17 ANSWERS BK8.QXD 12/6/07 16:19 Page 187 Answers to ... · PDF fileGraduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007 187 Answers to Homework Book 8 ... OCR GCSE

Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007 187

Answers to Homework Book 8

STAGE

8

1 Fractions

Exercise 1.1H (page 1)1 a) 1 b) 1

c) 3 d) 7

e) 2

2 a) 2 b) 2

c) 2 d) 2

e) 1

3 a) 9 b) 1

c) 2 d) 7

e) 5 f) 9

g) 8 h)

4 a) 4 b) 7

5 13 m

6 5 cut off, 4 left, not enough

Exercise 1.2H (page 2)1 a) b) 4

c) 10 d) 8

e) 1 f) 5

2 a) 2 b) 2

c) 12 d) 2

e) f)

3 a) 9 b) 16

c) 9 d) 2

e) 8 f)

g) 9 h) 3

i) 5 j) 2

k) 3 l) 14

4 a) 2 b) 2

c) 5 d) 3

e) 6 f) 4

2 Cubic and reciprocalgraphs

Exercise 2.1H (page 3)1 a)

b)

c) x = 0, x = 2·2 or x = –2·2

0 1 2 3

y = x3 – 5x

–1–2–3 x

–5

–10

–15

15

10

5

y

4–9

3––10

3–4

1–3

26––55

1–3

7––17

6–7

5–8

9––22

1–3

16––41

2–5

1–5

1–2

3–4

48––77

1–2

17––20

11––12

8–9

1––10

9––10

1–4

1–5

3–4

7––20

13––20

3–4

1–5

7––18

27––40

5––14

34––35

7––18

7––16

17––24

11––24

5––12

7––10

9––10

1–8

11––24

1–5

7––30

1––10

8––15

17––20

7––10

x –3 –2 –1 0 1 2 3

x3 –27 –8 –1 0 1 8 27

– 5x 15 10 5 0 –5 –10 –15

y –12 2 4 0 –4 –2 12

17_ANSWERS_BK8.QXD 12/6/07 16:19 Page 187

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8STAGE

2 a)

b)

c) x = –3·5, x = –1·6 or x = 1·1

3

4 a)

Three solutions

b)

No solution

y

O

x

y

O x

0 1 2 3 4

y = 3x

–1–2–3–4 x

–2

–4

–6

–8

–10

–12

12

2

4

6

8

10

y

0 1 2

y = x3 + 4x2 – 6

–1–2–3–4 x

–2

–4

–6

16

18

12

14

2

4

6

8

10

y

x –4 –3 –2 –1 0 1 2

x3 –64 –27 –8 –1 0 1 8

4x2 64 36 16 4 0 4 16

– 6 –6 –6 –6 –6 –6 –6 –6

y –6 3 2 –3 –6 –1 18

x –4 –3 –2 –1 –0·5 –0·25 0·25 0·5 1 2 3 4

y –0·75 –1 –1·5 –3 –6 –12 12 6 3 1·5 1 0·75



5

x = –2·5, x = –1·3 or x = 0·9

6

x = –2·2, x = 0 or x = 2·2

0 1 2 3

y = 5x – x3

–1–2–3 x

–2

–4

–6

–8

–10

–12

12

2

4

6

8

10

y

0 1 2

y = x3 + 3x2

y = 3

–1–2–3 x

2

4

6

8

10

12

14

16

18

20y

189

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x –3 –2 –1 0 1 2

x3 –27 –8 –1 0 1 8

3x2 27 12 3 0 3 12

y 0 4 2 0 4 20

x –3 –2 –1 0 1 2 3

5x –15 –10 –5 0 5 10 15

– x3 27 8 1 0 –1 –8 –27

y 12 –2 –4 0 4 2 –12


190

3 Probability


b)

2 a)

b) (i)

(ii) =

3 a)

b) (i)

(ii)

4 a)

b) (i)

(ii) =

(iii) =

Exercise 3.2H (page 5)1 a) = b) =

c)

