OCR Mathematics Series Editor: Brian · PDF file1 Foundation Initial and Foundation Bronze...

1Foundation Initial and

Foundation Bronze

Series Editor:Brian SeagerHoward Baxter Mike Handbury John Jeskins Jean Matthews Colin White

OCRMathematics

Homework Book Answers

GCSE Bfor

I S BN 978-1-444-13678-4

9 7 8 1 4 4 4 1 3 6 7 8 4

136784_SPEC_B_HWB1_ANS_CV.indd 1 18/10/2010 14:06Z01_ANS_OCR_GCSE_MATHS_HWB_BK1_SPEC_B.indd 1 20/10/2010 09:31

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© Howard Baxter, Mike Handbury, John Jeskins, Jean Matthews, Mark Patmore,Brian Seager, Colin White, Eddie Wilde, 2010

First published in 2010 byHodder Education,An Hachette UK Company338 Euston RoadLondon NW1 3BH

Impression number 5 4 3 2 1Year 2014 2013 2012 2011 2010

All rights reserved. Apart from any use permitted under UK copyright law, no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photo-copying and recording, or held within any information storage and retrieval system, without permission in writing from the publisher or under licence from the Copyright Licensing Agency Limited. Further details of such licences (for reprographic reproduction) may be obtained from the Copyright Licensing Agency Limited, Saffron House, 6–10 Kirby Street, London EC1N 8TS

Cover illustration Crush DesignIllustrations by Pantek Arts Ltd, Maidstone, KentTypeset in Avenir Book 10pt by Pantek Arts Ltd, Maidstone, KentPrinted in Great Britain by Hobbs the Printers, Totton, Hants

A catalogue record for this title is available from the British Library

ISBN: 978 1444 13678 4

Z01_ANS_OCR_GCSE_MATHS_HWB_BK1_SPEC_B.indd 2 20/10/2010 09:31

3

Homework exercise answers

Found

ation Initial

OCR Mathematics for GCSE Specifi cation B © Hodder Education 2010

Exercise 1.1H (page 1) 1 a) 430 b) 400 2 a) 140 b) 100 3 a) 48 860 b) 48 900 4 a) 631 750 b) 631 700 5 a) 9 212 670 b) 9 212 700 6 a) 350 b) 300 7 a) 890 b) 900 8 a) 4820 b) 4800 9 a) 1030 b) 100010 a) 650 b) 60011 a) 60 b) 10012 a) 1000 b) 100013 a) The nearest 1000 b) The nearest 100 c) The nearest 1014 (i) All of them could have been rounded to the

nearest 10. (ii) b, c, d and f could have been rounded to the

nearest 100. (iii) f could have been rounded to the nearest

1000.15 The 300 could be accurate but it could also have

been rounded to the nearest 10 so any number between 295 and 304 would be possible. It could also have been rounded to the nearest 100 so any number between 250 and 349 would be possible.

16 47 382 is the exact value, 47 380 is the number rounded to the nearest 10, 47 400 is the number rounded to the nearest 100, 47 000 is the number rounded to the nearest 1000 and 50 000 is the number rounded to the nearest 10 000.

17 The newspaper rounded to the nearest 1000, the radio rounded to the nearest 10 000 and the television rounded to the nearest 100.

Exercise 2.1H (page 2) 1 a) Circumference b) Radius c) Centre 2 Diameter 3

There are 9 diagonals.

Exercise 2.2H (page 2)Check students’ work.

Exercise 2.3H (page 2) 1 a) Cylinder b) Cube c) Cone d) Sphere 2 a) Yes b) Triangular prism 3 5 faces, 8 edges, 5 vertices

Exercise 3.1H (page 3) 1 a) 717 b) 829 c) 904 d) 891 e) 777 f) 905 g) 814 h) 676 i) 859 j) 988 2 977 3 862 4 754 5 676 6 1000 7 681 8 999 9 90010 96511 85112 72313 52014 It is not possible to make exactly 1000.

Exercise 3.2H (page 3) 1 a) 147 b) 151 c) 426 d) 311 e) 253 f) 211 g) 317 h) 196 i) 286 j) 218 2 135 3 361 4 309 5 271 6 428 7 386 8 213 9 30610 30811 75412 27513 25214 Yes, as 724 – 167 = 557, one of the other

numbers.




