 b 0.32 m3 c 0.0045 m3

11 50 m2

1 a 8 cm b 17 m c 24 km d 21 mme 6 m f 16 mm

2 a 90 cm b 80 cm c 170 cmd 32 cm e 16.6 m f 6.33 km

3 a 90 mm b 4015 m c 102.1 cm4 21.9 m 5 108 m6 a 1.5 b 7 c 6 d 2

e 5 f 0.8157 a 4 km b 6.48 km c 9.72 km8 a i 9 combinations ii 5 b 14 combinations

1 a 12 m2 b 15 m2 c 15 m2 d 9.3 m2

e 16 m2 f 24.3 m2

2 a 10 mm2 b 12 cm2 c 17 cm2

d 45.5 m2 e 6.205 m2 f 15.19 km2

3 a 9 mm2 b 21 cm2 c 7.5 m2

d 138 cm2 e 44 mm2 f 8 cm2

g 12.25 cm2 h 3.04 m2 i 0.09 cm2

j 6.5 mm2 k 18 cm2 l 2.4613 cm2

m 1.125 cm2 n 0.4223 m2 o 172.5 m2

4 a 44.4357 mm2 b 15 cm2 c 75 m2

5 2.16 m2 6 52.7 m2 7 0.51 m2

8 2.31 m2 9 6610 a i 1.5 m ii 1.5 m b 78 m2

1 a 12 cm2 b 48 cm2 c 364 cm2

2 a 17 cm2 b 3.5 cm2 c 21.74 cm2

d 6.75 m2 e 189 cm2 f 115 cm2

3 a 300 m2 b 16 cm2 c 22.5 m2

4 a 90 cm2 b 15 m2 c 9 m2 d 10 cm2

e 5.83 cm2 f 7.51 cm2

5 a 2 b 2 c 4 d 5e 10 f 14 g 0.8 h 2 i 6

6 a 1.5 cm b i 1.5 cm ii 4.5 mm iii7 8 cm

1 a 6.28 cm, 3.14 cm2 b 94.25 mm, 706.86 mm2

c 62.83 cm, 314.16 cm2 d 8.80 m, 6.16 m2

2 28.27 m 3 4.1 m 4 11 689.9 cm2

5 31.42 cm 6 18 265.416 m2

7 a 5.14 mm, 1.57 mm2 b 18.93 cm, 22.06 cm2

c 11.41 m, 6.81 m2 d 9.28 m, 2.65 m2

8 a i 706.86 cm2 ii 353.43 cm2

b i 53.6 cm ii 77.1 cm9 103.67 cm2

10 a 188.50 cm b i 376.99 cm ii 1979.20 cmc 530.5

11 a 157.08 cm b i 314.16 cm ii 3141.59 cmc i 0.95 ii 6.37 iii 63.66 iv 636.62 d 318.31

12 a i 3.18 cm ii 2.26b i 3.18 mm ii 0.06 cm iii 3.99 cm iv 0.78 mc 2 d 5.6 m

1 a 18.28 m, 22.28 m2 b 19.42 m, 26.14 m2

c 84.42 mm, 326.37 mm2

2 a 28.57 cm, 44.57 cm2

b 71.42 cm, 121.46 cm2

c 37.34 km, 54.6 km2

3 a 37.70 m, 92.55 m2 b 20.57 mm, 16 mm2

c 18.00 cm, 11.61 cm2 d 12.57 m, 6.28 m2

e 25.71 cm, 23.14 cm2 f 33.56 m, 83.90 m2

4 a 85.84 cm2 b 6.86 m2 c 100.53 cm2

d 7.95 m2 e 180.03 cm2 f 669.82 km2

g 8.74 mm2 h 21.99 cm2 i 23.83 mm2

5 189.27 m2 6 68.67 cm2

7 a i 75.4 cm ii 452.4 cm iii 1809.6 cmiv 12 666.9 cm b i 5 ii 4 iii 3

8 5267.1 cm2 9 a 34 cm, 18 cmb 226.9 cm2 c 385.1 cm2

1 a 22 cm2 b 48 m2 c 280 mm2

d 22 cm2 e 17.82 m2 f 562.5 m2

2 a 39 mm2 b 224 cm2 c 9.01 m2

3 a 96 cm2 b 199.8 cm2 c 44.2 m2

d 28 cm2 e 22 cm2 f 0.96 m2

4 6 m2 5 12.12 m2 6 34 000 cm2

7 a 23.6 m2 b 2.36 L8 a {6, 10, 14, 18, 22, 26, 30, 34, 38}

b T � 4n + 29 a 1400 cm2 b 1152 cm2

1 a 18.85 cm2 b 150.80 cm2 c 87.96 m2

2 a 18.85 mm2 b 116.87 cm2 c 904.78 km2

3 678.58 cm2 4 a 31.42 cm2 b 345.58 cm2

c 56.55 cm2

3HExercise

3GExercise

3FExercise

3EExercise

23 km

3DExercise

3CExercise

3BExercise

0521681766ans_p524-579.qxd 7/14/08 2:00 PM Page 531 Techbooks[PPG-Quark]

An

swer

s


5 a 54.56 m2 b 218.23 m2 c 63.98 cm2

d 71.91 cm2 e 270.80 m2 f 313.65 km2

g 326.41 m2 h 593.92 m2 i 43.71 mm2

6 3455.75 cm2 7 80 424.8 cm2

8 a 18 849.556 cm2 b i 1.88 m2 ii 37.70 m2

c 239

1 a , 10 cm b , 5 m c , 1.5 cmd , 5 mm e , 2 km f , 10 m

2 a circle b triangle c rectangled trapezium e hexagon f triangle

3 a 8 cm3 b 84 m3 c 21 mm3

4 a 4 cm3 b 10.5 m3 c 11.96 cm3

d 48 mm3 e 14.88 m3 f 8.1351 cm3

g 108 m3 h 450 mm3

i 0.382 044 cm3

5 a 75 m3 b 30 cm3 c 1.25 cm3

6 a 16 cm3 b 42.875 m3 c 15 cm3

7 a 125.7 m3 b 0.2 mm3 c 2356.2 cm3

8 a 35.3 cm3 b 28 m3 c 8.9 km3

d 28 m3 e 0.4 m3 f 29 232 mm3

9 8000 cm3 10 0.2 m3 11 0.62 m3

12 a 55 m2 b 825 m3

13 a 1178.10 cm3

b i 40 cm3 ii 1218.10 cm3 iii 15.5 cm iv 148

1 a b cd e f

2 a b c3 a 13 cm3 b4 a b c5 a b c6 a b c

d 7 $500 8 0.121 km2

9 a 27 m3 b 24.389 m3

10 a $600 b $84 c $13.5 d $810

Multiple-choice questions1 C 2 E 3 B 4 A 5 D6 B 7 A 8 E 9 C 10 A

Short-answer questions1 a 380 cm b 1270 m c 2.73 cm2

d 52 000 cm2 e 10 000 cm3 f 53.1 cm3

2 a 14 m b 51 mm c 16.2 cm3 a 4 cm2 b 1122 mm2 c 30.34 mm2

d 7.5 m2 e 15 cm2 f 3 cm2

4 a 2.5 m2 b 37.4 m2

5 a 28.27 cm2, 18.85 cm b 5.38 m2, 9.51 mc 2.36 cm2, 6.71 cm

6 a 8.86 m, 4.63 m2 b 45.56 cm, 128.54 cm2

7 a 46 cm2 b 82.5 m2

8 a 659.73 mm2 b 30.21 m2

9 a 30 cm3 b 54 m3 c 31.42 mm3

10 a b

Extended-response questions1 a 517.08 cm b $65 c 15 853.98 cm2

d 1.58 m2 claim is correct2 a 1 cm b 15.71 cm2 c 125 680 cm3

d 0.125 68 m3 e 18.85 cm f 15 m2 g $1200

Chapter 4

1 a 2 b 2 c 1 d 2 e 3f 3 g �3 h �1 i �3

j �1 k �2 l �3 mn �1 o 1 p 3

2 a 9 b 2 c 9 d �6e �6 f 24 g �15 h �4i 6 j 20 k 28 l �18m 2 n 0 o 8 p �28

3 a b 9 c d 6 e �18

f �12 g 14 h i 0 jk l

4 a 3 b 9 c 4 d 4 ef g �9 h �8 i 5

j k 6 l

5 a 13 b 6 c �10 d �12 e 13

f 11 g 10 h 5 i 6 j k �7

l 8 m �2 n �7 o p

7 a a � b � c b

c

d a � c(b � d) e f

g h

i a � cd � b j a � b � cd

k l

1 a 1 b �1 c 4 d 2 e �3f 8 g 1 h �1 i �6 j 1k 2 l m n o 03

234

23

4BExercise

a �d � 3ef

4ca �

2(be � 3c)

d

a �2d(b � 3)

ca �

c(3 � d)

2b

a �b

2aa � �

cd

b

a �c � d

b

a �c � b

2

�73

23

143

�32�6

5

43

52

� 425

12

23�8

3

152

274

�53

4AExercise

� 12 cm2� 9 cm2

� 10 cm� 5 cm� 3.5 cm� 7 cm

1250 cm3� 750 cm3� 150 cm3� 150 cm3� 80 cm3� 36 cm2

� 19 cm3� 750 cm3� 432 cm3� 150 cm3� 2 cm� 4 cm� 4 cm� 5 cm� 4 cm� 3 cm

3JExercise

3IExercise

0521681766ans_p524-579 6/6/06 4:01 AM Page 532

2 a 1 b �8 c 1 d e 2f 0 g 1 h 5 i 5 j 1

3 a 1 b �3 c 2 d 6e 16 f 3 g 3 h �1 i

4 a �1 b c �23 d �14e �16 f 3 g 18 h �2 i �13j �22 k 2 l �1

5 a �3 b 8 c �2 d ef �37 g 100 h 40

7 a b x � �c c x � b

d e

f

1 a b c d 10

e f g 15 h �82 a b 1 c 13 d 5 e 1

f 59 g h3 a �4 b �3 c 5 d 1

e �1 f 64 a b c d e

f g h5 a b c 0 d 2

e 6 f 16 a b �5 c �19 d �4

e �1 f �6

7 a x � 2ab b c

d e

f g

h i j

k l

m x � ab � 2a n

o

1 a 26 b 28 c 3 d 28 e 8 f2 10, 18 3 56 cm, 224 cm 4 $25

5 4 days 6 10 km, 20 km 7 16, 488 $360, $640 9 19 km

10 100 km, 150 km, 200 km, 250 km11 140 12 $122.50, $175, $102.5013 $15 20014 a T � 8x � 7200 b 300 c R � 24x

d x � 350 e 3825

1 a 2 b �4 c 12 d 5 e �52 $17.80 3 4 fiction, 8 non-fiction 4 105 18, 22, 44 6 187 54 km, 27 km, 18 km, 54 km 8 55 � 50, 709 a 27, 28, 29 b i x, x � 2, x � 4 ii 4, 6, 8

c i x, x �2, x � 4 ii 15, 17, 19d i x, 2x, 3x ii 14, 28, 42

10 8 hours 11 8 pm 12 813 438 km14 Anna Rose, 6; Bob, 4; Chloe, 12

1 a 30 b 24 c 4 d 2e 452.16 f 33.49 g 249.86h 64.20 i 15.71

2 a 4 b 36 c 4.14 d 60 e 3.39f g

3 a b c

d e

f g

h i

j

4 a 88.89 km/h b i d � st ii 285 km

5 a i 212°F ii 100.4°F b

c i �10°C ii 36.67°C

6 a 35 m/s b 2 s

7 a 58.14 b 21.30

8 a 73 b 476.3

C �59

(F � 32)

A � (4C � B)2

g �4�2l

T2p � �q ; 1A

h �S � 2�r2

2�rV � ;2PR

r � ;B v

�hx �

cd � a

b

n �p

m� xR �

100I

PTr �

A

2�h

136�10

3

4FExercise

4EExercise

247

4DExercise

x �2ab � a2

a � b

x �a � b

1 � a

x �ad � b

c � dx �

b � bca � c

x �c � a

bx �

ac

bx �

acc � a

x � �a2

2a � b � a2x �6b � a

5

x �4c � 3b

3a � 4x �

bd � be � acc

x �ac

c � bx �

2bd

2a � bc

�52

72

16

�16

524

512

38�1

28

15112

136

�54

237

85

152

67

245

247

307

4CExercise

x � �ab � bc

a � b � 1

x �d � bd � c

a � bx �

4c � ab

5a

x ��by � c

2a

43

152

72

59

92 A

nsw

ers

Answers 533

0521681766ans_p524-579 6/6/06 4:01 AM Page 533

1 a b

c d

e f

g h

i j

k l

m n

o p

q r

s t

2 a b cd e fg h

3 a b cd e fg h ij k l

4 a b cd e f

5 a b cd e fg h i

6 a b cd e f

7 a b cd e f

8 a b cd e f

9 less than 18 1011 a i ii 80 m2

b i ii 130 m2

12 a b

c d e

f g

h i

j k

l

1 a yes b yes 2 a no b yes3 a x � 1, y � 3 b x � 4, y � 1

c d x � �2, y � �1e x � 2, y � 6 f x � �2, y � 8

4 a x � 2, y �5 b x � �1, y � 5c x � 1, y � 0 d x � 2, y � 5e x � 4, y � 3 f x � �7, y � �1g x � 4, y � 2 h x � �2, y � 10i x � 2, y � 1

5 a x � 3, y � �1 b x � 1, y � 3c x � 0, y � 4 d x � 4, y � 3e x � 4, y � 1 f x � �1, y � 5g x � �5, y � �4 h x � 3, y � 9i x � �1, y � �3

6 a x � 1, y � 1 b x � 5, y � 1c x � 4, y � �2

7 a

b

c

d

e

f

1 a x � 5, y � �4 b x � 2, y � �4c x � 5, y � 12 d x � 1, y � 1e x � 2, y � 2 f x � 2, y � �1

2 a x � 2, y � 4 b x � 6, y � �1c x � �2, y � 6 d x � �3, y � �13e x � 2, y � 3 f x � 1, y � 3

3 a x � �5, y � �3 b x � 2, y � 1c x � 2, y � 1 d x � �2, y � �4e x � 5, y � 4 f x � 7, y � �5