2

3

4 a) b) =

5 a) 0·85b) 0·65

6 a) 0·003b) (i) 0·15

(ii) 0·01(iii)0·91(iv) 0·18

c) (i) 0·0081(ii) 0·0009

1––18

2––36

1––36

1–––169

1–4

49–––400

3–5

12––20

1–4

5––20

1–9

3––27

1–9

3––27

1––27

2nd spin

1

21

3

1st spin

1

2

3

1

2

3

3rd spin1

2

31

2

31

2

31

2

31

2

31

2

31

2

31

2

31

2

3

3

2

2–9

1–9

LunchtimeCanteen

GymCar

Shopping

Travel

Canteen

Gym

Shopping

Canteen

Gym

Shopping

Bus

Cycle

2–3

4–6

1–6

Food

Muesli

ToastTea

Grapefruit

Drink

Muesli

ToastCoffee

Grapefruit

1–6

Spinner

1

2H

3

Coin

1

2T

3

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b) (i) (ii)

2 a)

b) (i) (ii)

(iii) =

3 a)

b) (i) =

4 a)

b) (i) 0·064(ii) 0·288(iii)0·784

5 a)

b) (i) 0·15(ii) 0·1

6 a)

b) (i)

(ii) = 3–5

9––15

1––15

Drink

Mineral water15

ColaDailyGazette

Orange

Newspaper

25

13

23

25

Mineral water15

ColaDailyNews

Orange

25

25

LunchtimeCanteen

Gym

0.1

0.5

0.4

0.1

0.5

0.4

0.1

0.5

0.4

0.2

0.5

0.3

Car

Shopping

Travel

Canteen

Gym

Shopping

Canteen

Gym

Shopping

Bus

Cycle

Day 3Rain0.4

0.6 No rain

Rain0.4

0.6 No rain

Rain0.4

0.6 No rain

Rain0.4

0.6 No rain

Day 2

Rain0.4

0.6 No rain

Rain0.4

0.6 No rain

Day 1

Rain0.4

0.6No rain

11––40

110–––400

Second ball

R

G

W

1120

520

420

First ball

R

G

1120

520

R

G

W

1120

520

420

W

420

R

G

W

1120

520

420

176––––1125

528––––3375

484––––3375

1331––––3375

Third ball

R

W

Second ball1115

415

R

W

1115

415

R

W

1115

415

First ball

R

W

1115

415

R

W

1115

415

R

W

1115

415

R

W

1115

415

88–––225

16–––225

Second ball

R

W

1115

415

First ball

R

W

1115

415

R

W

1115

415

191

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192

4 Equations andinequalities

Exercise 4.1H (page 8)1 x = 4 11 x = 1

2 x = 20 12 x =

3 x = 6 13 x = 15

4 x = 14 x = 12

5 x = 35 15 x = 6

6 x = 8 16 x = 2

7 x = 50 17 x = 23

8 x = 3 18 x = 2

9 x = 9 19 x = –3

10 x = –2 20 x = 5

Exercise 4.2H (page 9)1 x � 14 8 x � 30

2 x � 7 9 x � 8

3 x � 6 10 x � 14

4 x � 7 11 x �

5 x � 9 12 x �

6 x � 5 13 x � –5

7 x � 12 14 x � 12

Exercise 4.3H (page 9)1 b � 7 = 21, base = 6 cm

2 = + 2 , n = 24

3 a) x – 7 = x

b) x = 28, he had 28 m of rope

4 a) 80 – x � x

b) x > 60, £60·01

5 a) x + x + x – 50 = 180

b) x = 150°; 100°, 30°, 50°

6 a) (i) x

(ii) x + 30

(iii)x + 30

b) x + 30 > (x + 30)

c) x < 30, 29 or 29 years 364 days

7 a) x – 15 + x + 3 + x – 27 + x – 3 = 68

b) x = 40; 25 cm, 13 cm, 13 cm, 17 cm

5 Percentage increase anddecrease

Exercise 5.1H (page 11)1 a) 1·2(0) b) 1·07

c) 1·045 d) 1·0625e) 2·2(0)

2 a) 0·8(0) b) 0·93c) 0·65 d) 0·16e) 0·985

3 a) £946·08 b) £1024·92c) £1708·20 d) £2102·40e) £932·94

4 a) £595 b) £469c) £672 d) £210

5 £187·206 £1116·257 £10 937·508 a) £112·75

b) £114·95She will be £2·20 per week better off.