4

Exercise 3.3H (page 4) 1 a) 183 b) 518 c) 621 d) 282 e) 106 f) 328 g) 484 h) 155 i) 505 j) 188 2 357 3 672 4 445 5 919 in total 6 54 kilometres 7 Melissa is correct, there are two different sets of three

numbers. 23 + 29 + 48 = 100 and 26 + 29 + 45 = 100.

Exercise 3.4H (page 4) 1 a) 48.74 b) 87.71 c) 77.3(0) d) 14.31 e) 21.84 f) 133.32 2 a) 22.41 b) 21.1(0) c) 63.18 d) 8.45 e) 36.56 f) 1.98 3 a) £23.82 b) £35.57 4 a) £19.15 b) £34.33 5 a) 4.6 m b) 7.19 m c) 1.82 m d) 2.895 m 6 6.25 m 7 £53.65 8 60 cm or 0.6 m

Exercise 4.1H (page 5) 1 5, 7, 10 2 6, 12, 17 3 8, 20, 28 4 4, 6, 9 5 2, 6, 19 6 10, 3, 7 7 8, 64, 80 8 19, 31, 115

Exercise 4.2H (page 5) 1 15, 21 2 8, 14, 18 3 8, 11, 15 4 15, 30, 54

Exercise 4.3H (page 6) 1 + 3 2 ÷ 3 3 − 7 4 � 4, + 7

Exercise 4.4H (page 6) 1 2, 5, 13 2 5, 20, 35 3 11, 16, 22 4 4, 10, 17

Exercise 4.5H (page 7) 1 = 9 2 = 15 3 = 12 4 = 37 5 = 21 6 = 19 7 = 17 8 = 24 9 ® = 8 10 H = 9

Exercise 4.6H (page 7) 1 a = 12 2 b = 19 3 c = 6 4 d = 4 5 e = 4 6 f = 1 7 g = 10 8 h = 9 9 j = 111–

210 k = 1811 m = 1312 n = 0.813 p = 714 q = 2315 r = 2916 s = 20017 t = 918 u = −419 v = −520 w = −2

Exercise 5.1H (page 8) 1 a) Warmer b) Colder c) Colder d) Colder e) Warmer 2 a) −5°C, −3°C, 2°C, 3°C, 7°C b) −3°C, −2°C, 0°C, 4°C, 5°C c) −18°C, −15°C, −3°C, 15°C, 20°C d) −8°C, −7°C, −5°C, −4°C, 3°C, 6°C, 9°C e) −15°C, −12°C, −9°C, 3°C, 6°C, 18°C, 21°C 3 a) 14 b) Down 7 c) 7 d) −3 e) 5 f) −3 4 a) −5°C, 0°C, 5°C b) 1°C, −1°C, −3°C c) 5°C, 8°C, 11°C d) −7°C, −10°C, −13°C e) −20°C, −10°C, 0°C 5 a) 20°C b) 4°C c) 14°C d) 62°C e) 2°C 6 The differences for each country are: Northern Ireland

48.3°C, England 64.6°C, Wales 56.9°C, Scotland 60.1°C so England has the biggest difference between its highest and lowest temperatures.




5

Exercise 6.1H (page 10) 1 a) Very likely (depending on local climate, time of

year etc.) b) Very unlikely c) Evens d) Unlikely e) Very unlikely f) Evens g) Unlikely h) Very likely 2 a) Evens b) Unlikely c) Impossible d) Very likely 3 a) 10 b) 5 c) 0 d) 1, 2, 3 or 4

Exercise 6.2H (page 11) 1

c) a) e) b)

Impossible Evens Certain

d)

2Impossible Evens Certain

c) a) b)

3 a) C b) A c) D d) B


c) b) a) d)

0 0.5 1

2

0 0.5 1

a) b)c)

3 a) C b) A c) E d) E

Exercise 7.1H (page 13) 1 3.5 2 2.7 3 4.8 4 7.2 5 25.2 6 8 7 38.7 8 44.8 9 31.210 25.811 4212 49.8