4IExercise

x �ab � a

a � b� b, y �

ab � a

a � b

x �2a

a � b, y �

2ab

a � b� a

x �a � ab

a � b, y �

a � ab

a � b� a

x �a � b

2, y �

a � b

2

x �b

a � 1, y �

1a � 1

x �b

a � b, y �

b2

a � b

y � 32x � 1

2,

4HExercise

x �c � b

b � a

x b � 1b � a

x �b � c

1 � a

x b �ca

x b � cd

a

x ca

� bx �b � cd

2

x cd � b

ax �

ac

bx � a(b � c)

x � b � ax b � c

a

x � 13x � 8

w 13p � �44

3x � 3x 17h � 3

8y �35a � 5

2

x �27q �5x 5

2

x � �1m �8x 1x � �4x �8

3x 7n � 30x � �15x � 20m � �11

2n � �2x �6x � 10x � �5x � 3x � 4

7n � �1x 6x � 1

2n �225x 4

x 1n � 32x 6

t � �12x � 12y � �32d �9

4d 23b � �2

n �4x � 2p 4a 3y 6x 5

�4 � x 0�2 x � 2�3 � x � 11 x 4x � �1x � 3x 0x 1

–7 –6 –5 –4 –3 –2x

2 3 4 5 6x

–3 –2 –1 0 1 2 3 4 5 6 7x

0 1 2 3 4x

–1 0 1 2 3x

–3–2–1 0 1 2 3x

–2 –1 0 1 2x

–1 0 1 2 3x

–14–15–16 –13 –12x

7 8 9 10 11x

–10 –9 –8 –7 –6x

–6 –5 –4 –3x

–2–3 –1 20 1x

–2–3–4 –1x

–2 –1 0 1 2x

10–1 2x

1 2 3 4 5x

–1 0 1 2x

–1 0 1 2 3x

0 1 2 3x

4GExercise

An

swer

s


0521681766ans_p524-579 6/6/06 4:01 AM Page 534

g x � 7, y � �1 h x � �3, y � �2i x � 1, y � �4

4 a x � 3, y � �5 b x � 2, y � 4c x � 2, y � �3 d x� 3, y � 1e x � �1, y � 4 f x � 3, y � �2g x � 9, y � �8 h x � �2, y � �2i x � 2, y � 1 j y � �3k x � �1, l x � �1, y � �2

6 a

b

c d x � 0, y � b

e f , y � 6

g h

i x � 0, j y � c

k

l x � 1, y � 0

m

n

o

p

q

r

1 lip gloss $9; eye shadow $32 cricket ball $12; tennis ball $5 3 18, 244 18.5 cm � 23.5 cm 5 15 m � 45 m6 a b x � 2, y � 2

c x � 16, y � 327 4 chips, 16 hot dogs 8 300 adults, 120 children9 11 five-cent and 16 twenty-cent pieces

10 35 11 April $100; Kristy $5012 potatoes 480; corn 340 13 jogging 3 km/h;

cycling 9 km/h14 160 adult and 80 children15 a i $1.50 ii C � 1.5n � 300 iii R � 2n

iv loss of $50 v 1000 b $2.50

Multiple-choice questions1 D 2 D 3 D 4 C 5 A6 A 7 C 8 C 9 B 10 A

Short-answer questions1 a b 22 c 1 d 6 e 2

f 2 g 2

2 26 3 $16 4 a b

5 a 89.6°F b 23.89°C

6 a ,

b ,

c ,

7 a x � 2, y � 9 b x � 1, y � 4c x � 4, y � 2 d x � 1, y � �1

8 19 science fiction and 5 adventure

Extended-response questions

1 a 7500 joules b i ii 4.14 kg

c i ii

d i 160 000 joules ii 640 000 joulese 20.89 m/sf i 200 000 joules ii 50 000 joules

2 a Tranh x; Vinh 4x; Amber 4x � 2; Lucas 4x � 4; Chloe 2x � 2

b i 10x � 4 � 5x � 11ii Tranh 3; Vinh 12; Amber 14; Lucas 8;

Chloe 4c Tranh 9; Vinh 36; Amber 38; Lucas 32;

Chloe 16

Chapter 5

1 a i ii obtuse ivb i ii acute iv 35°c i ii reflex iv 310°d i ii straight angle iv 180°e i ii obtuse iv 105°f i ii right iv 90°

2 a 45° b 90° c 105° d 200°e 180° f 360°

3 a i 125° ii 35° b i 133° ii 43°c i 102° ii 12° d i 170° ii 80°e i 91° ii 1° f i 165° ii 75°g i 142° ii 52° h i 112° ii 22°i i 139° ii 49° j i 107° ii 17°

4 a C b S c N d Ce S f N g S h N

�AOB�ROB�SRT�XYZ�PRQ

120��BAC

5AExercise

;29.44 m/sV � ;B2km

m �2k

v2

135

14 3 16 17 18x

5 5 5 5

x � 145

11 12 13 14 15 16 17xf � 13

20 21 22 23 24 25xx � 21

m �p2

2Eb �

cd � ax

12

y � 73x � 7

3,

4JExercise

x �c � f

a � d, y �

af � cd

b(a � d)

x �c � f

a � d, y �

cd � af

b(a � d)

x � �b

a � bc, y �

bc � 2a

a � bc

x �3b

a � 3b, y �

3b � 2a

a � 3b

x �a � 2b

a � b, y �

3a

a � b

x �c � bd

a(b � 1), y �

c � d

b � 1

x �b � 4

ab � 4, y �

1 � a

ab � 4

x � �ca,y � b

a

x � 3b7a, y � �b

7x � 3b7a, y � b

7

x � �4ay � b

3ax � 13,

x � 5a2 , y � �3a

2b

x � b2a, y � �b

2

x �a � b

2, y �

a � b

2

y � �92

x � 12,

An

swers

Answers 535


5 a 360° b 180° c 90° d 270°e 60° f 120° g 90° h 108°i 432° j 216° k 6° l 288°m 720° n 540° o 8640° p 60 480°

6 a 180°, 180° b 150°, 210° c 60°, 300°d 30°, 330° e 150°, 210° f 30°, 330°g 180°, 180° h 30�, 330� i 0�, 360°j 90°, 270°

7 a 72° b 108° c interior 120°; exterior 60°d interior 135°; exterior 45°

1 a no, angles are not equalb yes, corresponding angles are equalc yes, alternate angles are equald no, don’t add to 180°e yes, cointerior angles add to 180°f yes, corresponding angles are equal

2 a 125°, alternate b 70°, cointeriorc 80°, corresponding d 66°, alternatee 96°, vertically oppositef 126°, corresponding g 62°, supplementaryh 115°, corresponding i 116°, cointerior

3 a a � 60°, b � 120° b c � 105°, d � 105°c e � 100°, f � 100°, g � 100°d x � 70°, y � 40° e t � 58°, u � 122°,

z � 122�f u � 110°, v � 50°, w � 50°

4 a 40° b 51° c 12° d 55° e 5°f 13° g 69° h 30° i 50°

5 a 50° b c 50° d 10° e 80°

1 a obtuse isosceles, 40° b acute scalene, 30°c right-angled scalene, 90°d acute equilateral, 60°e obtuse isosceles, 100°f right-angled isosceles, 45°g obtuse scalene, 110°h acute equilateral, 60°i obtuse isosceles, 120°j obtuse isosceles, 40°k right-angled scalene, 90°l acute scalene, 70°

2 a 120° b 20° c 70° d a � 60°, x � 120°e a � 100°, b � 140° f c � 50°, d � 50°

3 a g � 108°, j � 102° b z � 68°, y � 44°c p � 30° d u � 48°, v � 48°e p � 120°, q � 120°, r � 120°f x � 100°, y � 100°, z � 80°

4 a 10° b 15° c 10° d 12°e f � 24°, e � 20° f 17°

5 a b � 20, x � 80, r � 20b q � 30, m � 66, p � 75

6 a i ii 9x � 180 iii 20°

b i ii x � 10 � 60 iii 50°

c i ii 4x � 8 � 90 iii 20.5°

7 a b 5x � 180 c 36°

1 a 115° b 159° c 20° d 121°e 140° f 220°

2 a 80° b 30° c t � 26°, r � 50°d 17.5° e 20° f 100°g u � 45°, r � 120° h 60°i x � 30°, y � 37.5° j x � 95°, w � 10.5°k 50° l 60°

3 a OE, AE, 2P, AA, 2AS b OE, 2P, AAc 1P d 2AS e OE, 2Pf OE, AE, 2P, 2AS

4 3 5 a i 8x � 40 � 180 ii 17.5°b i 4x � 210 � 360 ii 37.5°

6 a

b S � 180(n � 2) c 1440°, 1800°

1 a yes (AAS) b yes (AAS) c yes (SSS)d yes (SAS) e no f yes (SAS)g no h yes (RHS)

5EExercise

5DExercise

3x

x

x

2x + 4

x + 10 x + 10

x + 10

3x

3x

3x

5CExercise

503

5BExerciseAn

swer

s


Number of Number of Sum ofsides triangles interior angles

5 3 540°6 4 720°7 5 900°8 6 1080°


2 a 4 b x � 3, y � 5 c 55°d 70° e 6 f 7 g g � 4, i � 3h x � 4, z � 60° i m � 5, n � 4, l � 110°

3

4 no—they can be of different size5 yes—by the reason of SSS

1 a

b

c

d

2 a no b yes c yes d no

3 a 2 b 9 c 16 d 38.5

e 9 f

4 a x � 9, y � 15 b

5 a i all angles equalii a � 60°, c � 7

b i all angles are equal iic i 2 pairs of corresponding sides are in the

same ratio and the angles included betweenthem are equal ii 6

d i 2 pairs of corresponding sides are in thesame ratio and the angles included betweenthem are equal ii 10

e i 2 pairs of corresponding sides are in thesame ratio and the angles included betweenthem are equal ii

f i all angles equal ii 24

6 a i 55° ii 100° iii 55° iv 25°b all angles are equal

7 a 2 pairs of corresponding sides are in the sameratio and the angles included between themare equal b 40 m

8 a all angles are equal b 9 6 m10 20 m 1112 a, b

c 233.33 cm d i 116.67 cm ii 77.78 cm

1 a cuboid b pyramid c cylinderd trapezoidal prism e ovoid f cubeg cylinder h octagonal pyramid

2 a cylinder b ovoid c cylinderd cone e sphere f dodecahedral prismg cuboid h cube

3 a octagonal prism b cubec triangular prism d tetrahedron

6

7 b

c

d

b

c

a

d

5GExercise

whiteboard

pen

30 cm700 cm

365 m

152 m

x � 252

92

b � 132 ,

y � 214x � 15

2 ,

515

¢ABC ~¢PQR�

AC

PR�

3.24.8

�23

BC

QR�

57.5

�23

AB

PQ�

46

�23

¢XYZ ~¢MNO�

�X � �M�Y � �LN

¢PQR ~¢TUS�

ST

PR�

105

� 2

SU

QR�

2613

� 2

�P � �T � 90�

¢ABC~¢EFD�

DF

BC�

164

� 4

�B � �F

EF

AB�

123

� 4

5FExercise

¢MNO � ¢RQP¢LMN � ¢KIJ¢FGH � ¢BCD¢PBR � ¢FDE

An

swers

Answers 537537

Top view Side view

Top view Side view

Top view Side view


e

1 a b

c d

e f

2 a cylinder b hexagonal prismc tetrahedron d cuboide cylinder f cubeg square pyramid h pentagonal pyramidi square pyramid

3–7 Drawings may vary.

Require constructions.

Multiple-choice questions1 B 2 D 3 C 4 C 5 D6 A 7 D 8 C 9 B 10 C

Short-answer questions1 a obtuse, 100° b right angle, 90°2 a 25° b 115°3 a a � 80°, b � 40° b d � 80°, c � 50°

c 110° d 70°

4 yes, 4 5 a x � 10b x � 15, y � 12

6 x � 12, y � 87 a polyhedron b cylinder

c square pyramid d polyhedron

Extended-response questions1 a 6 m b i 7.14 m ii 4.1 m

c i 8.66 m ii 5.2 m2 a 490 cm b i 175 cm

ii 164.29 cm, 10.71 cm lowerc i 262.5 cm ii 207.14 cm, higher by 55.36 cm

Chapter 6

1 a bcde fg hi jkl

2 a 16 b 16 c 243 d 8e �8 f �1 g 9 h 625i �1 j �8 k �625l �16 m �81 n �16 o �16p �1 q r s t

u v w x3 a 1728 b 1 419 857 c 191 102 976

d �4 e �3375 f �49 g �125h 20 736 i �1 j 8 k �20 736

l 1 m n o

p q r4 a 43 b 97 c x2 d (2m)4

e 7c4 f 43d2 g h

5 a b c

d

6 a b cd e f

7 a 2 � 3 b 23 c 24 � 32

d 29 e f

1 a x7 b p7 c t9 d y5 ef g h i jk l m no p 12x7m230c9d2

10d 6f 46a53px2y53x4y9x9y4x7y6p12a8y8

f 3

6BExercise

53 � 2223 � 33

216m3n38p3q3125b2y3

100a2b236x2y2343p3y2

a 7x

9b 2 a y

4b 3

a 34b 2 a 1

5b 4a 2

3b 4a 3

4b 5

53f 2a3b2

� 162401� 1

27� 2187823 543

162401

12527

2187128

�312532

116� 8

2781256

254

1343

916

827

7pq � pq � pq2xp � xp � xp � xp � xp � xp � xp

5ay � ay � ay � ay3pq � pqpq � pq7x � 7x � 7x � 7x � 7x

5a � 5a � 5a � 5a3y � 3y � 3yxp � xp � xp � xp � xp � xp � xpa � a � a � a � a

b � b � b � ba � a � a

6AExercise

5IExercise

5HExercise

An

swer

s


3 cm 3 cm

7 cm

3 cm

3cm

3 cm

3 cm

6 cm5 cm

4 cm

6 cm

3 cm

5 cm

2 cm

3 cm2 cm

8 cm

5 cm

8 cm

5 cm 5 cm

5 cm

5 cm

5 cm

5 cm

5 cm

Top view Side view

0521681766ans_p524-579 6/6/06 4:01 AM Page 538

2 a b c d d e

f g h i 5m j

k l 5a m n o

p q r s t 2xy

3 a b c d x ef g h h ij k l

4 a b c d e

f g h i

5 a b c d e

f g h i

6 a 4x b 12x2 c 10x3 d �4xe f g h

7 a b c de f g h

8 a b cd e fg h i

9 a is correct; b does not evaluate from left toright

1 a b c d ef g h ij k 2c6 l 7f 24

2 a 1 b 1 c 1 d 1 e �1 f 1g 1 h 1 i 1 j 1 k 4l �7 m 2 n 5 o �4 p 1q 3 r 1 s 0 t 1