9 583·7 mm10 £244·80

Exercise 5.2H (page 12)1 £24 520 6 £62 £45 7 £423 £1440 8 £754 £13 500 9 £72 0005 28 million

6 Linear inequalities

Exercise 6.1H (page 13)1 a) y � 3

b) x � –1c) y � x – 3d) y � 3x – 1e) 5x + 2y � 10

2

0 x54321–1–2–3–4–5

5

4

3

2

1

y

–5 –4 –3 –2 –1

x = –3

1–2

1–4

2–3

1–3

1–3

1–3

1–5

1–3

1–3

3–4

n–4

n–3

1–2

1–2

4–5

3–7

1–2

1–2

1–3

1–2

2–7

7––15

1–2

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3

4

5

6

Exercise 6.2H (page 15)1

2

3

4

0 x3 421–1–2–3

4

3

2

1

y

–3 –2 –1

y = 2x + 1

x = –2

y = 4

5

6

7

5 6 7

0 x54321–1–2–3–4–5

5

4

3

2

1

y

–5 –4 –3 –2 –1

y = –x x = 4

y = 3

0 x3 4 521–1–2–3

4

3

2

1

y

–3 –2 –1

x + 2y = 4

x = –1 5

0 x3 4 5 621

4

3

2

1

y

3x + y = 6

6

7

7

5

0 x3 4 5 621–1–2

4

3

2

1

y

–2 –1

4x + 3y = 12

6

5

0 x321–1–2–3–4

4

3

2

1

y

–3 –2 –1

y = 2x – 1

–5

5

0 x54321–1–2–3–4–5

5

4

3

2

1

y

–5 –4 –3 –2 –1

x + y = 3

0 x54321–1–2–3–4–5

5

4

3

2

1

y

–5 –4 –3 –2 –1

y = x

193

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8


194

5

6 x � –1, y � 2, 5x + 3y � 15

7 Cumulative frequencyand box plots

Exercise 7.1H (page 16)1 a) Median = 23, LQ = 10, UQ = 39

b)

2 a)

b) Median = 265, LQ = 232, UQ = 295,interquartile range = 63

c) See diagram above.3 a) 190

b)

4 a)

b)

c) Median = 62, interquartile range = 17

20 40

LQ

M

UQ

Mass (g)

Cum

ulat

ive

freq

uenc

y

60 80 100

80

100

60

40

20

0

0 10 20Height (m)

30 40

200150 250

LQ

M

UQ

Weekly pay (£)

Cum

ulat

ive

freq

uenc

y

300 350 400 450

40

50

30

20

10

0

0 20 40Age

60 8010 30 50 70 90

0 x3 421–1–2

4

3

2

1

y

–2 –1

y = 2x + 1

x = 1

x + y = 5

5

6

7

8

5 6 7 8

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Mass (m grams) Cumulative frequency

m � 40 7

m � 50 19

m � 60 43

m � 70 75

m � 80 93

m � 90 98

m � 100 100

Weekly pay (£ p) Cumulative frequency

p � 200 3

p � 250 18

p � 300 39

p � 350 46

p � 400 48

p � 450 49



5 a)

b) 200 – 180 = 206 a) and c)

b) Median = 30·5, interquartile range = 18·5d) 150 – 103 = 47

10 20

LQ

M

UQ

Height, h (cm)

Cum

ulat

ive

freq

uenc

y

30 40 50

d)

60

80

100

120

140

160

20

40

60

0

200 250

UQ

M

LQ

Taking (£t)

Cum

ulat

ive

freq

uenc

y

300 350 400

b)

450 500

100

150

200

50

0

195

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8


196

8 Repeated percentageand proportionate change

Exercise 8.1H (page 20)1 a) £793·44

b) £1776·29c) £7010·85

2 a) £258·80b) £5255·35c) £3549·64

3 5034 a) £15 200

b) £15 058·33Simple interest by £141·67

5 £31466 a) £339·30

b) £245·157 56·3 million8 8·5 years or 9 years9 5·04 or 6 years

10 4·5%: £2604·525%: £2552·564·5% for 6 years is better

11 £7527·35

Exercise 8.2H (page 21)1 a) 1

b) 1

c)

d)

e) 1

2 a) £805·26b) £8926·54c) £15 444·96

3 a) £163·84b) £3681·63c) £1788·91

4 4465 a) £8109·15

b) 7·8 or 8 years6 7·4 or 8 days

9 Transformations


2

3 a) Rotation 90° clockwise about (1, 1)b) Reflection in x = 1c) Reflection in y = x