13 19.414 108.815 112.216 53.617 127.218 12419 295.220 294.721 535.5 cm22 119.2 m

Exercise 7.2H (page 13) 1 0.2 2 0.3 3 2.4 4 1.7 5 2.5 6 0.3 7 0.4 8 0.6 9 0.910 0.411 4.712 4.713 9.414 9.715 12.516 13.517 5.418 19.219 5.920 9.521 23.5 mm22 13.9 g

Exercise 7.3H (page 14) 1 a) 370 b) 780 c) 7 d) 5 e) 0.3 2 a) 3700 b) 7800 c) 70 d) 50 e) 3 3 a) 37 000 b) 78 000 c) 700 d) 500 e) 30 4 a) 7.3 b) 2.1 c) 6.7 d) 2.97 e) 0.526 5 a) 0.73 b) 0.21 c) 0.67 d) 0.297 e) 0.0526 6 a) 0.073 b) 0.021 c) 0.067 d) 0.0297 e) 0.005 26 7 a) 0.0036 b) 1.87 c) 8.21 d) 0.3751 8 1200 cm or 12 m 9 70 mm or 7 cm




6

Exercise 8.1H (page 15) 1 a) 1–

4 b) 3–4

2 a) 1–2 b) 1–

2

3 a) 3–4 b)

1–4

4 a) 1–2 b) 1–

2

5 a) 1–2 b) 1–

2

6 a) 1–4 b) 3–

4

Exercise 8.2H (page 15) 1 Any two parts shaded 2 Any three parts shaded 3 Any six parts shaded 4 Any two parts shaded 5 Any three parts shaded 6 Any two parts shaded

Exercise 8.3H (page 16) 1 a) 5 b) 18 c) 25 d) 4 e) 11 2 a) 3 b) 5 c) 9 d) 50 e) 2 3 a) 6 b) 18 c) 27 d) 75 e) 24


6 = 1–3 b) 3–8

c) 5––15 = 1–3 d) 6––

10 = 3–5 2 a) 4–

6 = 2–3 b) 5–8

c) 10––15 = 2–3 d) 4––

10 = 2–5 3 a) 6––

10 = 3–5 b) 6–8 = 3–4

c) 7––15 d) 5–

8

4 a)

4––10 = 2–5 b) 2–

8 = 1–4 c) 8––

15 d) 3–8

5 Check students’ diagrams.

Exercise 8.5H (page 17) 1 43 2 15 3 16 4 30 5 139 6 £132

Exercise 8.6H (page 17) 1 84 2 370 3 168 4 208 5 141 6 204 7 270 8 730 9 They are the same, £90.10 a) 8 b) 2411 £31.65

Exercise 9.1H (page 18) 1 a) Centimetres b) Kilometres c) Metres d) Millimetres 2 a) 20 mm b) 140 mm c) 13 mm d) 6000 mm e) 1426 mm f) 3790 mm 3 a) 700 cm b) 246 cm c) 310 cm d) 4 cm e) 5.7 cm f) 2.96 cm 4 a) 2 m b) 3.16 m c) 42.1 m d) 9 m e) 1.246 m f) 41.62 m 5 517 mm, 610 mm, 3.1 m, 420 cm

Exercise 9.2H (page 18) 1 a) Grams b) Grams or kilograms c) Kilograms d) Grams 2 a) 2300 g b) 500 g c) 60 g d) 45 000 g 3 a) 6.8 kg b) 0.3 kg c) 23.4 kg d) 7.25 kg 4 69.9 g, 832 g, 0.9 kg, 1.3 kg, 1521 g 5 4.5 kg 6 545 g 7 2.99 kg 8 No, total weight is 386 kg.