3 a b c x d ef g h i jk

4 a b 6 c d 1 e fg h i

5 a b c d e

f

6 a b c d

e f

7 a i 1 ii 1 iii 1 iv 1 v 1 b i �1 ii �1iii �1 iv �1 v �1 c i 1 ii �1

d i 2 ii 0 iii 0 iv �2

1 a b c de f g hi j k lm n op q 1 r st u vw x

2 a b c d e

f g h

3 a b c d

e f g h

i j k

l

4 a b cd e f gh i jk l

5 a b c de f g h

i j k 15n l

m n o

7 a b fg 8

1 a b c d e

f g h i j k

l m n o p1

4e3f 3

v2

5u8

9

d2e3

2

xy2

a4

b4

m

n2

q2

p7

2

b6

3

d5

4

x2

1

52

17

18

1

m7

1

y3

1a

6EExercise

23ag2af 5x10

yz

m11 np5m11 np5x11zy2

�3a4b525w8y2

4x6

�27x6

125a15b9

12c8d72m10n428x24b24

21264a18b2a17b8a10b11

128x8y2z6160m15p5t10

�49d 4f 8g224a11b9�40a15b39a58a4�12a6b854x6y9

�64a2b6c15d 327ab68ab3

�25w8y2

4z2x6

�9x4y6

4a10b6

�27b6c9

64x9

25w8y2

4x6

9x2

4x6g10

9f 2

64g10

27n9

8m12

27h3

64k3

16r4

n4

27k3m9

64n21

8a6

2732m5

n5

s6

49x4

81625

p8

4

r6

27

y3

r7

s7

p3

q3

x4

y4

8m12n3p9�16c8d12e4

25s14t281a8b12�3p8q2r2�27w9y32b20c5d152x6y2

7p6q12243x15y10625c8d12

16x2y216g4k4m3n3125v6

16h8�343r3�8p3�125n3

9r2125a616y216x4

6DExercise

63x21y24

3227a17

80b27

5kl74f 8g4h2

3c8e2a17b5

a12

9

2f 6g

3d 2e

23x810

x3

4

x5

a7x5a3f 2y32892

x14y5

a11f 13d25y16m18a10b13x115987

4p28

8k27614330514

26m18y12x10b12

6CExercise

4my�3�2xpaqb�5a x�y�2

w�x�2b x�3a

x�yb y�xa

x�yb x�y

a3x�2b x�325a22a�b

10 p�q�r2p�q�rt

x�y10 p�y

3x�ytx�y5a�b2x�y

�20x485

5x440x6

k2m

57m4n5

2

5x3y

6b3g

2c3d4h610b43n4y4

�3m2n3

26k3m3

9x4y

212x4b2

6f 66b5

g7f 3e3c5

d 5

a4

b2

3m5n6g5h46b2g3c2d3x10f 6

d 6c7b6a6

43

mn29

gh243

x6y3p7

4

a

5w

5b6

47x2

18y32y82a5d5

3

2a5y8a2x4 An

swers

Answers 539539


2 a a b c d e 2w

f g h i ab j

k l m n

o p

3 a b c d e

f g h

4 a b c d

e f g h

i j k l

m n o p

5 a b c de f g hi j k l 3

m n o 3 pq r �1000

6 a 10 b 100 c �2000 d 16e �6 f 64

7 a b c �36 d e �2 f 10

8 a i 5 ii 16 iii 64 iv 16 v 64 vi 256 viiviii ix x

b x � 2 and y � 2 or x � 4 and y � 1

9 a a2b � n2 b c10 a 65 b 8 c 9 d

e f

1 a 3 � 106 b 1.5 � 1010 c 1.2 � 1012

d �2.1 � 104 e �4.5 � 106 f �6.4 � 104

g 5 � 106 h 3.4 � 104 i 5 � 104

2 a 4 � 10�4 b 3 � 10�6 c 2.4 � 10�8

d 7.3 � 10�10 e 3 � 10�5 f 1.25 � 10�10

g �3.45 � 10�5 h �8.76 � 10�3

i �8.09 � 10�9

3 a 6 � 103 b 7.2 � 105 c 3.245 � 102

d 7.869 03 � 103 e 8.459 12 � 103

f 2 � 10�1 g 3.28 � 10�4 h 9.87 � 10�3

i �1 � 10�5 j �4.601 � 108

k 1.7467 � 104 l �1.28 � 102

4 a 5.23 � 108 b 6.2 � 108 c 4.5 � 107

d 8 � 106

5 a 240 000 b 3 600 000 c 47 000 000 000d 58 600 000 e 423 000

f 3 780 000 000 000 g 126 000 000h 303 i 978 300

6 a 0.000 000 036 b 0.000 004 6c 0.000 000 000 002 d 0.000 027 4e 0.3678 f 0.000 000 789 g 0.000 04h 0.3 i 0.000 000 9

7 a 94.3 b 856.1 c 4.59d �1 270 000 000 e 7000 f �3g 0.06 h 0.072 13 i �0.000 095 7j 41 k �600 000 l �450 600 000m 0.000 89 n �4 010 000 000 000o �0.000 091 p 28.19

8 a 6 � 1024 b 4 � 107 c 1 � 10�10

d 1.5 � 108 e 6.67 � 10�11 f 1.5 � 10�4

g 4.5 � 109

9 a 5 900 000 000 b 6 000 000 000 000 000c 0.000 038 4 d 0.0018e 0.000 000 000 000 01 f 560 000

10 a 1.84 � 109 b 2.647 � 109

1 a 2.441 � 10�4 b 2.107 � 10�6

c �4.824 � 1015 d 4.55 � 10�5

e 1.917 � 1012 f 1.995 � 108

g 3.843 � 102 h 1.71 � 10�11

i 1.524 � 108 j 3.325 � 1015

k 4 � 103 l �9.077 � 10�1

2 a 9.3574 � 101 b 2.1893 � 105

c 8.6000 � 105 d 8.6288 � 10�2

e 2.2985 � 1015 f 3.5741 � 1028

g 6.4 � 108 h 1.2333 � 109

i 1.9951 � 101 j 5.4459 � 10�1

3 1.98 � 1030 4 4.36 � 106 km5 3.35 � 1013

6 a 5.400 46 � 1012

b i 3.24 � 1013 ii 2.27 � 1014 iii 9.72 � 1014

Multiple-choice questions1 C 2 E 3 D 4 E 5 A6 C 7 C 8 B 9 C 10 A

Short-answer questions1 a b c d

e f

2 a b c de 1 f

3 a b c

d e f 1

4 a b cg12

f 55y519

b4a8a15b6

23

p6

q846h16k1553d6

w6y154 � 3x28113n8u9

3x2

44b6

6x2y6a2b22m6g8

6GExercise

6FExercise

777225310; 6n2 � 36

116

14

116

14

13

�2764

499

481

425

18

125

12�3

423

� 1200

125�1

8� 125

116

181

14

110

�e6

100c2d4

�27a6

125b3

x

3y

�64

p3q6

9

c4d 6

m2

41

4a2

1

9h2

x2mn5

10y3

12w6

tu2v2

4m2h3

5pk2

3d2f 2

4ge6

2b5

c2a4

y3

5a3

u3

v2

2y2

x4

n4

m3

3435

649

812

q5

p

y3

x2

b5

a5

n4

m4

�5u2t

7

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5

�2b8�y3

4x2y4m3n2

d 2e6p65h43q2

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0521681766ans_p524-579 6/6/06 4:01 AM Page 540

5 a 4.68 � 101 b 9.834 � 10�2

c 4.65 � 106 d 4.65 � 10�5

6 a 6532 b 53 400 c 0.006 765 4d 0.000 347

7 a 9.62 � 104 b 1.91 � 103

c 2.30 � 1025 d 9.49 � 101

e 1.35 � 103 f 1.46 � 1012

Extended-response questions1 a b c2 a 1.6727 � 10�73 b 2.7814 � 10�73

c i 1.1087 � 10�73 ii 0.6677d 4.4571 � 10�73 e 4 � 106

Cyclic revision A

Chapter 1

Multiple-choice questions1 D 2 A 3 A 4 E 5 B

Short-answer questions1 9.446 2 $200 : $400 : $600 3 9

Extended-response question1 a $18 b $270 c i $14.85 ii $157.50 loss

d i 212 shirts ii $19.90

Chapter 2

Multiple-choice questions1 D 2 D 3 C 4 C 5 C

Short-answer questions1 a 3(x � 2)(x � 2) b 4a(3b � 2)

c xy(xy � 3x � 4y) d 2(a � 5)(x � 3)2 a 5(a � b) b 10x2 � 33x � 20

3 a b

Extended-reponse questions

1 a b

c i $7 ii $5.502 a (x � 2a)(y � 2a) b 30a � 4a2

c i 26 m2 ii 44 m2

Chapter 3

Multiple-choice questions1 C 2 B 3 D 4 E 5 A

Short-answer questions1 a 146.27 mm2 b 20 cm2 c 6.01 m2

2 a 11 b 6 c 113 a 125.66 mm3 b 1.68 cm2 c 5.86 cm

Extended-response question1 a 270 000 cm2 b 659.7345 cm2

c i 6597.345 cm2 ii 65 973.446 cm2

d 15.16 e 409.3

Chapter 4

Multiple-choice questions1 C 2 A 3 E 4 B 5 D

Short-answer questions1 a 2 b 12 c 7 d

e 2 f

2 a b

3 a x � 2, y � 9 b x � 1, y � 4c x � 5, y � 3 d

Extended-response question1 a i ii 354

b i andii 528

c second option

Chapter 5

Multiple-choice questions1 C 2 D 3 C 4 C 5 B

Short-answer questions1 a a � 30°, b � 60°, c � 60°

b a � 100°, b � 50° c x � 60°, y � 40°

2 a

b x � 3, y � 2

Extended-response question1 a

b X is 4 cm from S

Chapter 6

Multiple-choice questions1 C 2 C 3 E 4 C 5 A

Short-answer questions1 a 2a5 b 4a6b3 c a12b8 d 5

e 35 � x8 f

2 a 2.684 � 10 bc d 4.65 � 10�43.45 � 107

6.78 � 10�2

b5

a4

12 cm

8 cm

4 cmX

P

Q

x � 30

C � 60 � 0.35(n � 100)(n 100)(n � 100)C � 0.6n

C � 125 � 0.24n

x � 135 , y � �6

5

x �p2w2

va �

p � b

x

�47

x � �4

$Cn

� 5$ aCnb

5 � x

6a2

2

916

29n � 32n29n � 32n29n � 32n

An

swers

Answers 541541

0521681766ans_p524-579 6/6/06 4:01 AM Page 541

3 a 676 500 b 254 000c 0.006 54 d 0.000 104

Extended-response question1 a i 74 000 000 000 ii 7.4 � 1010

b 2.523 � 1017 c 8.716 � 10�7

Chapter 7

1 a 10 b 13 c 17 d 15 e 25f 41 g 50 h 30 i 25

2 a 3.61 b 2.24 c 5.68 d 0.08e 7.07 f 4.53

3 a 21.63 b 150 c 50.99 d 155.32e 1105.71 f 15.37

4 a 12.39 b 5.32 c 56 d 75.11e 2.63 f 0.58

5 3.86 6 42 7 a 10 b 11.668 a 5 b 9 a 5.66 b 5.66, 8

10 a 8.944 b 22.36 c 10, 20

1 a 9 b 8 c 40 d 21e 60 f 27 g 20 h 16 i 48

2 a 3.46 b 8.66 c 1.02 d 4.68e 0.22 f 6.23

3 a 40 cm b 1.50 m c 5.29 cmd 2.24 km e 12 cm f 16.52 mm

4 a 3.54 b 2.83 c 2.76 d 4.02e 1.03 f 1.58

5 a 13.67 b 23.81 c 406 a 3.46 b 8.66 c 1.02 d 4.68

e 0.25 f 6.23 g 6.71 h 39.75 i 30.087 x � 6.32, y � 10.20 8 a 5.10 b 4.969 a 1.58, 4.74 b 2.77, 4.16 c 2.91, 4.07

10 a i ii iiib OB � 2.6, OC � 2.79, OD � 2.96c rounding errors

1 4.4 m 2 250 m 3 35.3 m4 5.3 m 5 49 cm 6 3 m

7 495 m 8 60 m 9 2.4 m 10 5.83 m11 a 77.78 cm b 1.39 m c 0.08 m

d 43.73 cm12 42.43 cm, 66.49 cm

1 142.9 m 2 3 m 3 3823 mm4 1060 m 5 9 m 6 310.78 m7 a 6.4 m b 5.7 cm c 6.3 m d 6 m8 a b 4 cm 9 85 cm

10 a 27 m b 118.3 11 a 28.28 cmb i 80 cm ii 68.28 cm iii 48.28 cm

12 a 1.1 km b 1.1 km c 3.8 km

1 a 11.18 mm b 0.34 m c 19.75 cm2 a 3.6 cm b 2.5 m c 3.1 cm3 a 180 mm b 70 mm c 37 mm4 a 1.41 cm b 1.7 cm5 a 14.42 cm b 15 cm 6 a i 2.83 cm

ii 3.7 cm b i 7.07 cm ii 5.5 cm 7 84 m8 a i 11.82 m ii 12.15 m iii 11.56 m

iv 11.56 m

1 a i 25 ii (7n, 24n, 25n) b i 15 ii (3n, 4n, 5n)c i 41 ii (9n, 40n, 41n) d i 29 ii (20n, 21n, 29n)e i 78 ii (5n, 12n, 13n) f i 143 ii (5n, 12n, 13n)

2 a 60, (1, 60, 61) b 37, (12, 35, 37)c 145, (3, 4, 5)

3 a e.g. (10, 24, 26), (15, 36, 39), (20, 48, 52)b e.g. (16, 30, 34), (24, 45, 51), (32, 60, 68)c e.g. (14, 48, 50), (21, 72, 75), (28, 96, 100)

4

7FExercise

7EExercise

C

BA4 cm

1 cm

7DExercise

7CExercise

2627222

7BExercise

253

7AExercise

An

swer

s


Adjacent side Pythagoreanlengths Hypotenuse triad Base triad Triad family3, 4 5 (3, 4, 5) (3, 4, 5) (3n, 4n, 5n)14, 48 50 (14, 48, 50) (7, 24, 25) (7n, 24n, 25n)24, 32 40 (24, 32, 40) (3, 4, 5) (3n, 4n, 5n)8, 15 17 (8, 15, 17) (8, 15, 17) (8n, 15n, 17n)18, 80 82 (18, 80, 82) (9, 40, 41) (9n, 40n, 41n)


5 a (7, 24, 25) b (3, 4, 5) c (5, 12, 13)d (5, 12, 13) e (7, 24, 25) f (3, 4, 5)g (3, 4, 5) h (14, 48, 50) i (5, 12, 13)

6 b, c and e are Pythagorean triads7 a sides are doubled b e.g. (9, 12, 15), (12,

16, 20), (18, 24, 30) c (3n, 4n, 5n)8 15 and 36 9 They form a Pythagorean triad.