4

5

0x321 54

D

E

F–1–2–3–4

3

4

2

1

y

6 7 8 9

0x321 1054

B

C

A

x = 5

y = 1

–1–2–3

3

4

5

2

1

y

6 7 8 9

0 x321

S

TP3

4

2

1

y

–3–4 –2 –1

0 x3 421

R

QP3

4

2

1

y

–3–4 –2 –1

12

y = xx = –

4––15

11––12

1–3

7–8

1–4

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2

3 a) Enlargement, scale factor 2, centre, (–4, 1)

b) Translation ( )c) Enlargement, scale factor , centre (2, 0)

4

5

6

Exercise 9.3H (page 26)1 Rotation, 180° about (5, 1)2 Rotation, 90° anticlockwise about (7, 3)

3 Translation by vector ( )4 Enlargement, scale factors –2, centre (0, 0)5

Reflection in x = 3

6

Enlargement, scale factor 2, centre (0, 6)

0x321 5 64

3

2

1

–1–2–3–4–5

y

4

5

6

A

A’

C’B’

A”

C”B”

CB

0x3

A

A’

C’B’

21 5 64

3

4

2

1

–1–2–3–4

y

A”

B”C”CB

12

–5–7 0 x321 5 64

3

2

1

–1–2–3–4–5–6–7

y

–1–2–3–4

4

5

6

–6

–5–6 0 x321 5 64

3

2

1

–1–2–3–4–5–6

y

D

E

F

–1–2–3–4

4

5

6

–5 0 x321 54

3

2

1

y

BA

C

–1–2–3–4

4

5

6

1–2

–61

0 x321 54

3

2

1

y

XY

Z

6 7–1–2–3–4

4

5

7

6

0 x321 54

T

–1–2–3–4

3

4

5

2

1

y

R

P QS

6 7 8–1–2–3–4

197

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8


198

7

Reflection in y-axis (x = 0)

8

Rotation 90° clockwise about (4, –1)

9

Enlargement, scale factor –3, centre (1, 1)

10

Translation by ( )

10 Simultaneous equations


x = 2, y = 3

2

x = 2, y = 4

0 1 2 3 4 5

y = x + 2

y = 3x – 2

x

–2

6

8

10

12

14

4

2

y

0 1 2 3 4 5

y = x + 1

y = 4x – 5

x

–2

–4

–6

6

8

10

12

14

16

4

2

y

–22

0 x321

3

2

1

–1–2

y

A

BB’

B” C”

C’

A’

C

C”’B”’

–1–2–3

4

5

6

0 x321

4

2

1

–1–2–3–4–5–6

y

A

C

C’

C”

B’

B”

B

–1–2–3

3

0–1–2

x321 54

3

9

2

1

y

A

A’A” B”

C”

BB’

C

C’4

5

6 7 8

0 x3 421

3

4

2

1

y

A

BB”

C”

A”

C

C’

B’

–1–2–3

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3

x = –1, y = 2

4

x = 1, y = 3

5

x = 1 , y = 31–2

0 1 2 3 4 5

4x + 2y = 12

y = 2x

x

–1

–2

–3

–4

3

4

5

6

7

8

9

10

2

1

y

0 1 2 3 4 5

x + y = 4

y = 4x – 1

x

–2

6

8

10

12

14

16

18

20

4

2

y

0 1–1–2–3 2 3

y = x + 3

y = 3x + 5

x

–2

–4

6

8

10

12

14

4

2

y

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8


200

6

x = 2·7, y = 3·3

7

x = 2·2, y = 2·6

Exercise 10.2H (page 29)1 x = 3, y = 22 x = 2, y = –13 x = 13, y = –44 x = –2, y = –35 x = 6, y = –1

6 x = 3 , y = 2

7 x = 5, y = –108 x = 4, y = 3

9 x = 5, y =

10 x = 1 , y = 3

11 x = 5, y = –212 x = –2, y = –3

13 x = –1, y = 3

14 x = 2 , y = –

15 x = 3, y = –7

16 x = 1 , y = 2

17 x = 5, y = 318 x = 3, y = –2

Exercise 10.3H (page 29)1 x = 1, y = 42 x = 2, y = 33 x = –1, y = –34 x = 2, y = –1