Exercise 9.3H (page 19) 1 a) 8000 ml b) 700 ml c) 9020 ml 2 a) 6.8 litres b) 0.09 litre c) 0.707 litre 3 82 ml, 0.39 litre, 670 ml, 5.4 litres 4 475 ml 5 2.375 litres

Exercise 9.4H (page 19) 1 A 3 cm, B 7 cm, C 8.5 cm 2 3.6 kg 3 A –8°C, B 23°C 4 55 mm or 5.5 cm 5 103 mm or 10.3 cm 6 a) A 2.4 B 0.6 b) C 3 D 12.5 c) E 13 F –3 d) G 130 H 320 e) I –12 J 19




7

Exercise 10.1H (page 21) 1 a) 14, 17 b) Starts with 2, and 3 is added each time. 2 a) 22, 20 b) Starts with 30, and 2 is subtracted each time. 3 a) 6, 6.5 b) Starts with 4, and 0.5 is added each time. 4 a) 9, 11 b) Starts with 1, and 2 is added each time. 5 a) 65, 75 b) Starts with 25, and 10 is added each time. 6 a) 45, 52 b) Starts with 17, and 7 is added each time. 7 a) 38, 35 b) Starts with 50, and 3 is subtracted each time. 8 a) 4.5, 3 b) Starts with 10.5, and 1.5 is subtracted each time.

Exercise 10.2H (page 21) 1 a) Add 3, 17 b) Add 5, 125 c) Subtract 9, 18 d) Subtract 100, 420 e) Multiply by 3, 162 2 a) 38, 52 b) 76, 64 3 a) Yes, 80 – 44 = 36, subtract 6 six times b) No, 80 – 51 = 29, subtract 9 three times will give

only 27

Exercise 10.3H (page 21) 1 Increase by 1, answer increases by 15; 5 � 14 + 5 = 75 2 Outer digits down 1, inner up 1, answer decreases

by 18; 64 − 46 = 18 3 1, 111, 123 454 321

Exercise 11.1H (page 22) 1 a) £15 b) 35 cm c) $8 d) 12.5 kg 2 a) 20 kg b) £7 c) 125 m d) $4.50 3 a) £45 b) 12 km c) $900 d) £22.50 4 £1.30 5 a) £180 b) £60

Exercise 11.2H (page 22) 1 £5 2 £0.75 or 75p 3 £45 4 £17 5 £2.16 6 £0.34 or 34p 7 £0.24 or 24p 8 £42.50 9 £610 £26.2511 £8.3012 £24.60

13 £5414 £40.5015 £3.7816 £0.68 or 68p17 £4218 £6319 £10820 £13621 54622 3123 27 kg24 £34525 11.2 g26 15% of £600 = £90, 10% of £800 = £80 so 15% of

£600 is greater.27 Kevin paid £30, Karim paid £25, Keiron paid £30 so

Kevin and Keiron paid the most.28 In the first week of the sale, the price would be £360.

In the second week of the sale, the price would be £324. In the third week of the sale, the price would be £291.60. So the selling price of the television was £291.60.

Exercise 12.1H (page 24) 1 a) C25 b) G24 c) G29 d) B28 2 a) P96 b) P98 c) R97 3 a) R b) T c) Q d) P and S

Exercise 12.2H (page 26) 1 a) North b) West c) South-west 2 Broad Marsh Bus Station 3 Middle Hill, third, Stoney Street, a car park, St Mary’s

Church 4 Other routes are possible. a) Turn left out of the shopping centre on Collin

Street. Turn left into Middle Hill. Take the second right into Pilcher Gate. The car park is on your left. b) Turn left along Low Pavement, continuing into

Middle Pavement. Take the second left into Weekday Cross,

continuing into Fletcher Gate. Take the second right into Warser Gate and

continue straight on into Woolpack Lane.




8


First session Second session

Third session

S S S

S S F

S S T

S F S

S F F

S F T

S T S

S T F

S T T

F S S

F S F

F S T

F F S

F F F

F F T

F T S

F T F

F T T

T S S

T S F

T S T

T F S

T F F

T F T

T T S

T T F

T T T

2 a) 347, 374, 437, 473, 734, 743 b) 244, 424, 442 3 Red, silver, blue Red, blue, silver Blue, red, silver Blue, silver, red Silver, red, blue Silver, blue, red

4 PFLR, PFRL, PLFR, PLRF, PRFL, PRLF, FPLR, FPRL, FLPR, FLRP, FRPL, FRLP,

LPFR, LPRF, LFPR, LFRP, LRPF, LRFP, RPFL, RPLF, RFPL, RFLP, RLPF, RLFP


FO O

RAA

A

R

AF A

A R

R

RR

R

R

R RR

F

F

F

2 a) Obtuse b) Obtuse c) Reflex d) Acute

Exercise 14.2H (page 28) 1 a) 720° b) 270° 2 a) 50° b) 105° c) 220° d) 73° e) 146° f) 312° g) 270°

Exercise 14.3H (page 30) Check students’ diagrams.