Multiple-choice questions1 B 2 A 3 A 4 C 5 B6 D 7 B 8 A 9 B 10 D

Short-answer questions1 a 8.94 cm b 35.71 cm c 4.022 a 13 b 13.933 4.49 m 4 19.365 a 4.91 m b x � 2.83 cm, h � 2.65 cm6 a 24 b (3n, 4n, 5n)

Extended-response questions1 a 2.15 m b 0.95 m c i 3.05 m ii yes2 a

b 32 km, 23.6 km, 22.8 kmc 78 km d 13 km/h

Chapter 8

1 a

b

c

2 a

b

y

x0–1

–1

1

1 2 3 4

2

3

4

–2

–3

–4

–5

–2–3–4

x �4 �2 0 2 4y 3 1 �1 �3 �5

y

x0–1

–1

1

1 2 3 4

2

3

4

–2

–3

–4

–2–3–4

x �4 �2 0 2 4y 2 1 0 �1 �2

y

x0–1

1

3

1 2 3 4

4

5

6

7

2

–1–2–3–4

x �1 0 1 2 3y �1 1 3 5 7

y

x0

–1–1

1

1 2 3 4

2

3

4

5

6

7

8

9

–2

–3

–2–3–4

x �1 0 1 2 3y �3 0 3 6 9

y

0–1–1

1

1 2 3 4

2

3

4

5

–2

–3

–2–3–4

x �1 0 1 2 3y 1 2 3 4 5

8AExercise

N

A

C

E

G

F

H

D

B

I

5

34

43

52

6

An

swers

Answers 543543

0521681766ans_p524-579 6/6/06 4:01 AM Page 543

An

swer

s


c

3 a

b

c

d

e

f

4 a y � x � 3

b y � x � 1

c y � 2x � 2

d y � 4 x � 3

x �3 �2 �1 0 1 2 3y �15 �11 �7 �3 1 5 9

x �3 �2 �1 0 1 2 3y �4 �2 0 2 4 6 8

x �3 �2 �1 0 1 2 3y �4 �3 �2 �1 0 1 2

x �3 �2 �1 0 1 2 3y 0 1 2 3 4 5 6

y

x

x

y

x

y

x

y

x

y

x

y

1

2

–2

1–1 2

3

4

–1

y

x0–1

–1

1

1 2 3 4

2

3

4

–2

–3

–4

–2–4 –3

x �4 �2 0 2 4y �1 0 1 2 3

0521681766ans_p524-579 6/6/06 4:01 AM Page 544

5 a i $25 ii $45b

6 a b

c d

e f

7 a b

c

8 a y � 4 � x b y � �2x � 1 c y � 2x � 19 a (1, 2) b

1 a b

c d

e f

g h

i j

k l

2 a b

c d

e f y

x1–2

x

y

–6

2

x

y

–6

6

x

y

–5

5

x

y

–1

2

x

y

–1

3

x

y

–4

12

x

y

–5

2

y

x–21

3

y

x

–9

3

y

x

–4

2

y

x

–32

y

x

4

2

y

x

32

y

x

3–3

y

x

–4

4

y

x

4

4

y

x1

1

8BExercise

(12, �

92)

y

x

12

2, –

32

–2,

y

x

(–2, 3)3

52,

y

x

y

x

y

x

y

x

y

x

y

x

y

x

50

40

30

20

10

54321

C

n

(5, 45)

An

swers

Answers 545545

0521681766ans_p524-579 6/6/06 4:01 AM Page 545

g h

3 a b

c d

e f

4 a 8 m b 4 seconds c

5 a b

c d

e f

g h

i

6 a b

c

7 a (0, 0) is the x- and y-interceptb Plot a point with, say, x � 1.c i ii

iii

8 a ( 0), (0, ) b ( 0), (0, c)c ( 0), (0, )

1 a b

c d

2 a b

–2

y

x2

y

x

y

x

–3

y

x

–1

y

x

5

y

x1

8CExercise

�cb

ca,

�cba ,c

bca,

x

y

1, – 34

x

y

(1, –2)

x

y

(1, 2)

x

y

12

12

8x

y

2

x

y

2

3

x

y

–103

52

x

y

5

–2.5

x

y

2

–4

x

y

–10

2

x

y

–3

4

x

y

2

–6x

y

4

3

x

y

5–3

x

y

4

8

8

4t

d

x

y

–9–6

x

y

–10–5

x

y

–4 8

x

y

–4 10

x

y

4

5x

y

6

4

y

x–3 –3

y

x2

4

An

swer

s


0521681766ans_p524-579 6/6/06 4:01 AM Page 546

c d

3 a b

c d

e f

g h

4 a 15 b 685

6 a y � �2 b y � 4 c x � �27 a y � 3 b x � 5 c x � �2

d y � 08 a y � 2x b y � �x c y � 3x9 a y � 2x b y � 3x c y � �2x

d y � �4x10 a y � 250 b y � �45

11 a b

c d

e f

g h

12 a (2, 3) b (�1, 7) c (0, �4) d (2, 0)e (0, 0) f (1, 4) g (2, �24)h (100, 10 000)

13 a (b, c) b

1 a positive, 1 b positive, 2 c zero, 0d zero, 0 e negative, f negative, g undefined h undefined i positive, j positive, 2 k negative,

l positive, 2 a 2 b 1 c d

e 2 f 2

g �1 h i j

k l3 a b 17.5 c d 7.54 variable answers5 a 4 b 8 c 2 d �8 e �0.46 a i ii

b i ii y

x

y

x

�12y

x

�15� 1

20

32

14

�52

23

12

32�1

3

32

�45

12

�34�2

3

8DExercise

m �c

b

–75

1,

x

y

(1, 4)

x

y

(1, 6)

x

y

(1, –4)

x

y

0.9

x

y

x

y

–12

x

y

–6x

y

7

x

yk e

a

h

fb

di

c

l

gj

y

x(1, –1)

y

x

(1, –4)

y

x

(1, –3)

y

x

(1, –2)

y

x(1, 1)

y

x

(1, 5)

y

x

(1, 4)

y

x

(1, 2)

–5

y

x

y

x5

An

swers

Answers 547547

0521681766ans_p524-579 6/6/06 4:01 AM Page 547

iii iv

v

c i ii iii iv v d

1 a 5, (0, �3) b �7, (0, 3) c �5, (0, �1)d (0, 6) e 2, (0, 0) f �3, (0, 0)g 0.1, (0, 0) h �8.4, (0, 0)

2

3 a b 0.5 c 3, d e 0, 2 f 0, �4 g 0, �0.7

h 0, i �4, 0 j 6, 0 k 0l 0 m �1, 7 n �3.2, 1.5 o �3, 1p �1, 0.2

4 a 1, �2, b 2, �1,

c 1, d 2,

e �3, 3, f 1,

g 0, h

5 a �1, 4, b 1, �6,

c 2, d , 3,

e , �2, f �3,

g 4, h , �4,

i , , j , 0,

k , 0, l , 0,

6 a y5 b y4 c y3 d y1 e x � 2f y2

7 a b

c d y

x3

8

y

x

–5

2

y

x(1, 2)

–1

y

x

(1, 3)2

y

x

(5, 1)

15

y

x

(2, 1)

12

y

x

(4, –1)

�14

y

x

3, 73

43

43

13

y

x

–4 (2, –3)

12

y

x

4

3

�43,

x

y

4–3

34,

x

y

3–2

23

x

y

(2, 2)3

�12

x

y

3

2

�23,

x

y

(1, 5)–6

x

y

(1, 3)4

x

y

3, 143

–13

�13,

53,

x

y

(3, –4)

�43,

x

y

(2, 4)

32,

x

y

3

1

x

y

(2, 1)2

�12,

x

y

(2, 2)1

12,

x

y

(1, 1)

–1x

y

(1, –1)–2

�,27,13

1312,��7

3,�12�1

2,

12,

8EExercise

�ba

32

13�2�1

5�13

y

x

y

x

y

x

An

swer

s


Equation Gradient, m y-intercept, cy � 2x �1 2 1y � �2x � 3 �2 3y � x � 8 1 �8y � �4x � 5 �4 �5y � 3x 3 0y � 5 0 5y � 10 � 4x 4 10y � 5 �x �1 5

0521681766ans_p524-579 6/6/06 4:01 AM Page 548

e f

g h

i j

k l

8 c, d, f, h

1 a y � x � 2 b y � x � 3c y � �2x � 4 d y � 2x � 2e y � �x � 4 f y � 8x � 8

2 a b

c y � x d y � �2x � 2 e

f � 1

3 a y � 4x � 5 b y � �2x � 2c y � 3x � 9 d y � x � 4e y � �3x � 3 f y � 7x � 7

4 a b

c y � �6x � 3 d

e f

5 a i 2 ii y � 2x � 2 b i �1 ii y � �x � 4c i �4 ii y � �4x � 10d i �1 ii y � �x � 4

6 a 3 b 6 c 6 d 1

7 a 1 b 8 c �6 d

8 a y � 5x b y � � 2

9 a 2 b i y � 2x � 2 ii y � 2xiii y � 2x � 7iv y � 2x � 17 c y � mx � e � md

1 a W � 20x � 400b c $640

d 30

2 a C � 40t � 200b c $400

d 4 hours

3 a C � 120t � 300b c $1020

d 3 hours

4 a C � 35n � 700b c $2450

d 100 guests

n

21001400

700

100

280035004200

C

t

500300

10

1000

1500

C

t

200

10

400

600

C

x

400

40

800

1200

W

8GExercise

13x

2

52

y � �143

x �73

y �53

x � 5

y �12

x � 2

y �13

x � 2y �43

x � 4

y � �13

x

y �35

x

y � �34

x � 3y �34

x � 3

8FExercise

x

y

2

3x

y

(1, 4)

8

x

y

(2, –1)

y

x(4, 3)

y

x2–1

y

x

5 (1, 4)

y

x(1, –1)

y

x

6

An

swers

Answers 549

0521681766ans_p524-579 6/6/06 4:01 AM Page 549

5 a C � 50n � 40b

c $240 d $6406 a C � 45t � 50

b

c $230d 4 hours and 20 minutes

7 a F � 18t � 17 b 3 minutesc 2.5 minutes

8 a i C � 0.4n � 20 ii 160 b i P � 0.8n � 20ii 25 iii 120

9 a

b V � 1500 � 50tc the number of litres drained per minuted 1250 L e 15 minutes

10 a C � 10x � 6700 b $8700 c 630d $11 700 e 670 f P � 10x � 6700

g T � h 1340

1 a (1, 3) b (�1, 2) c (2, 2) d nonee none f none

2 a (3, 2) b (3, 2) c (2, �4) d (2, 2)e (1, 2) f (2, 1) g (3, 7) h (2, 4)i (4, 1) j (1, 3) k (�1, �5) l (�1, 3)

3 a

b 750 4 (1200, 7200)5 a (0, 0) b (0, 0) c no intersection

d no intersections e (0, 1) f (0, 3)6 a A(0, 8), B(4, 0) b C(0, 2), D(�2, 0)

c E(2, 4) d i 16 ii 12 iii 6

1 a 5 km/h b 20 km/h c $200/dayd 40 km/L e 5 L/h f $8.5/hg 70 km/h h $4.75/item i 3.8L/h

2 a $40/h b $3/h c 40 km/hd 4 km/h e 2 L/s f 1 L/sg $20/g h 2 g/cm3 i 3 kg/m3

3 a 3 km/min b 120 km/min c 2000 mL/sd 240 mL/min e 0.5 kg/L f 2100 kg/Lg 0.5°C/s h 90°C/h i 0.2 g/mL

4 a 45 000 L/min b i 750 L/s ii 2 700 000 L/hc 64 800 000 L

5 a $26/m b 180°/h c 50 m/sd 3840 revs/min e $14/m3 f 72 g/cm3

6 a 2 g/cm3 b 10 kg/L c 0.5 g/cm3

d 0.5 kg/L7 a 0.6 km/h b 10 m/s c 5 g/s

d 0.2 kg/s e 30 kg/L f 10 cents/sg 500 m/s h $720/h i 36 km/h

1 a 12 km b i 0 km ii 6 kmc i 6 km/h ii 0 km/h d 2.4 km/h

2 a 2 b i 6 km ii 0 km iii 12 km iv 0 kmv 16 km vi 6 km c i 6 km/h ii 0 km/hiii 12 km/h iv 0 km/h v 32 km/h vi 12 km/hd 7.00 am to 8.00 am e 10.00 am to 10.30 amf 40 km g 4 hours h 10 km/h i 13.3 km/h

3 a B b C c A d i 12 km/hii 10 km/h iii 3 km/h

4 a 9.45 am b hour c 16 km/hd 3 hours e 6 km/h f 9.15 am to 9.45 amg i 10.15 am ii km/h8

3

12

8JExercise

8IExercise

5000(750, 3750)

4000

3000

2000

1000

1000

C/R

n

R

C

8HExercise

10x � 6700x

1500

30

V

t

t

C

500

400

300

200

100

10

50

n40

20

1040

C

An

swer

s


0521681766ans_p524-579 6/6/06 4:01 AM Page 550

5 a b

c d

6 a b

7 a A 60 L, B 44 L, C 4 L, D 80 L, E 80 L, F 60 L,G 24 L, H 16 L, I 16 L, J 0 L

b i 8.00 am to 8.15 am ii 1.30 pm iii 6.00 amand 10.45 am iv 7.30 am and 11.30 am

c i 16 L ii 40 L iii 16 Ld i tank is filled ii rest periodse i �16 ii �40 iii 0 iv �8 v �48 vi �16

vii 0 viii �32f The rate of change of volume of fuelg 136 L h 1496 km i $170

Multiple-choice questions1 C 2 B 3 E 4 C 5 A6 D 7 C 8 C 9 B 10 A

Short-answer questions1

2 a b

3 a b

c d

e

4 a b 1 c 5 a b �5

6 a 1, (0, �3) b 3, (0, 3)c �1, (0, �2) d (0, 2)

7 a y � �x � 2 b y � x � 3 c y � 2x � 48 a T � 40t � 60 b $220 c 6.5 hours9 a 20 km/min b 100 km/h c 8 m/s

d 1200 revs/min e 32 km/L f $1.70/m10 a 7.30 am to 7.45 am b 8.15 am to 8.45 am

c 7.45 am to 8.15 am d 4 km e 0 km/hf 8 km/h g 0 km/h h 2.4 km/hi 9 km j 3 hours k 3 km/h

11 a (1, �1) b no intersection point

Extended-response questions1 a i $12 000 ii $14 000

b i F � 0.03p ii F � 0.02p � 6000c i $27 000 ii $24 000d

e p � 600 000, F � 18 0002 a

b Walker C c 5.125 km/h d 0.7 km/he 6.8 km/h

Distance (km)

80

(6, 30)

(7, 30)

(13, 52)

(12, 52)

(16, 82)

60

40

20

2 4 6 8 10 12 14 16 Time (hours)

F($)

30000

20000

100006000

500000 1000000P($)

23,

23�1

232

x

y

(2, –3)

x

y

(2, 3)

x

y

(1, 7)

x

y

–6x

y

4

x

y

5

2.5x

y

5

–2

y

x1

4

–4

–8–12

–14

8

12

–1–2 2

x �2 �1 0 1 2y �14 �8 �2 4 10

Distance (m)

160

120

80

40

56 8 11

10 15 Time (s)

Distance (km)

90

60

30

1 2 3 Time (hours)