5 x = –5 , y = 9

6 x = 3, y = –17 x = 3, y = –18 x = 4, y = 4

9 x = 1 , y = 3

10 x = –1, y = 1011 x = 4, y = 312 x = –3, y = –513 x = –2, y = 5

Exercise 10.4H (page 30)1 x + y = 40, x – y = 14, x = 27, y = 13

2 2 = –2m + c, 1 = 4m + c, c = 1 , m = –

, y =

–x + 1

3 2a + 4c = 27, a + 3c = 17, adult £6·50, child£3·50

4 3p + 2r = 135, 4p + 3r = 190, pen 25p, ruler30p

5 a = 2c, 2a + 3c = 84, adult £24, child £126 a) x + y = 46

b) y + 1 = 3(x + 1)y – 3x = 2

c) Alan 11 years old, mother 35 years old

2–3

1–6

1–6

2–3

1–2

1–2

1–2

1–3

5–7

1–7

1–2

1–2

1–2

1–2

1–2

0 1 2 3 4 5

2x + y = 7

2y = x + 3

x

–1

–2

–3

3

4

5

6

7

2

1

y

0 1 2 3 4 5 6

x + y = 6

y = 2x – 2

x

–1

–2

3

4

5

6

7

8

9

10

2

1

y

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11 Significant figures andstandard form

Exercise 11.1H (page 31)1 a) 9 b) 10

c) 60 d) 0·8e) 500 f) 7g) 700 000 h) 0·08i) 0·005 j) 0·0009

2 a) 19 b) 790c) 7800 d) 79 000e) 90 f) 0·31g) 0·057 h) 0·0047i) 0·031 j) 0·99

3 a) 7·39 b) 72·5c) 19 100 d) 236e) 17 900 f) 8·24g) 67·1 h) 0·893i) 0·0490 j) 2·72

Exercise 11.2H (page 31)1 a) 6 � 104 b) 8·4 � 103

c) 8·63 � 105 d) 7·25 � 107

e) 9·02 � 106 f) 7·8 � 101

g) 8·56 � 105 h) 5·63 � 102

i) 6 � 106 j) 1·36 � 108

2 a) 8 � 10–2 b) 9·6 � 10–3

c) 3·08 � 10–4 d) 6·3 � 10–5

e) 4·8 � 10–6 f) 2·3 � 10–8

g) 8·6 � 10–1 h) 3·62 � 10–6

3 a) 3000 b) 46 000c) 0·000 02 d) 720 000e) 0·000 19 f) 5 780 000g) 287 000 000 h) 0·000 005 13i) 0·002 07 j) 72 800 000k) 0·000 063 4 l) 0·0838

4 4·4 � 1013

Exercise 11.3H (page 32)1 a) 1·8 � 1010 b) 2 � 103

c) 3·6 � 104 d) 6 � 10–7

e) 4 � 104 f) 1·5 � 106

g) 1·4 � 1010 h) 4 � 10–5

i) 7·2 � 10–3 j) 7·5 � 104

k) 7·98 � 105 l) 6·03 � 108

m) 5·2 � 10–3 n) 5·83 � 10–5

2 b) because 4 � 105 � 9 � 103 = 3·6 � 109

3 c) because 5 � 10–3 � 4 � 10–4 = 2 � 10–6

4 a) 4 � 105 � 2 � 104 = 8 � 109, 6·7332 � 109

b) 4 � 106 � 2 � 10–3 = 8 � 103, 6733·2 or6·7332 � 103

c) 4 � 10–4 � 2 � 10–5 = 8 � 10–9, 6·7332 � 10–9

5 a) 1 � 107 ÷ 6 � 102 = 0·17 � 105 = 1·7 � 104,23 000 or 2·3 � 104

b) 1 � 105 ÷ 6 � 10–3 = 0·17 � 108 = 1·7 � 107,23 000 000 or 2·3 � 107

c) 1 � 10–5 ÷ 6 � 10–2 = 0·17 � 10–7 = 1·7 � 10–8,0·000 000 023 or 2·3 � 10–8

6 a) 1·188 � 1012 b) 1·495 � 109

c) 5·89 � 107 d) 2·35 � 106

e) 9·36 � 108 f) 6·85 � 104

g) 5·835 � 105 h) 1·404 � 108

i) –3·3373 � 10–3 j) 287·35 � 104

12 The equations of astraight-line graph

Exercise 12.1H (page 34)1 a) 3 b)