Exercise 14.4H (page 31) 1 a = 140° b = 105° c = 54° d = 85° e = 40° f = 72° g = 40° h = 35° i = 32° j = 35° 2 a = 345° b = 140° c = 125° d = 179° e = 133° f = 155° g = 63° h = 90° i = 134° j = 90° 3 a) a = 125° Vertically opposite angles are equal. b = 55° Vertically opposite angles are equal or Angles on a straight line add up to 180°

or Angles around a point add up to 360°. b) c = 30° Vertically opposite angles are equal. d = 150° Vertically opposite angles are equal or Angles on a straight line add up to 180°

or Angles around a point add up to 360°. c) e = 137° Vertically opposite angles are equal. f = 43° Angles on a straight line add up to

180°. g = 43° Vertically opposite angles are equal or Angles on a straight line add up to 180°

or Angles around a point add up to 360°.




9

d) h = 121° Angles on a straight line add up to 180°. i = 59° Vertically opposite angles are equal. j = 121° Vertically opposite angles are equal or Angles on a straight line add up to 180°

or Angles around a point add up to 360°. e) k = 82° Vertically opposite angles are equal. m = 98° Angles on a straight line add up to

180°. n = 98° Vertically opposite angles are equal or Angles on a straight line add up to 180°

or Angles around a point add up to 360°. f) p = 175° Angles on a straight line add up to

180°. q = 175° Vertically opposite angles are equal or Angles on a straight line add up to

180°. r = 5° Vertically opposite angles are equal or Angles on a straight line add up to 180°

or Angles around a point add up to 360°. g) s = 31° Vertically opposite angles are equal and

a right angle is 90°. h) t = 90° Vertically opposite angles are equal. u = 53° Vertically opposite angles are equal or Angles on a straight line add up to

180°. v = 37° Vertically opposite angles are equal or Angles on a straight line add up to 180°

or Angles around a point add up to 360°. i) w = 60° Vertically opposite angles are equal. x = 70° Vertically opposite angles are equal or Angles on a straight line add up to

180°. y = 50° Vertically opposite angles are equal or Angles on a straight line add up to 180°

or Angles around a point add up to 360°. j) z = 120° Angles around a point add up to 360°.

Exercise 15.1H (page 33) 1 a) 1620 b) 0555 c) 2315 d) 0742 e) 1245 f) 1035 g) 1325 h) 0155 2 a) 5 a.m. b) 12:20 p.m. c) 11:40 p.m. d) 1:50 a.m. e) 8 p.m. f) 5:07 p.m. g) 2:25 a.m. h) 12:40 a.m. i) 10:53 a.m. j) 7:45 p.m. 3 7 hours 25 minutes 4 4:05 p.m. 5 1 hour 55 minutes 6 6:30 p.m. 7 1820 in London 8 1746

Exercise 16.1H (page 34) 1 a) 400 b) 300 c) 340 d) 260 2 a) 20 cm b) 52 cm c) 26 cm d) 32.8 cm 3 a) 40p b) 35p c) 65p d) £1.18 4 a) 4 b) 11 c) 16 d) 25 5 a) 120 min b) 320 min c) 220 min d) 128 min 6 a) £54 b) £252 7 a) £5 b) £6.50 8 a) 120 km/h b) 72 km/h 9 a) 12 cm2 b) 11.2 cm2

10 a) 16 euros b) 59.2 euros

Exercise 16.2H (page 35) 1 a) 6 m b) 17.1 m 2 a) 22 cm b) 9.2 cm 3 a) 72 b) 63 4 a) £52 b) £213 5 a) 2700 g b) 1775 g