(3, 70)

Time (s)

600

30

Distance (m)

Time (min)

400

200

21

Distance (m)

Time (hours)

(3, 250)300

200

100

321

Distance (km)

Time (hours)

(2.5, 40)40

20

321

Distance (km) An

swers

Answers 551

0521681766ans_p524-579 6/6/06 4:01 AM Page 551

Chapter 9

1 a i ii 0.2 iii 20% b

2 a i ii 0.25 iii 25% b3

4 variable answers5 variable answers6 0.15, 1 in 4, 0.28, 2 in 3, 0.7, 0.97 a Hayley 0.31; Roger 0.25; Rosemary 0.33;

Rino 0.33; Alicia 0.27b Roger c at least 15

8 variable answers

37,

25,

13,

29,

0 0.25 0.5 0.75 1

14

0 0.2 0.4 0.6 0.8 1

15

9AExercise

An

swer

s


Percentage Decimal Fraction Number linea 50% 0.5

b 25% 0.25

c 75% 0.75

d 20% 0.2

e 60% 0.6

f 85% 0.85 0 0.85 11720

0 0.2 0.60.4 0.8 135

0 0.2 0.60.4 0.8 115

0 0.25 0.5 0.75 134

0 0.25 0.5 0.75 114

0 0.5 112

1 a 0.6 b 0.6 2 a 0.375 b 0.3753 a

b 0.77 4 a b 0.4 c5 a 0, 0.4, 0.6, 0.65, 0.64, 0.6

b

c 0.6 d 0.66 3 blue, 2 red, 4 green, 1 yellow7 2 strawberry, 3 caramel, 2 coconut, 4 nut, 1 mint

1 a i {1, 2, 3, 4, 5, 6, 7} ii iii ivb i {2, 2, 6, 7} ii iii iv

c i {1, 2, 2, 2, 2, 3} ii iii ivd i {1, 1, 2, 2, 3, 3} ii iii ive i {1, 1, 2, 3, 3, 4, 4} ii iii ivf i {2, 2, 2, 2} ii 1 iii 0 iv 1

2 a b c d e 1 f 0

3 a b c d e 0 f 1

4 a b5 a b c d e f6 a {Sharon, Alisa, Rocco, Stuart}

b i ii iii7 a b c d e f 1

g 0 h i89 a b c d e f

g h10 a b c d e f 1

g h11 a b c d e f

g h12 a 31 minutes b

c i ii iii iv v vi

1 a

b c 14

116

9DExercise

1131

831

531

2031

431

431

331

512

712

512

712

712

512

34

14

12

13

12

13

56

16

16

2526

2326

1213

213

126

12

113

152

125

34

14

58

38

38

14

18

12

12

14

35

45

45

25

15

15

78

18

34

56

58

12

14

16

38

12

37

67

17

23

23

13

56

13

23

12

12

12

27

67

17

9CExercise

Exp

erim

enta

l pro

babi

lity

Number of trials

0.5

10

(1, 0)

20

1

50 100

1475

115

Exp

erim

enta

l pro

babi

lity

Number of throws

0.5

10

(1, 0)

20

1

50 100

9BExercise

Die 11 2 3 4

1 (1, 1) (2, 1) (3, 1) (4, 1)2 (1, 2) (2, 2) (3, 2) (4, 2)3 (1, 3) (2, 3) (3, 3) (4, 3)4 (1, 4) (2, 4) (3, 4) (4, 4)

Die

2

0521681766ans_p524-579 6/6/06 4:01 AM Page 552

2 a b c d3 a

b 36 c i ii iii iv

4 a b 6 c i ii iii

5 a b 12 c i iiiii

6 a

b i ii iii iv v

7 a

b i ii iii c i ii8 a i ii iii iv v vi

vii b 7, 9 7, 8, 9, 10, 11

10 a b c d e

11 a b

1 a

b 4 c i ii iii iv

2 a

b 9 c i ii iii iv

3 a

b i ii iii iv v

4 a

b i ii iii5 a b c d6 a b c d e7 a b c d e 15

161116

516

116

116

116

14

38

14

116

827

127

29

49

12

38

18

Person 1 Person 2 Person 3 Outcome

O

OO, O, O

O, O, N

O, N, O

O, N, N

N, O, O

N, O, N

N, N, O

N, N, N

N

N

O

N

O

N

O

N

O

N

O

N

78

18

12

38

18

Toss 1 Toss 2 Toss 3 Outcome

HH

H, H, H

H, H, TH, T, H

H, T, TT, H, H

T, H, TT, T, H

T, T, T

T

T

H

TH

T

H

T

H

TH

T

49

89

59

19

Spin 1 Spin 2 Outcome

1

2

12

1, 11, 2

2, 1

3, 13, 23, 3

2, 22, 3

1, 33

3

123

123

34

34

12

14

Toss 1 Toss 2 Outcome

HH H, H

H, T

T, H

T, T

T

TH

T

9EExercise

120

125

231250

492500

11250

150

12500

16

16

16

512

712

112

112

136

125

825

45

15

125

1316

316

38

316

116

12

12

13

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

( , )

A

B

12

12

13

( , )

( , )

( , )

( , )

( , )

( , )

A

B

59

112

16

136

34

34

18

18 An

swers

Answers 553

Die 11 2 3 4 5 6

1 (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)2 (1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)3 (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)4 (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)5 (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)6 (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

Die

2

Toss 11 2 3 4

1 2 3 4 52 3 4 5 63 4 5 6 74 5 6 7 8

Toss 2

Guess 1

A B C D E

A (A, A) (B, A) (C, A) (D, A) (E, A)B (A, B) (B, B) (C, B) (D, B) (E, B)C (A, C) (B, C) (C, C) (D, C) (E, C)D (A, D) (B, D) (C, D) (D, D) (E, D)E (A, E) (B, E) (C, E) (D, E) (E, E)

Gue

ss 2

0521681766ans_p524-579 6/6/06 4:01 AM Page 553

8 a

b 12 c i ii iii iv v

9 a b c d e

f 0 g h i j10 yes

1 a i {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}ii A � {1, 3, 5, 7, 9} iii B � {2, 3, 5, 7}

b

c i {3, 5, 7} ii {1, 2, 3, 5, 7, 9}iii {2, 4, 6, 8, 10} iv {1, 4, 6, 8, 9, 10}

d i 5 ii iii 3 iv

2 a

b i {6, 12, 18} ii {3, 6, 9, 12, 15, 18}iii {1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20}iv {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16,

17, 19, 20}c i 6 ii iii 3 iv v 6 vi

3 a i F ii T iii F iv F v T vi F vii T viii Fb i ii iii 0

4 a i odd numbers less than 12ii multiples of 3 up to 12

b i ii iii iv v vi vii

5 a b

c d

6 a i {Fred, Rick, Rachel} ii {Fred, Rachel,Helen} iii { } iv {Fred, Rachel}

b i ii iii 0 iv 1 v vi 17 a 26 b 5 c 3 d e f g8 a i {2, 3, 5, 7, 11, 13, 17, 19} ii {1, 2, 3, 4, 6,

12} iii {2, 3} iv {1, 2, 3, 4, 5, 6, 7, 11, 12,13, 17, 19} v {1, 4, 6, 12} vi {5, 7, 11, 13,17, 19} vii {1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15,16, 18, 20} viii {2, 3, 5, 7, 8, 9, 10, 11, 13,14, 15, 16, 17, 18, 19, 20}

b i ii iii iv v vi viic they are equal

1 a i ii b $100 2 a i ii b $5253 4 : 1, 3 : 1, 7 : 3, 2 : 1, 3 : 2, 3 : 4, 2 : 5, 1 : 34 a $45 b $22.5 c $25 d $52.50

e $47.505 a B b i $53.33 ii $486 a Air runner b $106.677 a B b $10 profit8 a 0.6 b $7.33 profit

9 a i ii b i ii

c i 6 ii 3 iii 5

10 a i ii

b i a � b ii a � bc i 2a � b ii a � 2bd i 4a � 3b ii 3a � 4b

Answers depend on simulation results.

Multiple-choice questions1 C 2 B 3 E 4 B 5 D6 D 7 E

Short-answer questions1 a i ii 0.5

iii

b i ii 0.2 iii 0 0.2 1

15

0 0.5 1

12

9HExercise

b

a � b

a

a � b

58

38

a

3 � a

33 � a

57

27

45

15

9GExercise

25

910

910

45

25

15

110

513

326

2126

526

12

14

34

A BA B

A BA B

16

13

13

23

16

12

12

12

12

310

320

310

A

3

9 15

19

2

20

4 5

7

11

8

13

10

14 16

6

1812

17

1

B

310

12

A

1

9

4 6 8 10

3

57

2

B

�

9FExercise

1718

19

23

19

12

718

718

19

19

23

14

12

13

112

To A To B To C

Bike

Train

Train

Bike

Train

Car

Bike

Train

Car

Bike

Train

Car

Bike

Train

Car

Bike

Train

Car

An

swer

s


0521681766ans_p524-579 6/9/06 11:30 AM Page 554

c i ii 0.95 iii

2 a i 0.6 ii 0.5 iii 0.4 iv 0.525b 0.525 c 50%

3 a b c d e4 a

b5 a

b i ii iii6 a i ii b $133.337 a b i {2}

ii {1, 4, 6, 8, 9, 10}c i 5 ii 8iii iv

8 Check by running the program.

Extended-response questions1 a i {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

ii {4, 8, 12, 16, 20}iii {2, 3, 5, 7, 11, 13, 17, 19}

b i ii iii c i ii iiid i $2.50 ii $2.50 iii $1.50 e i ii iii 0

2 a i 0.09 ii 50 b i (H, 4) ii (T, 4)iii (H, 1) or (T, 5)

c

d i ii iiie i ii iii iv 1 v

Chapter 10

1 a b

c d

e f

g

2 a 5 b 4 c 3 d 3 e 43 a b c d e 1

f g h4 a b

c d

5 a b , , c , ,

6 a b c d ef

7 a i ii iii iv v vi

b i equal ii equal8 a 20 mm, 21 mm, 29 mm b i ii

iii iv v vi9 a i 5 ii , b i 25 ii , ,

c i 15 ii , d i 10 ii , , 43

35

45

34

45

35,

724

2425

725

34

45

35,

2029

2120

2129

2021

2029

2129

2312

232

123

232

12

43

45

34

35

35

45

125

513

1213

125

513

1213

34

45,

35,

H

O

θθ

O H

θ

O H

θ

H O

2y3x

x2y

45

mn

67

12

35

H

A

O

θ

H

AO

θH

O

A

θ

H A

O

θH

A

O

θ

H

A

O

θ

H

A

O

θ

10AExercise

56

112

23

112

112

16

112

120

14

35

34

12

25

14

12

110

12

A

46

10

8

1 9

7

5

3

2

B

58

38

12

38

18

Question1

Question2

Question3

Outcomes

T, T, T

T, T, F

T, F, T

T, F, F

F, T, T

F, T, F

F, F, T

F, F, F

T

T

F

F

T

FT

F

T

F

T

F

T

F

29

813

513

613

313

113

0 0.5

0.95

1

1920 An

swers

Answers 555

Jelly bean 1Black (b) Red (r) Green (g)

Black (b) (b, b) (r, b) (g, b)Red (r) (b, r) (r, r) (g, r)

Green (g) (b, g) (r, g) (g, g)Jelly

bea

n 2

Die1 2 3 4 5 6

H(5) 6 7 8 9 10 11T(1) 2 3 4 5 6 7

Coin

0521681766ans_p524-579 6/6/06 4:01 AM Page 555

10 a b 8 units c , ,

11 a b 3 c , ,

12 a , b i ii

iii

13 a 8 b , , c , ,

1 a 1.03 b 5.12 c 95.41 d 8.91e 2.48 f 11.61 g 3.95 h 0.40 i 3.67

2 a 0.39 b 1.36 c 3.83 d 1.62e 5.95 f 8.40 g 13.38 h 29.00i 17.62 j 40.10 k 9.75 l 8.5m 5.48 n 4.23 o 1.01 p 1.34

3 a 12.59 m b 5.31 m c 3.25 m 4 0.675 44.99 6 10.11 7 7.368 a 10.80 b 16.1 c 56.2, 129.69 a 1 b 3.46 c 4

1 a 2.44 b 6.61 c 25.72 d 4.18e 0.85 f 85.96 g 27.82 h 5.89 i 6.43

2 a 13.45 b 16.50 c 57.90 d 26.33e 15.53 f 38.12 g 47.02 h 49.81i 28.70 j 21.75 k 32.56 l 9.15

3 a x � 7.5, y � 6.4 b a � 7.5, b � 10.3c a � 6.9, b � 8.0 d x � 9.5, y � 12.4e x � 12.4, y � 9.2 f x � 21.1, y � 18.8g m � 56.9, n � 58.2h x � 15.4, y � 6.0

4 17.4 m 5 40 m 6 3848 m7 a 26 m b 97 m 8 41.05 m9 a 17.26 m

b height is increased or decreased by 0.3 mc height is increased or decreased by 0.3 m

10 a 4 b i 8 ii 2 c i 2.31 ii 7.73

1 a 30° b 60° c 45° d 30°e 45° f 60° g 0 h 40°

i 90° j 40° k 90° l 70°m 6° n 10° o 63°

2 a 44° b 12° c 41° d 25°e 48° f 4° g 79° h 10° i 45°

3 a 36.87° b 8.21° c 61.04° d 60°e 36.87° f 38.94° g 33.69°h 59.04° i 84.29°

4 a 67° b 51°5 a sin b sin c cos d tan 6 a 47° b 49° c 67° d 16°

e 73° f 50° g 49° h 41°7 17° 8 18.43° 9 23.13°

10 25.4° 11 26.6° 12 4.61°13 a 45° b i 30°, 150� ii 60°, 60°, 300° iii 45°, 225°14 a AB � 9.6, �

b PR � 9.7,

1 2.45 m 2 53.46 m 3 4.54 m4 25 m 5 32 m 6 15 cm7 7.145 m 8 45 m 9 24°

10 30° 11 a 23.2° b 15.2 m12 a 6° b 209 m 13 yes, by 244.8 m14 4634 mm 15 15°, 4319 mm 16 4541 mm17 22,138 18 295 cm19 a i 47.5 km ii 16.25 km b no

c yes20 a yes, 3.22 km b 12.42 m c no

1 29 m 2 180 m 3 45 m4 16 m 5 262 m 6 38 m7 90 m 8 0.9 m 9 37°

10 53° 11 6° 12 10°13 a 1312 m b 236.16 km/h14 a i 291 m ii 266 m b i 76 m ii 190 m

1 a i N32° E ii 032° T b i S 35° E ii 145° Tc i S70°W ii 250° T d i N52° W ii 308° T

2 a i 40° T ii 220° T b i 142° T ii 322° Tc i 210° T ii 030° T d i 288° T ii 108° T