c) –2 d) –3

e) – f) 1

g) –3

2 a) 6 b) 4

c) 1 d) –1

e) f) –2

g) – h) 0

i) –4 j) 2

k) –3 l) –1

3 100, speed = 100 km/h80, returning home at 80 km/h

4

The lines are parallel.Gradient = –2

0 1 2 3

y = –2x + 3

y = –2x

–1–2–3 x

–4

–2

–6

8

4

10

6

2

y

1–4

7–4

1–2

1–2

3–7

1–2

1–2

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a) Gradient = 3

b) Gradient =

c) Gradient = –2

6 Gradient of AB = –

, gradient of BC = –1 ,

gradient of CA = 1

7 Gradient = 0·65, representing the cost inpounds per kilogram

8

a) Gradient = b) Gradient = c) Gradient = 5 d) Gradient = 5e) Gradient = –2 f) Gradient = –2

Exercise 12.2H (page 37)1 a) Gradient = 4, y-intercept = 2

b) Gradient = –3, y-intercept = 5c) Gradient = 2, y-intercept = –3d) Gradient = 5, y-intercept = 4e) Gradient = –5, y-intercept = 4

f) Gradient = – , y-intercept = 2

g) Gradient = – , y-intercept = 3

h) Gradient = , y-intercept = –

i) Gradient = , y-intercept = –

j) Gradient = – , y-intercept = 55–4

8–3

2–3

7–3

2–3

1–2

2–3

1–2

1–2

0 1 2 3

y = –2x + 4

y = 5x – 4

y = 5x

y = –2x

y = x + 312

–1–2–3 x

–5

–10

–15

–20

10

5

15

20y

y = x12

1–2

1–2

1–2

1–2

0 1 2 3

y = –2x + 7

y = 3x – 2

y = x + 112

–1–2–3 x

–4

–2

–6

–8

–10

–12

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2

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4 Accept any value of k for each part except thevalue given in the question.a) y = 2x + kb) y = –4x + kc) y = k – 3x

d) y = x + k

e) y = k – x

f) 3x + y = kg) x + 5y = kh) 3x – 2y = k

13 Similar figures

Exercise 13.1H (page 38)1 x = 4·8 cm2 A and B; length is 1 � width or equivalent

statement (scale factor = 1·25)C and E; length is 1 � width or equivalent statement (scale factor = 0·75)

3 x = 4·2 cm4 ST = 4·8 cm, SU = 4·2 cm5 AB = 3 cm, EF = 8·75 cm

6 a) Angle A is common.Angle ABC = Angle ADE(Corresponding angles.)Angle ACB = Angle AED(Corresponding angles.)So all the angles are equal, so the trianglesare similar.

b) BD = 2·8 cm, CE = 3·6 cm7 Angles are the same but 6 ÷ 4 = 1·5 and

10 ÷ 7 = 1·43 or equivalent explanation8 a) In first triangle,

3rd angle = 180 – (72 + 66) = 42°So both triangles have angles 42°, 66°and 72°, so the triangles are similar.

b) x = 10 cm9 a) PSR = 85°

b) AB = 10·5 cm, SR = 10 cm

14 Comparingdistributions

Exercise 14.1H (page 41)1 a) Alice: median = 15·5, range = 18

Bob: median = 15, range = 25b) On average Alice’s scores were higher,

and more consistent.2 a) Seashore: mean = 8·96, range = 5·9

Clifftop: mean = 2·88, range = 9·8b) Seashore gets more sunshine on average

and is more consistent.3 a) Men: median = £320,

interquartile range = £150Women: median = £200, interquartilerange = £100

b) Men have higher wages and a widerspread of wages.

4 a) English: median = 47, interquartile range = 11·5Maths: median = 52, interquartile range = 24

b) Maths marks were, on average, higher buthad a wider spread. English marks weremore consistent.