Exercise 17.1H (page 36) 1 a) 18 b) 10 c) 27 2 a) 2.1875 b) 2.6 c) 24.84 3 a) 2 b) 9.2 c) 0.5 4 a) 130 b) 42.9 c) 94.5 5 a) 26.1 b) 3 c) 2 6 a) 0.2 b) 50 c) 4.2 7 a) 2.05 b) 7.75 c) 2.85 8 a) 73.93 b) 4.27 c) 0.92

Exercise 18.1H (page 37) 1 a) 44 b) 24 c) 71 d) 105 2 a) 40 b) 50 c) 16 3 a) 85 miles b) 234 miles c) Manchester d) Liverpool and Maidstone 4 a) £415 b) £1570 c) (i) £315 extra (ii) School holidays begin.




10

Exercise 18.2H (page 39) 1 a) 1100 from London b) 1245 c) 1100 d) 1000; 2 hours 6 minutes e) 2 hours 17 minutes 2

Birmingham Paris Duration

0630 0900 1 hour 30 minutes





3 a) 1112 b) Yes (42 minutes) c) 4 hours 49 minutes

Exercise 19.1H (page 41) 1 a) 10% b) 40% c) 40% 2 a) 60% b) 40%


5 b) 4–6 = 2–

3

c) 4––12 = 1–

3 d) 5–8

2 a) 3–5 b) 2–

6 = 1–3

c) 8––12 = 2–

3 d) 3–8

3 a) 3––10 b) 5–

8

c) 7––10 d) 4–

5 4 a) 0.3 b) 0.625 c) 0.7 d) 0.8 5 Check students’ diagrams. 6 a) 0.25 b) 0.75 c) 0.6 d) 0.9

Exercise 19.3H (page 43) 1 a) 9 b) 12 c) 16 d) 54 e) 30 f) 91 g) 27 h) 165 2 a) 20% b) 25% c) 80% d) 90% e) 30% f) 70% g) 75% h) 60% 3 a) £8 b) £9 c) £52 d) 3 m e) 288 m f) £25.20 g) 3.9 m h) 63 m 4 a) 20% b) 6 5 a) £13 b) £52 6 a) £3.60 b) £75.60

Exercise 20.1H (page 44) 1 a) 75° b) 140° c) 100° 2 a) 5 cm b) 9 cm c) 1.5 cm 3 5 m (will vary) 4 300 m (will vary) 5 10 to 12 m 6 16 m 7 16 to 24 m

Exercise 20.2H (page 47) 1 a) 1 kg b) 1 metre c) 50 to 90 cm d) 5 to 10 litres e) 6 to 10 m 2 a) 4 to 6 m b) 8 to 12 m 3 45 to 65 m 4 a) 8 to 10 m b) 45 to 55 m

Exercise 21.1H (page 48) 1 a)

10

1000

2000

3000

Dis

tanc

e (k

m)

4000

5000

6000

2 3 4Time (h)

5 6 7 8

b) (i) 3750 km (ii) 1125 km c) (i) 11–

3 hours or 1 hour 20 min

(ii) 71–3 hours or 7 hours 20 min

2 a) (i) $56 (ii) $95 b) (i) €90 (ii) €32 c) $168




11

3 a) (i) 40 inches (ii) 67 inches b) (i) 125 cm (ii) 53 cm c) 496 cm 4 a), b)

100

Dol

lars

($)

20

20

40

60

80

100

120

140

160

30 40Pounds (£)

50 60 70 80 90 100

c) (i) $71 (ii) $121 d) (i) £70 (ii) £37 e) $1.42 5 a) 40 hectares b) 112 acres c) 2.5 acres

Exercise 22.1H (page 50) 1 a) 108 b) 364 c) 432 d) 435 e) 228 2 a) 1700 b) 2580 c) 1180 d) 2520 e) 3720 3 a) 426 b) 1060 c) 685 d) 3696 e) 2233 4 a) 28.2 b) 47.6 c) 43.5 d) 28 e) 47.2