3 3.28 km 4 59.45 km 5 3.4 km6 11 km 7 a 39 km b 320° T8 a 11 km b 070° T9 a 2599 m b 160° T

10 a 592 km b 463 km 11 310 km12 4 km 13 6743 m14 a 620 km b 606 km c 158 km15 a i 115 km ii 96 km b 184 km

c i 68 km ii 39.5 min

10GExercise

10FExercise

10EExercise

�P � 37.3��O � 52.7�,�B � 40.3�A � 49.7�,

10DExercise

10CExercise

10BExercise

43

35

45

34

45

35

122

122,

23232

,123

232

,34

35

43

35

45

θ

4A B

C

5

158

817

1517

θ15

17

An

swer

s



1 a x � 4.25, y � 7.41 b x � 4.89, y � 13.05c x � 10.80, y � 14.86

2 a AC � 15.89, BC � 25.81b AC � 18.67, BC � 6.78c AC � 9.00, BC � 7.28

3 a 3.1 m b 5.9 m45 a AB � 42, AT � 87 m b 45 m6 a 19.7 m b 32.7 m 7 42.42 km8 78 m 9 18 m 10 a 45 km b 67 km

11 a 7.5 km b 20.7 km c 42.8 km12 a 90° b 5.7 km c 4.0 km d 3.3 km13 a 69.3 km b 80 m14 a 6 m b no 15 46.39 km16 a i 64.95 km, 10.42 km

ii 37.5 km, 59.09 km b no

Multiple-choice questions1 C 2 B 3 C 4 A 5 A6 D 7 C 8 A 9 B 10 A

Short-answer questions1 a 0.64 b 2.25 c 0.722 a 11.33 b 48.02 c 50.713 5.0 m 4 28.01 m 5 25 m6 a 59.45 b 53.537 177.91 m 8 36.87 9 63.2 m

10 5.3 m 11 a 52.5 b 13.59

Extended-response questions1 a

b 470 m c 3° d 1530 m2 a 35 km b 398.9 km

Chapter 11

1 a i x � 0 ii minimum iii (0, 0)b i x � 0 ii minimum iii (0, �4)c i x � 2 ii minimum iii (2, �1)d i x � 3 ii minimum iii (3, �1)e i x � 0 ii maximum iii (0, 2)f i x � �2 ii maximum iii (�2, �1)g i x � 0 ii maximum iii (0, 0)

h i x � �1 ii maximum iii (�1, 6)i i x � �3 ii minimum iii (�3, 2)

2 a i x � 2 ii (2, �1) iii minimumiv (1, 0), (3, 0) v (0, 3)

b i x � 0 ii (0, �4) iii minimumiv (�2, 0), (2, 0) v (0, �4)

c i x � 0 ii (0, 3) iii maximum iv (�1, 0), (1, 0)v (0, 3)

d i x � 0 ii (0, 4) iii maximum iv (�2, 0), (2, 0)v (0, 4)

e i x � 2 ii (2, �1) iii minimum iv (1, 0), (3, 0)v (0, 3) f i x � �1 ii (�1, 7) iii maximumiv (�4, 0), (2, 0) v (0, 6)

3 a i 1 s, 3 s ii one time is on the way up and theother on the way down

b i 2 s ii 12 m iii 4 s4 a 100 m b 155 m c 5 s

d journey down takes 1 s longer

1 a

b

x

y

1

1

4

8

12

2–2 –1

y = 3x2

y = x2

y = x213

x �2 �1 0 1 2

y 0

x �2 �1 0 1 2y 12 3 0 3 12

x �2 �1 0 1 2y 4 1 0 1 4

11BExercise

11AExercise

100 m

12°

12°

PB � 47.83PO � 32.01,

10HExercise An

swers

Answers 557

43

43

13

13

0521681766ans_p524-579 6/6/06 4:01 AM Page 557

An

swer

s


14

14

45

15

15

45

Axis ofsymmetry Turning point x-intercept y-intercept

y � x2 x � 0 (0, 0) (0, 0) (0, 0)y � 3x2 x � 0 (0, 0) (0, 0) (0, 0)

x � 0 (0, 0) (0, 0) (0, 0)y �13

x2

�12 �1

2

c

d i narrower ii wider2 a i

ii

iii axis of symmetry: x � 0; turning point: (0, 0); x- and y-intercept: (0, 0) iv narrower

b i

iii axis of symmetry: x � 0; turning point: (0, 0); x- and y-intercept: (0, 0) iv narrower

c i

iii axis of symmetry: x � 0; turning point: (0, 0); x- and y-intercept: (0, 0) iv wider

d i

iii axis of symmetry: x � 0; turning point: (0, 0); x- and y-intercept: (0, 0) iv wider

3 a i

ii

iii axis of symmetry: x � 0; turning point: (0, 0); x- and y-intercept: (0, 0)

iv dilated by a factor of 2 in the y direction andreflected in the x-axis

b i


iv dilated by a factor of 3 in the y direction andreflected in the x-axis

c i


iv dilated by a factor of in the y direction andreflected in the x-axis

d i

iii axis of symmetry: x � 0; turning point: (0, 0), x- and y-intercept: (0, 0)

iv dilated by a factor of in the y direction andreflected in the x-axis

4 a narrower b narrower c narrowerd wider e wider f widerg narrower h wider

5 b, c, h, i6 i d ii c iii a iv e v f vi b7 a y � 4x2 b y � 7x2 c y � x2

8 y �67

966 289x2

13

x �2 �1 0 1 2y 0

12

x �2 �1 0 1 2y �2 0 �2

x �2 �1 0 1 2y �12 �3 0 �3 �12

x

y

–4

–8

–12

y = – x213

y = – x212

y = –2x2

y = –3x2

x �2 �1 0 1 2y �8 �2 0 �2 �8

x �2 �1 0 1 2

y 0

x �2 �1 0 1 2

y 1 0 1

x �2 �1 0 1 2y 20 5 0 5 20

x

y = 4x2

y = 5x2

y

4

8

12

16

20

y = x214

y = x215

x �2 �1 0 1 2y 16 4 0 4 16

�43 �1

3 �43�1

3


1 a y � x2

y � x2 � 2

y � x2 � 2

b

c

d y � x2 � 2: y � x2 is translated 2 units upy � x2 � 2: y � x2 is translated 2 units down

2 a i

ii

iii y � x2 � 4: y � x2 is translated 4 units upy � x2 � 4: y � x2 is translated 4 units downy � x2 � 5: y � x2 is translated 5 units upy � x2 � 5: y � x2 is translated 5 units down

3 a ii all up iii noneiv

b ii all down iii noneiv

c ii two up and two down iii alliv

d ii two up and two down iii alliv

4 a i up ii no iii (0, 5) b i down ii noiii (0, �7) c i up ii no iii (0, 8)d i up ii yes iii (0, 3.6)e i up ii no iii (0, 7.2)f i down ii yes iii (0, �0.02)

5 a y � x2 � 4 b y � �x2 � 3c y � x2 � 3 d y � 4 � x2

e y � x2 � 4 f y � �x2 � 3

Axis ofsymmetry Turning point y-intercept

y � 3 � x2 x � 0 (0, 3) (0, 3)y � 4 � x2 x � 0 (0, 4) (0, 4)y � �3 � x2 x � 0 (0, �3) (0, �3)y � �4 � x2 x � 0 (0, �4) (0, �4)


y � �x2 � 3 x � 0 (0, 3) (0, 3)y � �x2 � 4 x � 0 (0, 4) (0, 4)y � �x2 � 3 x � 0 (0, �3) (0, �3)y � �x2 � 4 x � 0 (0, �4) (0, �4)


y � x2 � 4 x � 0 (0, 4) (0, 4)y � x2 � 4 x � 0 (0, �4) (0, �4)y � x2 � 5 x � 0 (0, 5) (0, 5)y � x2 � 5 x � 0 (0, �5) (0, �5)

x

y

4

5

6

9

7

8

3

2

1

–1

–2

–3

–4

–5

0

y = x2 + 5

y = x2 + 4

y = x2

y = x2 – 4

y = x2 – 5


y � x2 � 2 x � 0 (0, 2) (0, 2)y � x2 � 2 x � 0 (0, �2) (0, �2)

x

y

4

5

6

3

2

2

1

1–1

–2

–2 –1

y =

x2 +

2y

= x2

y =

x2 –

2

0

x �2 �1 0 1 2y 2 �1 �2 �1 2

x �2 �1 0 1 2y 6 3 2 3 6

x �2 �1 0 1 2y 4 1 0 1 4

11CExercise An

swers

Answers 559


y � x2 x � 0 (0, 0) (0, 0)y � x2 � 5 x � 0 (0, �5) (0, �5)y � x2 � 6 x � 0 (0,�6) (0, �6)y � x2 � 7 x � 0 (0, �7) (0, �7)y � x2 � x � 0 (0, � ) (0,� )1

212

12


y � x2 � 5 x � 0 (0, 5) (0, 5)y � x2 � 6 x � 0 (0, 6) (0, 6)y � x2 � 7 x � 0 (0, 7) (0, 7)y � x2 � x � 0 (0, ) (0, )1

212

12


6 a y � x2 � 3 b y � x2 � 4c y � x2 � 3 d y � x2 � 5

7 a y � 2x2 � 1 b y � 2x2 � 1c y � 2x2 � 3 d y � 2x2 � 2

1 a

b axis of symmetry: x � �1; turning point:(�1, 0); x-intercept: (�1, 0); y-intercept: (0, 1)

c translation of 1 unit to the left2 a i

ii axis of symmetry: x � 2; turning point: (2, 0); x-intercept: (2, 0); y-intercept: (0, 4)

iii translation of 2 units to the rightb ii axis of symmetry: x � �2; turning point:

(�2, 0); x-intercept: (�2, 0); y-intercept:(0, 4)

iii translation of 2 units to the leftc ii axis of symmetry: x � 3; turning point:

(3, 0); x-intercept: (3, 0); y-intercept: (0, 9)iii translation of 3 unit to the rightd ii axis of symmetry: x � �3; turning point:

(�3, 0); x-intercept: (�3, 0); y-intercept: (0, 9)iii translation of 3 units to the left

3 a ii y � (x � 1)2 and y � (x � 5)2 translated left;y � (x � 4)2 and y � (x � 3)2 translated right

iii

b ii all translated right

iii

c ii all translated rightiii

4 a right b left c left d righte right f right g left h righti right

5 a ii b iv c vid i e iii f v

6 a y � (x � 3)2 b y � (x � 2)2

c y � (x � 4)2 d y � x2

7

1 a (1, 4) b (3, �5) c (3, 6)d (�1, 1) e (�2, �1) f (�3, 2)g (0, 0) h (0, 0) i (0, 0)j (0, 1) k (0, �2) l (0, 1)m (2, 0) n (3, 0) o (�1, 0)p (5, 2) q (7, 5) r (2, 7)

2 a y � (x � 1)2 � 2 b y � (x � 2)2 � 1c y � (x � 3)2 d y � �(x � 2)2 � 9e y � (x � 1)2 � 4 f y � �(x � 1)2

3 a i translated 2 units to the right and 1 unitdown

ii x � 2, (0, 3), (2, �1)iii

b i translated 1 unit to the right and 1 unit upii x � 1, (0, 2), (1, 1)

y

x

3

2

1

–12 310

11EExercise

y � �1

500(x � 100)2

y

x

4

3

1

2 431–2–4 –3 –1 0

2

y = (x + 3) 2y = (x + 2) 2 y

= (x

– 3

)2

y =

(x –

2)2

y

x

4

3

2

1

2 31–2–3 –1 0

y = x2y = (x + 1)2

11DExercise

An

swer

s



y � (x � 1)2 x � �1 (�1, 0) (0, 1)y � (x � 2)2 x � �5 (�5, 0) (0, 25)y � (x � 4)2 x � 4 (4, 0) (0, 16)y � (x � 3)2 x � 3 (3, 0) (0, 9)


y � (1 � x )2 x � 1 (1, 0) (0, 1)y � (2 � x )2 x � 2 (2, 0) (0, 4)y � (3 � x)2 x � 3 (3, 0) (0, 9)y � (4 � x)2 x � 4 (4, 0) (0, 16)


y � �(x � 1)2 x � 1 (1, 0) (0, �1)y � �(x � 2)2 x � 2 (2, 0) (0, 4)y � �(x � 3)2 x � 3 (3, 0) (0, �9)


iii

c i translated 2 units to the right and 1 unitdown

ii x � 2, (0, 3), (2, �1)iii

d i reflected in the x-axis, translated 3 units tothe left and 2 units up

ii x � �3, (0, �7), (�3, 2)iii

e i reflected in the x-axis, translated 4 unitsto the left and 3 units down

ii x � �4, (0, �19), (�4, �3)iii

f i reflected in the x-axis, translated 3 units tothe left and 1 unit up

ii x � �3, (0, �8), (�3, 1)iii

g i reflected in the x-axis, translated 2 units tothe left and 3 units up

ii x � �2, (0, �1), (�2, 3)

iii

h i reflected in the x-axis, translated 2 unitsto the right and 1 unit up

ii x � 2, (0, �3), (2, 1)iii

i i reflected in the x-axis, translated 3 units tothe right and 4 units up

ii x � 3, (0, �5), (3, 4)iii

j i translated 5 units upii x � 0, (0, 5), (0, 5)iii

k i translated 2 units to the rightii x � 2, (0, 4), (2, 0)iii

x

y

0 2 4

4

x

y

–2 –1 0 1

5

2

x

y

0

–5

4

1 2 3 4 5

x

y

1

1

2 3 4–1

–2

–3

0

x

y

–1–1

–2–3

2

3

–4

1

0

x

y

0

–8

–2–3–5 –1–4

x

y

–2 0–4

x

y

–7

–3 0

2

x

y

1 3

3

–10 2

y

x

2

1

210

An

swers

Answers 561

0521681766ans_p524-579 6/6/06 4:01 AM Page 561

l i reflected in the x-axis, translated 6 units upii x � 0, (0, 6), (0, 6)iii

4 a

b

c

d

5 a

b

c

d

x

y

2

1

21 3 4

4

3

0

y

x

2

1

–1

–2

2–2 10–1

x

y

1–1 0

5

y

x

3

–12–2 1–1 0

y

x0

1

9

y

x0

123456789iii i ii

1 2–1–2–3

y

x–1–2–2

2

0

–8

–3 2 4

–4

1 3

i

iii

ii

y

x0–1–1

–2

1

1

2

3

4

5

–2–3

i

ii

iii

–3

x

y

0

2

4

–1 1 2 3–2–3

6

An

swer

s


0521681766ans_p524-579 6/6/06 4:01 AM Page 562

e

f

g

h

i

j

k

l

m

n

x

y

5

11

20 4 6 8

(4, 5)

y

x

–2

–1–2–3–4

2

0

(–2, 2)

x

y

–1–1–2–3

1

2

3

0

(–2, –1)

x

y

1

1

–1–1

–2

–2

–3

–3(–1, –3)