5 Girls spend longer on average (girls’ median = 64 seconds, boys’ median = 36 seconds); the spread of times for the boys isvery slightly less than the spread for the girls(girls’ interquartile range = 35 seconds; boys’interquartile range = 34 seconds).

1–3

1–2

1–2

1–4

014 4

y = –2x + 8 y = 4x + 1

y = x + 3

–6 – x

3

1

8

y

12

0 1 6

y = –x + 6

y = 3x – 5y = 2x + 5

x

–5

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y

12

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6 Duane if you want the chance of a really fasttime as his mean time is faster.Matt if you want to rely on his time as he ismore consistent.

7 a)

b) Boys are, on average, taller (the median ishigher) and have a greater spread (boys’interquartile range = 19 cm, girls’interquartile range = 15 cm).

8 Boys have slightly larger heads on average(median = 54·7 cm as opposed to 54 cm forgirls) and have a greater spread ofcircumference (boys’ interquartile range = 3 cm, girls’ interquartile range = 2 cm).

9 a) Make B – if you are buying one batteryyou need it to be a reliable one.

b) Make A – if you are buying a largequantity the spread is less important andthe higher average life is more important.

15 Trigonometry


2

3

4

5

6

Exercise 15.2H (page 46)1 a = 6·34 cm

b = 5·60 cmc = 11·8 cmd = 25 cme = 35·2 mf = 13·4 cmg = 11·9 cmh = 18·4 cm

2 a) w = 30·3 cmb) h = 62·5 cm

3 a) a = 14 cmb) b = 24·25 cmc) c = 12·61 cmd) 258 cm2

4 a) 180 kmb) 126 km

AH

O

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AH

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Exercise 15.3H (page 48)1 a = 2·60 cm

b = 12·2 mc = 99·7 cmd = 10·1 me = 9·20 mf = 5·35 cmg = 42·7 cmh = 15·3 m

2 l = 2·32 m3 a) a = 21·1 cm

b) 84·2 to 84·4 cm2

4 16·8 km

Exercise 15.4H (page 50)1 a = 34·5°

b = 32·6°c = 8·6°d = 61·5°e = 46·7°f = 53·4°g = 71·8°h = 32·5°

2 33·7°3 120·2°4 x = 108·7°

16 Dimensions

Exercise 16.1H (page 52)1 Volume2 Area3 None4 Length5 Area6 None7 None8 Volume9 None

10 Area11 Area12 Volume13 Length14 None15 Volume16 None17 None18 Volume19 Volume20 Area21 Length22 None23 Area24 Area25 Volume

26 None27 Area28 Volume29 Area30 None31 Square32 Square33 Cube34 Power four

17 Quadratics

Exercise 17.1H (page 54)1 x2 + 9x + 82 x2 + 10x + 243 a2 + 2a – 354 b2 + 7b – 305 x2 – 8x + 126 a2 – 13a + 227 c2 – 368 y2 + 14y + 499 a2 – 18a + 81

10 a2 – 2511 b2 + 11b + 2812 6 + 5c + c2

13 a2 – 11a + 2414 9 – 6d + d2

15 c2 + c – 3016 a2 – 2a – 3517 t2 – 13t + 3018 s2 – 12119 a2 – 99a – 10020 d2 + 30d + 200

Exercise 17.2H (page 54)1 (x + 3)(x + 1)2 (x + 4)(x + 1)3 (x + 4)(x + 3)4 (x – 1)(x – 1) or (x – 1)2

5 (x – 1)(x – 4)6 (x – 10)(x – 2)7 (x + 20)(x + 1)8 (x – 14)(x – 2)9 (x + 9)(x + 1)

10 (x + 3)(x + 3) or (x + 3)2

11 (x + 5)(x + 4)12 (x + 12)(x + 2)13 (a – 8)(a – 1)14 (b – 2)(b – 1)15 (a – 2)(a – 8)16 (s – 12)(s – 2)17 (y – 6)(y – 5)18 (y + 10)(y + 3)19 (x – 16)(x – 1)20 (c – 16)(c – 2)

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Exercise 17.3H (page 55)1 (x + 5)(x – 3)2 (x – 7)(x + 4)3 (x + 7)(x – 1)4 (x – 4)(x + 3)5 (x – 7)(x + 2)6 (x – 10)(x + 1)7 (x + 9)(x – 4)8 (x – 12)(x + 3)9 (x + 10)(x – 1)