Exercise 22.2H (page 50) 1 a) 425 b) 504 c) 684 d) 976 e) 1722 f) 2550 g) 1204 h) 1624 i) 3854 j) 4266 2 a) 29.8 b) 77.67 c) 28.5 d) 45.36 e) 46.13 3 a) 45 333 b) 18 993 c) 33 540 d) 44 448 e) 41 223 4 360 5 2808

Exercise 22.3H (page 50) 1 a) 13 b) 28 c) 19 d) 4 e) 6

2 a) 76 b) 25 c) 45 d) 122 e) 89 3 a) 45 b) 43 c) 29 d) 58 e) 23 4 a) 51 rem 9 b) 32 rem 12 c) 24 rem 20 d) 24 rem 20 e) 29 rem 23 5 8 6 23


2

3

4 No reflection symmetry 5

6 No reflection symmetry 7 No reflection symmetry 8

9

10 No reflection symmetry

Exercise 23.2H (page 52) 1 COOK 2 BIKE 3 BID 4 l308 5 3 + 8 = ll 6 HOCK


OCR Mathematics for GCSE Specifi cation B © Hodder Education 2010 1212 OCR Mathematics for GCSE Specifi cation B © Hodder Education 2010


2

3

4

5

6

Exercise 23.4H (page 54) 1 2

3 4

5

6


2

3

4

5

x

y

1

2

3

4

5

5

–5

–5

−4

−3

−2

−11 2 3 4−4 −3 −2 −1 0





13

6 a), b), c), d)

x

y

1

2

3

4

5

6

−4

−5

−6

−3

−2

−11 2 3 4 5 6−4−5−6 −3 −2 −1 0

AB

C

xP

xQ

e) Reflection in the x-axis

Exercise 24.1H (page 56) 1 a) Red 8, blue 6, green 4, white 6, black 7, silver 9 b) Silver 2

0

Num

ber

of s

tude

nts

1

Bus

2

3

4

5

6

7

8

9

WalkMode of transport

Car Bike

3 a) e.g. Monday

Tuesday

Wednesday

Thursday

Friday

represents 4 people b)

Monday

Tuesday

Wednesday

Thursday

Friday

4 a) 6 b) Biographies c) 43

Exercise 24.2H (page 58) 1 a) 14°C in January, February and December b) 7°C 2 a) 09:00 b) 37.5°C

3 a)

0Te

mp

erat

ure

(°C

)

2

06:0

007

:00

08:0

009

:00

10:0

011

:00

12:0

013

:00

14:0

015

:00

16:0

017

:00

18:0

0

Time

4

6

8

10

12

14

16

18

20

22

b) Between 09:00 and 10:00


Number of matches Frequency

45 1

46 11

47 14

48 7

49 9

50 5

51 3

b)

0

Freq

uenc

y

2

45

4

6

8

10

12

14

46 47 48

Number of matches

49 50 51

c) 5 boxes




14

2 a)Number of hours Frequency

5 5

6 2

7 1

8 7

9 4

10 3

11 2

b)

0

Freq

uenc

y

1

5

2

3

4

5

6

7

6 7 8 9 10 11

Number of hours

c) 8 hours 3

0

Feq

uenc

y

2

0

4

6

8

10

12

14

16

1 2 3 4

Number of cars

4 a)

0

Freq

uenc

y

5

Pizza

Chines

e

Burg

er

Keba

b

Fish

& chips

Other

10

15

20

25

30

Type of fast food

b)

0

Freq

uenc

y

10

Car Van

Lorry Bu

s

Mot

orbik

eOth

er

20

30

40

50

Type of vehicle

c)

0

Freq

uenc

y

2

Oak

Beec

hPin

e

Syca

mor

eLim

eOth

er

4

6

8

10

12

Type of tree

5 a)

0

Freq

uenc

y

5

Blue

10

15

20

25

Red Green Yellow Pink Black OtherFavourite colour

b)

0

Freq

uenc

y

2

39

4

6

8

10

12

14

16

40 41 42 43 44 45 OtherShoe size




15

c)