0

y

x–2–3

–4

–5–6–7–8 –1

0

–2(–4, –2)

14

y

x

11

2

1–2–3–4–5–6 –1 0

(–3, 2)

y

x

5

1

–2–3–4 –1 10

(–2, 1)

y

x

1

2

–2–3 –1 10

(–1, 1)

y

x

1

–2–3 –1 0

y

x321 4 50

9

An

swers

Answers 563

0521681766ans_p524-579 6/6/06 4:01 AM Page 563

o

6 a y � �(x � 1)2 b y � �(x � 2)2

c y � (x � 2)2 d y � (x � 3)2

e y � (x � 4)2 � 1 f y � (x � 2)2 � 4g y � �(x � 1)2 � 3

7 a y � 9 � (x � 2)2, turning point (2, 9)y � (x � 7)2 � 4, turning point (7, �4)

b

1 a 0, 1 b 0, �2 c 0, 5 d 2, �1e 3, �4 f 5, 2 g 0, 3 h 0, 1i 0, �2 j �2, 1 k �2, 7 l 2, 9m �3 n �2, o � , 5 p ,

q � , r , �2 a 1 b �1 c �2 d 7

e 2 f 1 g 1 h 5i 3 j k lm n o

3 a 0, 4 b 0, 6 c 0, 5 d 0, �10e 0, �4 f 0, �12 g 0, 5 h 0, �2i 0, 7 j 0, 6 k 0, �1 l 0, �4

4 a 0, b 0, c 0, 4 d 0, �3e 0, �9 f 0, �7 g �5, 5 h 0i �1, 1 j 0, 5 k 0, 9 l 0,

5 a b c de f g h

i j k l

6 a b c d

e f g h

i7 a �1 b �3 c �5 d 2

e 4 f 3 g �4 h �7

i �9 j 6 k 11, �1 l �5, 4m 5, 10 n �5, 10 o �3, 4 p �1, �3q �1, �10 r �2, �4 s 1t �4, 2 u �3, 2

8 a 6 b 1 c 3 d 0, 7e 4 f 3 g �3, �4 h �7, 6i 0, 5 j 5, 7 k �1, 11 l �5, 4m 0, �3 n 5, 10 o �3, �6

9 a

b x2 � ( x � 1)2 � (x � 2)2

c x2 � 2x � 3 � 0 d 3, 4, 510 a A � (x � 2)(x � 3) b x2 � 5x � 14 � 0

c 5 m � 4 m

1 a i 0, �4 ii 0 b i 0, �2 ii 0c i 0, �3 ii 0 d i 5, �1 ii �5e i �2, 6 ii �12 f i �3, 7 ii �21g i �5, 1 ii 5 h i �5, �1 ii �5i i 4, 3 ii 12

2 a i y � x(x � 3) ii 0, 3iii 0 iv x � v ( , � )

vi

b i y � x(x � 1) ii 0, �1iii 0 iv x � �

v (� , � )14

12

12

y

x0 3

32

94

,

32

–

94

32

32

11GExercise

x

x + 2x + 1

; 54

; 32; 1

2;2;6

;5;4;3;2

;2;3;3; 65

; 32; 5

4;1;6;10;4;1;2

52

12

12

25

53

65

52�1

234

13

92

35

54

32

43

13

32

12,

11FExercise

x

y

1

0

2 3 4 5 6 7 8 9 10–1–2

(–2, –7)

(7, –4)

(10, 5)

(2, 9)9

5

–7

x

y

–1

2

1

10 2 3

3(1, 3)

An

swer

s


0521681766ans_p524-579 6/6/06 4:01 AM Page 564

vi

c i y � x(x � 5) ii 0, 5 iii 0iv x � v ( , � )

vi

d i y � x(2 � x) ii 0, �2iii 0 iv x � �1 v (�1, �1)vi

e i y � x(3 � x) ii 0, 3iii 0 iv x � v ( , )vi

f i y � x(5 � x) ii 0, �5iii 0 iv x � �

v (� , � )

vi

g i y � �x(x � 8) ii 0, �8iii 0 iv x � �4 v (�4, 16)vi

h i y � �x(2 � x) ii 0, �2iii 0 iv x � �1 v (�1, 1)vi

i i y � �x(x � 1) ii 0, 1iii 0 iv x � v ( , )vi y

x0 1

2

1

4

1

2

1

4,

1

14

12

12

y

x0–1

(–1, 1)

1–1

–2

1

y

x0

16

–4

(–4, 16)

–8

y

x0–5

5

2

25

4, ––

25

4–

5

2–

254

52

52

y

x0

32

94

,

94

32

32

y

x0

–1–1–2

(–1, –1)

y

x0 5

254

–52

254

, –

254

52

52

y

x–1

1

12

14

,– –

0

An

swers

Answers 565

0521681766ans_p524-579 6/6/06 4:01 AM Page 565

3 a i y � (x � 2)(x � 1) ii 1, 2iii 2 iv x � v ( , )vi

b i y � (x � 3)(x � 1) ii �3, 1iii �3 iv x � �1v (�1, �4)vi

c i y � (x � 3)(x � 1) ii 3, 1iii 3 iv x � 2 v (2, �1)vi

d i y � (x � 1)2 ii �1iii 1 iv x � 0 v (0, �1)vi

e i y � (x � 2)2 ii �2 iii 4iv x � �2 v (�2, 0)vi

f i y � (x � 4)(x � 2)ii �4, 2 iii �8iv x � �1 v (�1, �9)vi

4 a

b

c y

x0 3–3

9

x

y

0–2

4

2

x

y

–1 1–1

x

y

(–1, –9)

0–4 –1 2

–8

–9

x

y

4

–2

x

y

0

1

–1

x

y

0

3

–11 2

(2, –1)

3

y

x0–1

(–1, –4)

–3

–4

1–3

x

y

0

2

1

214

–34

,

�14

32

32

An

swer

s


0521681766ans_p524-579 6/6/06 4:01 AM Page 566

d

e

f

g

h

i

j

k y

–4

x–1 43

2

0

–32

254

,

y

x0 1 4

4

5

2

52

94

, –

y

x0 2

–4

y

x0 33

2

32

92

, –

y

x–3

4 –3

8

–3

2

– –3

4

3

8,

0

y

x0 3

–94

32

32

94

, –

y

x0–5

–52

–254

,

–254

y

x0 –2

–4

4

(–2, –4)

An

swers

Answers 567

0521681766ans_p524-579 6/6/06 4:01 AM Page 567

l

m

n

o

5 a 30 m b 5, 35 c (5, 0), (35, 0)d x � 20 e (20, 225) f (20, 225)g 15 m

h

1 a 12 m b 16 m c 6 s d 16 me

2 a 64 b 48 c 8 s d 8 s e 64 mf

3 a $800b

c 20 d 50 toys, $900

x20 50 80

900

–1600

(50, 900)

0

P

t

64

80

h

t

16

12

8

4

2 6

h

0

11HExercise

y

x5 20 35

100

200

225(20, 225)

0

x0–5

25

y

x3

3

y

y

x0–1

1

y

x3–4

–12

0

12

494

,– –

An

swer

s


0521681766ans_p524-579 6/6/06 4:01 AM Page 568

4 a $375b

c $30 d $4005 a i P � 2x � 2y ii 80 � 2x � 2y

40 � x � yy � 40 � x

b i A � xy ii A � x (40 � x )c

d i 20 ii 400 m2

6 a i P � 2x � y ii 80 � 2x � yy � 80 � 2x

b i A � xy ii A � x(80 � 2x )� 2x(40 � x )

c

d i 20 ii 800 m2

7 a y � 36 � x b A � x(36 � x)c

d 324 m2

8 a A � x(50 � x)b

c 625 m2 d 25 m � 25 m9 a x � y � 10 b P � x(10 � x )

c 5 and 510 a 30 cm, 12 cm b i s ii 3 cm

c

Multiple-choice questions1 B 2 D 3 D 4 D 5 E6 E 7 B 8 A 9 C 10 DShort-answer questions1 a i

ii

iii axis of symmetry: x � 0; turning point: (0, 0); y-intercept: (0, 0)

iv dilated by a factor of 2 in the y directionb i

ii y

x–1–2

12

1 2

2

0

x �2 �1 0 1 2y 2 0 2

y

x–1

2

1

x �2 �1 0 1 2y 8 2 0 2 8

d

t0

23

5

8

12

54

3

d = 2t2 –5t + 5

d = 2t + 2

12

x25 50

625(25, 625)

0

A

18 360

324(18, 324)

x

A

x

800

20 40

P

(20, 800)

0

x20 40

A

400(20, 400)

0

x

400

–500

10 30 50

P

(30, 400)

0

An

swers

Answers 569

12

12

0521681766ans_p524-579 6/6/06 4:01 AM Page 569

iii axis of symmetry: x � 0; turning point:(0, 0); y-intercept: (0, 0)

iv dilated by a factor of in the y directionc i

ii

iii axis of symmetry: x � 0; turning point: (0, 2); y-intercept: (0, 2)

iv translated 2 units upd i

ii

iii axis of symmetry: x � 3; turning point: (3, 0); y-intercept: (0, 9) iv translated 3 units to the right

2 a

b

c

d

3 a 5, �6 b �9, �2 c 0, 3d 0, 6 e �5, �2 f �2, 2

4 a i (0, �6) ii (�2, 0), (3, 0) iii x �

iv ( , )b i (0, 0) ii (0, 0), (4, 0) iii x � 2

iv (2, �4)c i (0, �5) ii (5, 0), (�1, 0) iii x � 2

iv (2, �9)d i (0, 8) ii (2, 0), (4, 0) iii x � 3 iv (3, �1)

5 a i (0, 0), (0, 2) ii (0, 0) iii x � 1 iv (1, �1)b y � x (x � 2)

Extended-response questions1 a 60 m b 10 s c 64 m

d

2 b $2400c

d 2 e 9 f $2450

n

P

0

–1600

(9, 2450)2450

2 9 16

x

y

0

60

(2, 64)64

2 10

�254

12

12

x

y

0

–2

3(3, –2)

–11

x

y

0

3

–1

(–1, 2)2

x

y

0

9

3

y

x–1 10

3

y

x3

9

0

x �2 �1 0 1 2y 25 16 9 4 1

y

x–1

2

10

x �2 �1 0 1 2y 6 3 2 3 6

12

An

swer

s


0521681766ans_p524-579 6/6/06 4:01 AM Page 570

Chapter 12

1 a numerical b numerical c categoricald categorical e numerical f categoricalg numerical h categorical i numericalj categorical k numerical l numericalm categorical n categorical

2 a continuous b discrete c continuousd discrete e discrete f continuousg continuous h discrete

3 a nominal b nominal c ordinald nominal e ordinal f nominalg nominal h ordinal

4 a i numerical ii continuous b i numericalii continuous

c i numerical ii discreted i categorical ii nominale i numerical ii discretef i numerical ii discreteg i numerical ii discrete

5 a i numerical ii continuousb i numerical ii continuousc i categorical ii nominald i numerical ii discretee i categorical ii ordinal

1 a D b D c D d D e S2 a Q b O c O d M e Q

f Q g Q3 a (ii), (iii)

b (iv) How much money do you spend on CDseach month?0–19 20–29 30–39 40–49 50–59

(vi) What kind of music do you like to listen to?country pop classicalrock jazz rap

4 a (vi)b (i) How many hours of TV do you watch each

day?0–2 3–5 6–8 9–11(ii) What type of program do you prefer towatch? movies sport comedysoap opera documentary/newsgame shows(v) What is your age?0–4 5–9 10–14 15–19

1 a 400 000 b Queenslandc approximately 25%

2 a 208 m b 70 m3 a

b large sedan c 10%4 a

b pop c rap d 30 e 10.71%5 a 500 b cat admissions are higher6

7 a

b one million phones c i 200%ii 100% iii 37.5%

d 6–7 million phones

050 000

100 000150 000200 000250 000300 000350 000

Num

ber

of p

eopl

e

Fes

tiva

lof

Art

sG

rand

Pri

xA

ustr

alia

nO

pen

Rac

ing

Car

niva

lA

FL

Fin

als

Roc

k

Pop

Cla

ssic

al

Cou

ntry

Har

d R

ock

Rap

010203040506070

Num

ber

of s

tude

nts

Sed

an (

larg

e)

Sed

an (

smal

l)

Wag

on

Hat

ch

4WD

Oth

er

10

Car type20

Fre

quen

cy

12CExercise

12BExercise

12AExercise

An

swers

Answers 571

Mobile subscribersTime (millions)1986 0.1March 1994 1June 1995 2Feb 1996 3Dec 1996 4Oct 1997 5July 1998 5.5

0521681766ans_p524-579 6/6/06 4:01 AM Page 571

1 a

b, c

d 8 students2 a

b, c

d 28 families3 a

b

4 a

b

c 9 d 85 a

b

c 9

14121086420

145 150 155 160 165 170 175 180

Height (cm)

Freq

uenc

yFr

eque

ncy

8

3 6 9 12Class

15 18 21

6

4

2

0

2824201612

840

Freq

uenc

y

10 20 30 40 50Class

01 2 3 4 5 6

2468

1012141618

Fre

quen

cy

Number of children in family

1

12

2 3 4

Fre

quen

cy

Number of students

Musical instrumentsplayed

12DExercise

An

swer

s


Number of instrumentsplayed Frequency

1 122 53 24 1

Number of children Frequency1 142 163 124 45 26 2

Class Frequency0–9 24

10–19 1020–29 630–39 740–49 4

Class Frequency50–59 1060–69 1570–79 1080–89 25

Number of goals Frequency1–3 34–6 87–9 8

10–12 713–15 216–18 119–21 1

Height (cm) Frequency145–149 3150–154 6155–159 3160–164 12165–169 7170–174 10175–180 1

30

25

20

15

10

5

0

Freq

uenc

y

50 60 70 80 90Class

0521681766ans_p524-579 6/6/06 4:01 AM Page 572

6 a

b

c 85.5%7 a minimum wages, $204; maximum wages, $940

b i

ii

c i

ii

1 a i

ii There is a cluster at 4–5 and no outliers.

b i

ii No defined cluster and no outliers.2 a b 9

3 a b 7

4 a i Stem Leaf

1 5 5

2 3 3 1 3 6

3 1 3 5 5 1 4 0 7 9

4 8 2 5 5 2 5

5 0 1 0

2|4 represents 24

ii Stem Leaf

1 5 5

2 1 3 3 3 6

3 0 1 1 3 4 5 5 7 9

4 2 2 5 5 5 8

5 0 0 1

2|4 represents 24

b i Stem Leaf

15 9 9 7 8 9 9

16 7 1 1 4 7 7

17 5 7 7 5 3

18 5 5 7 9 4

19 3 3 6 8

20 5 2 0 0

16|1 represents 161

10 11 12 13 14 15 16 17

15 16 17 18 19 20 21 22

37 38 39 40 41 42 43 44

1 2 3 4 5 6 7

12EExercise

Freq

uenc

y 10

5

200

300

400

500

600

700

800

900

1000100

Weekly wages ($)

Freq

uenc

y

2530

15

15

10

10

20

5

50

Length of phone call (min)

An

swers

Answers 573

Length of phonecall (minimum) Frequency

0– 285– 12

10–15 15

Weekly wages ($) Frequency200– 2300– 7400– 6500– 6600– 11700– 11800– 5900– 2

Weekly wages Frequency200– 9400– 12600– 22800– 7

1000– 0

Freq

uenc

y 20

10

200 400 600 800 1000Weekly wages ($)

0521681766ans_p524-579 6/6/06 4:01 AM Page 573

ii Stem Leaf

15 7 8 9 9 9 9

16 1 1 4 7 7 7

17 3 5 5 7 7

18 4 5 5 7 9

19 3 3 6 8

20 0 0 2 5

16|1 represents 161

5 a Stem Leaf

14* 4 4

14 6 6 7 9

15* 0 0 0 0 1 2 2 3 4 4

15 5 5 6 7 7 8 9

16* 0 0 1 1 2 2 2 3 4

16 5 5

14*|4 represents 144

b 82.35%6 a 15.4 seconds and 16.7 seconds

b 14.9 seconds and 17.2 seconds are outliers7 a 4 9 8

5 9 2 7 6 4 1 7

6 9 4 8 9 8

7 3 9 6 4 1 0 9 2

8 5 1 6 0 3 9

9 0

10

11 7

4|9 means 49 metres

4 8 9

5 1 2 4 6 7 7 9

6 4 8 8 9 9

7 0 1 2 3 4 6 9

8 0 1 3 5 6 9

9 0

10

11 7

4|9 means 49 metres

b

c 9 bridges d 117-metre bridgee 23.33% f A stem-and-leaf plot shows all

information and groups the data.