10 (a + 4)(a – 2)11 (a + 6)(a – 2)12 (y – 5)(y + 3)13 (b + 8)(b – 3)14 (a + 6)(a – 4)15 (c – 9)(c + 4)16 (x – 14)(x + 2)17 (x + 14)(x – 1)18 (y + 8)(y – 6)19 (a – 7)(a + 3)20 (x + 25)(x – 4)

Exercise 17.4H (page 55)1 (x + 3)(x – 3)2 (x + 8)(x – 8)3 (x + 14)(x – 14)4 (x + y)(x – y)5 (5 + y)(5 – y)6 (4 + c)(4 – c)7 (a + 100)(a – 100)8 (9 + s)(9 – s)

18 Time series and movingaverages

Exercise 18.1H (page 56)1 a) and c)

b) 29, 29, 30·5, 31·25, 31·75, 32·75, 33, 33,33·25

d) There are seasonal fluctuations. Generaltrend is a slight increase.

2 a) and c)

b) 96, 96, 104, 109, 110, 108, 109, 113, 119, 119

d) There are some variations. General trendis an increase in occupancy during theyear.

0

20

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3 a) and c)

b) 1500, 1518, 1498, 1506, 1527, 1530, 1531, 1549, 1556, 1567, 1579, 1600, 1615, 1630, 1640, 1655,1652, 1668, 1663, 1671, 1679, 1693

d) Fairly steady increase in customers. Highest on Saturday and Sunday, much lower in the week,except Wednesdays.

e) Wednesday4 a) and c)

b) 136·75, 134·5, 135·5, 137·75, 147·25, 151, 146, 148, 144·25d) Number of units of gas used is fairly constant. Heaviest use is in the first quarter and the

lightest in the third.

0

50

100

150

200

250

1 2 3 4

Year 1

Uni

ts o

f gas

1 2 3 4

Year 2

1 2 3 4

Year 3

0

500

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1500

2000

2500

3000

3500

S M Tu W

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Th F Sa S M Tu W

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Th F Sa S M Tu W

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5 a) and c)

b) 113·7, 112·2, 108·7, 106·5, 106·8, 108·7, 103·8, 104·7, 104·2, 107·2, 108, 110·7, 113d) Overall trend is fairly constant. Highest always Saturday, lowest Monday or Wednesday.e) 76

19 Equations and formulae

Exercise 19.1H (page 59)1 x = –3 or x = –1 13 x = 2 or x = –1 25 x = 11 or x = –112 x = –5 or x = –1 14 x = 1 or x = 18 26 x = 1 or x = –223 x = 6 or x = –2 15 x = 3 or x = –4 27 x = 0 or x = 34 x = –5 or x = –3 16 x = 0 or x = –7 28 x = 2 or x = 95 x = 5 or x = –2 17 x = 2 or x = –5 29 x = 0 or x = 46 x = 4 or x = 5 18 x = 15 or x = –2 30 x = 2 or x = –117 x = 8 or x = –1 19 x = 0 or x = 5 31 x = 5 or x = –28 x = 7 or x = –3 20 x = 7 or x = –7 32 x = 5 or x = –79 x = –2 or x = –3 21 x = –6 or x = –2 33 x = 1 or x = –10

10 x = 6 or x = –5 22 x = 10 or x = –2 34 x = 5 (repeated)11 x = 1 or x = 7 23 x = –4 (repeated)12 x = 0 or x = –4 24 x = 0 or x = 8

Exercise 19.2H (page 60)1 r = 2 a = P – 1 3 c = a2 – b2

4 x = 4y 5 u = 6 r =

7 r = 8 x = 9 t =

10 x = 11 v = 2as + u2 12 t =

13 a) 183 cm3 b) r = c) 3·9 cm3V–––πh

30 – 2s––––––a

y + 4–––––3

2s––––––2u + a

qy–––––q + p

pq + p––––––q – 1

pq––––s + t

fv––––f – v

A––––2πh

0

40

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120

160

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Documents

17 ANSWERS BK8.QXD 12/6/07 16:19 Page 187 Answers to ... · PDF fileGraduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007 187 Answers to Homework Book 8 ... OCR GCSE