1 a i

ii Set A has values spread between 32 and 54while Set B has most of its values between40 and 53 with an outlier at 31.

b i

ii Set A has values between 1 and 50 with thefrequency decreasing as the numbersincrease whereas Set B has values between9 and 56 with the frequency increasing asthe numbers increase.

c i

ii Set A and B are similar. The frequencydecreases as the numbers increase.

2 a 48% b 15.79%3 a

10|4 represents 104

b Collingwood 79.2% and Carlton 50%c Carlton scores between 85 and 128 points per

game with an even spread of results.Collingwood scores between 89 and 136 pointswith most games between 98 and 136 points.

4 a

8|3 represents 8.3 hours

12FExercise

40 50 60 70 80 90 100 110

An

swer

s


Set A Set B

3 2 3 1

9 3

3 3 0 0 4 0 1 3 4 4

8 7 6 5 4 6 7 8 8 9 9

4 4 3 5 1 3

Set A Set B

9 8 6 4 3 2 2 1 0 9

7 7 6 1 1 0 0 1 8 9 9

9 6 4 3 3 2 2 0 1 3 4 7 8

7 6 6 5 0 3 1 7 7 8 9 9 9

8 3 1 4 0 1 1 3 4 4 5 7

0 5 0 0 1 3 3 4 4 5 6

Set A Set B

8 7 6 4 3 0 1 1 1 2 3 6 6 9 9

9 9 7 6 4 1 2 3 5 8 9

6 5 3 1 2 1 5 6

9 9 6 4 3 2 3 3 4 9

7 3 1 4 3 7 8

7 3 2 5 2 3 7

2 1 6 1 2

8 3 8 3 8

1 9

Final game scoresCollingwood Carlton

9 9 8 5 6 8 9 9

8 8 9 0 2 5 8 8 9

9 8 7 2 0 10 0 4 6 8 8

6 5 4 0 11 0 2 5 6

9 8 8 8 7 5 0 12 0 5 8 8

6 5 4 2 13

Battery lifetimeBrand A Brand B

3 7 2 3 4

7 5 6 8 9 9

4 2 8 0 1 3

9 8 7 5 8

4 4 3 2 1 0 9 0 1 2 3 4

9 9 8 7 6 5 5 9 5 6 8 8

0521681766ans_p524-579 6/6/06 4:01 AM Page 574

b Brand A, 12; Brand B, 8c Brand A consistently performs better than

Brand B.5 a

b Maths is spread between 45% and 100%.English is spread between 48% and 100%

c i 15 students ii 12 studentsd The spread of the results over maths and

English is nearly the same but Englishstudents have generally higher results.

1 a 7, 9, 5 b 6, 6, 7 c 22.28, –, 30d 54.12, 63, 34 e 7.01, 6.4, 4.4f 18.14, 18.6, 18.9 g 52.23, –, 65.8h 266.5, 234, 423

2 34.67 seconds 3 a 168 cm b 12 cm4 a 15 b 5 c 265 a 88 b 706 9 7 a � b � c � d � 40

8 a player A: mean

range � 5

player B: mean

range � 10 b player B

c player B, mean

range � 29 a mean � 970.1 mg b yes; 762.2 mg

c mean � 981.0 mg d The second meanfits the majority of the values.

1 a i 7 ii 7 b i 26.5 ii 10 c i 15.15 ii 19d i 24.13 ii 25 e i 33.95 ii 32f i 3.96 ii 4.2

2 a

mean � 12.32, modal class = 8�10

b

mean � 74.96, modal class = 80�893 a 175– b 1754 a 4– b 4.925 a 160– b 170.49

1 a i 0, 1, 2, 3, 5, 5, 6, 7, 8, 9, 11 ii 5iii 2 iv 8 v 6

b i 183, 197, 219, 228, 253, 316, 346 ii 228iii 197 iv 316 v 119

c i 18, 21, 26, 27, 29, 30, 36, 37, 38, 41ii 29.5 iii 26 iv 37 v 11

d i 0.8, 0.9, 1.2, 1.2, 1.3, 1.7, 1.8, 1.9, 2.1ii 1.3 iii 1.05 iv 1.85 v 0.8

e i 3, 12, 23, 28, 28, 43, 51, 64, 76, 163, 186,256, 343, 367, 520, 787, 854ii 76 iii 28 iv 355 v 327

f i 0.02, 0.1, 2.3, 10, 12, 23ii 10 iii 0.1 iv 23 v 22.9

2 a i 119.5 min ii 106 min iii 130 min iv 24 minb The middle 50% of videos rented varied in

length by 24 min.3 a i $12 000 ii $547 000 iii $71 500

iv $41 000 v $89 000 vi $48 000b The middle 50% of prices differs by less

than $48 000.c No effect on Q1, Q2 or Q3 but the mean

would increase.4 a i

iib 27 boiled lollies c 22 boiled lolliesd i iie Shop B is less consistent than shop A.f Shop A

1 a i 2 ii 15 iii 8 iv 4 v 11vi

b i 10 ii 88 iii 43 iv 34 v 56

x2

2

4 6 8

8

10 12 14 16

13115

12JExercise

IQR � 5IQR � 2

Q3 � 27Q2 � 24.5;Q1 � 22;Q3 � 27Q2 � 26;Q1 � 25;

12IExercise

12HExercise

�544

� 13.5

�575

� 11.4

�575

� 11.4

12GExercise

An

swers

Answers 575

Maths English

5 4 8

5 2 5 5

9 8 8 5 4 6 5 6 8

9 8 8 5 2 7 5 6 8

5 2 0 8 4 5 6 8

4 0 9 0 2 4 5 6

0 0 10 0 0 0

f x xf8 9 725 12 603 15 452 18 361 21 21

f x xf7 54.5 381.58 64.5 516

10 74.5 74512 84.5 10146 94.5 567

0521681766ans_p524-579 6/6/06 4:01 AM Page 575

vi

c i 244 ii 933 iii 435 iv 255 v 674vi

d i 0.1 ii 1.3 iii 0.6 iv 0.4 v 0.95vi

2 a

b i 100% ii 50% iii 75% iv 25%3 a

b

c

d

e

4 a i 12, 115 ii 83, 99, 109 iii 26b 12, Monday week 3 c road worksd

5 a mean � 14; b Set B; range � 9c i IQR � 4 ii IQR � 5 d Set B has a wider

range and higher IQR.

Multiple-choice questions1 C 2 D 3 A 4 C 5 B6 B 7 C 8 A 9 D 10 D

Short-answers questions1 a i 28.5 ii 27.5 iii 31.5 iv 4

b i 16 ii 14 iii 25 iv 11c i 0.6 ii 0.4 iii 1.3 iv 0.9

2 a

b 5 days3 a Stem Leaf

24 4 4 6 6 7 9

25 0 0 0 0 1 2 2 3 4 4 5 5 6 7 7 8 9

26 0 0 1 1 2 2 2 3 4 5 5

b 82.35%4 a 17.4,10 b 14.80,10�14

Extended-response questions1 a

b, c

d 6 customers e 72% f 2.04, 2, 12 a Stem Leaf

0 1 1 2 3 3 6 9

1 0 0 1 1 8

2 5 6 6 9

3 2 3 4 5 8 9

4 2 2 5 7 9 9 9 9

b

20

10

21 3 4 5Number of movies watched

Number of people

Freq

uenc

y

1 2 3 4 5 6 7

Q3 � 17

x0 20 40 60 80 100 120

12 71 83 99 109 115

x0 0.5

0.5

1.0 1.5 2.0 2.5

1.61.7 1.9 2.0 2.2

x30 40 50 60 70 80 90

32 53 61 7378 86

x80 90 100 110 120 130

83 89 94 103111 126

x7

7.3

8 9 10

8.5

11 12 13

12.38.1 9.6

x2

2

4 6 8

8

10 12 14

14105

x0 10 20 30 40 50

0.1 1.3

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0.4 0.6 0.95

x

244 255 933

200 300 400 500 600 700 800 900 1000

435 674

x

10 88

10 20 30 40 50 60 70 80 90

34 43 56

x

An

swer

s


Number of movies Frequency1 202 163 84 45 2

Class interval Frequency0– 7

10– 520– 430– 640–50 8

0521681766ans_p524-579 6/6/06 4:01 AM Page 576

c, d

e 40–50

Cyclic revision BChapter 7

Multiple-choice questions1 A 2 B 3 A 4 D 5 B

Short-answer questions1 72.11 km 2 4.133 a 15.9 m b 18.2 cm

Extended-response questions1 a i 12.42 km ii 28.45 km

b P to L to S by 16.03 km c 2.5 h, 5.7 h

Chapter 8

Multiple-choice questions1 C 2 A 3 D 4 C 5 A

Short-answer questions

1 a b (0, 3)

c

2 a b

c (11, 0), (0,

3 a i 40 km/h ii 32 km/hb i 28 km/h ii 37.33 km/h c 336 km

Extended-response question1 a i C � 40t � 102 ii C � 52t

b

c t � 8.5 d Job 1, Landscape Plus; Job 2,Beautiful Backyards

Chapter 9

Multiple-choice questions1 C 2 C 3 A 4 B 5 E

Short-answer questions1 a b c d2 a b $50 c increases 3 a 6 b i ii iii iv v

Extended-response question1 a

There are 8 outcomes.b i ii iii c d

Chapter 10

Multiple-choice questions1 D 2 B 3 D 4 D 5 B

Short-answer questions1 a 35.94 b 6.15 c 2.552 145° 3 758 m

Extended-response question1 a 17.75 m b 14.35° c i 18.22 m ii 5.47 s

Chapter 11

Multiple-choice questions1 D 2 E 3 B 4 B 5 C

Short-answer questions1 a y

x

3

1—1 0

2

78

12

12

38

18

N

NN

F

F

F

N

F

N

F

N

F

N

F

N, N, N

N, N, F

N, F, N

N, F, F

F, N, N

F, N, F

F, F, N

F, F, F

Person 3 OutcomePerson 2Person 1

23

23

12

12

16

380

110

23

59

49

19

1000

500

102

2010

C ($)

t (hours)

(20, 1040)(20, 902)

112 )

y � �12x � 11

2�12

x

y

3

6

�12,y � �1

2x � 3

10

5

2010 30 40 50

Freq

uenc

y An

swers

Answers 577

0521681766ans_p524-579 6/6/06 4:01 AM Page 577

b

c

d

2 a 0, �6 b �3, 2 c 0, 3d 0, 5 e �4, 2 f 4, �4

3 a i (�4, 0), (2, 0), (0, �8) ii x � �1iii (�1, �9)

b i (0, 0), (6, 0) ii x � 6 iii (3, �9)c i (�4, 0), (3, 0), (0, �12) ii

iii (d i (3, 0), (0, 9) ii x � 3 iii (3, 0)

Extended-response question1 a 50 m b 5 s c 10 s d 2 s or 8 s

e

Chapter 12

Multiple-choice questions1 C 2 C 3 A 4 B 5 E

Short-answer questions1 a

b 14%2 a Stem Leaf

1 6 8 8 8 9

2 0 0 0 4 7 8

3 0 2 2 4 5 6 8

4 8

1|9 represents 19

b outlier is 48, main cluster 18–203 a

b 40–50 c 45% d 28.5

Extended-response questions1 a discrete

b

c

d 57.5% e 10% f mode � 2; range � 5g 3 h 44; it is impossible

15

10

5

0

No. of wickets

Fre

qu

ency

Wickets taken

1 2 3 4 5 6

40

30

20

10

00–9 10–19 20–29 30–39 40–49

Score

Fre

quen

cy

Class scores

10 10

25

35

20

20

15

10

5

0

No.

of

stud

ents

Leisure activities

music

TVvid

eoco

mp.

games

Activities

12

17

6 78

readin

g

50

1050x

y

�494 )�1

2,x � �1

2

y

x

7

3

2 310

y

x

5

1

–2

(–2, 1)

–1 0

y

x1

1

0

An

swer

s


No. of wickets Tally Frequency1 |||| 42 |||| |||| ||| 133 |||| |||| | 114 |||| 55 |||| 56 || 2

0521681766ans_p524-579 6/6/06 4:01 AM Page 578

2 a discreteb Stem Leaf

0 6 7 7 8 9

1 0 1 2 4 5 5 6 7 8 8 8 9

2 0 0 1 1 2 4 4 6 6 7 7 7 8 9

3 0 2 2 3 5 6 7 8 8 9

4 0 1 2 2 3 3

5 2 4

6 3

3|2 represent 32

c 57d

e

f 20–29 g 26.5 h 48% i 22%

15

10

5

0

Fre

quen

cy

0–9

10–1

9

20–2

9

30–3

9

40–4

9

50–5

9

60–6

9

Spectator age

Age

An

swers

Answers 579

Group Tally Frequency0–9 |||| 5

10–19 |||| |||| ||| 1220–29 |||| |||| |||| 1430–39 |||| |||| 1040–49 |||| | 650–59 || 260–69 | 1

0521681766ans_p524-579 6/6/06 4:01 AM Page 579

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