0

Freq

uenc

y

0

5

10

15

1 2 3 4 ormoreNumber of sisters

6 a) 14 b) Dove c) 100 7 a) 100 b) 11 c) 6 8 a) 14 b) 45 c) 18

Exercise 25.1H (page 64) 1 12 cm 2 15 cm 3 23 cm 4 20 cm 5 20 cm

Exercise 25.2H (page 65) 1 a) 36 cm b) 30 cm c) 24 cm d) 24 cm 2 26 cm

Exercise 25.3H (page 67) 1 8 cm2

2 9 cm2

3 7 cm2

4 8 cm2

5 4 cm2

6 19 cm2

Exercise 25.4H (page 68) 1 12 to 14 cm2

2 38 to 43 cm2

3 10 to 11 cm2

Exercise 25.5H (page 69) 1 a) 18 cm3 b) 14 cm3

c) 18 cm3

2 40 3 168

Exercise 25.6H (page 70) 1 a) 12 cm2 b) 25 m2

c) 60 mm2 d) 3 km2

2 13.78 cm2

3 12.96 cm2

4 0.96 m2

5 a) 98 m2 b) £1176 6 15.12 cm2

Exercise 26.1H (page 71) 1 a) 87, 287, 708, 782, 1872, 2807 b) 48, 439, 843, 3047, 4389, 8372 c) 806, 1260, 10 086, 80 060, 100 000 2 a) 0.021, 0.249, 0.29, 0.902, 0.9402 b) 0.003 08, 0.0083, 0.083, 0.38, 0.803 c) 0.092, 0.0942, 0.409, 0.429, 0.9 3 a) 0.92, 6.347, 83.1, 762.53, 4270 b) 0.103, 1.003, 3.01, 13.01, 3100 c) 0.741, 4.017, 17.24, 70.14, 1472 4 a) 14 568 b) 86 541 5 a) 29–––

100, 0.3, 31–––100, 0.32, 0.33

b) 0.5, 0.54, 0.55,

56–––100, 57–––

100

c) 3 7––10, 3 72–––

100, 3.73, 3.78, 3.8

d) 8 4–––100, 8.39, 8.4, 8 43–––

100, 8.47

e) 0.25, 0.27, 28–––100, 3––

10, 0.35

f) 0.45, 0.46, 56–––100, 64–––

100, 0.65

Exercise 27.1H (page 72) 1 A(1, 4) B(3, 1) C(5, 3) D(1, −2) E(−3, −3)

F(−4, 0) G(−3, 4)

2

x

y

A

0

x

x

x

x

x

B

xF

xG

x H

C

D

E1

2

3

4

5

−5

−4

−3

−2

−11 2 3 4 5−5 −4 −3 −2 −1

3

x

y

1 2 3 4 5

A

0

x

x x

x

x

B C

D

E1

2

3

4

5




1616 OCR Mathematics for GCSE Specifi cation B © Hodder Education 2010


x

y

A

0

B

x

x

x

xC

D

1

2

3

4

5

−5

−4

−3

−2

−11 2 3 4 5−5 −4 −3 −2 −1

b) Kite

2 a)

x

y

A

0

B

x

x

x

x

C

D

1

2

3

4

5

−5

−4

−3

−2

−11 2 3 4 5−5 −4 −3 −2 −1

b) Parallelogram

3 a)

x

y

A

0

B

x

x

x

xC

D

1

2

3

4

5

−5

−4

−3

−2

−11 2 3 4 5−5 −4 −3 −2 −1

b) Trapezium

4 a), b)

x

yA

0

B

x

x

x

x

C

D1

2

3

4

5

−5

−4

−3

−2

−11 2 3 4 5−5 −4 −3 −2 −1

c) D(−5, 0)

5 a), b)

x

y

A

0

Bx

x

x

1

2

3

4

5

−5

−4

−3

−2

−11 2 3 4 5−5 −4 −3 −2 −1

c) Midpoint of AB (−1, 0)

6

x

y

A

0

B

x

x

x

xC

D

1

2

3

4

5

−5

−4

−3

−2

−11 2 3 4 5−5 −4 −3 −2 −1

D(−3, 3)




17

7

x

y

A

0

Bxx

x

xC

D

1

2

3

4

5

−5

−4

−3

−2

−11 2 3 4 5−5 −4 −3 −2 −1

C(1, −3)

8

x

y

A

0 B

x

x

x

xC

D

1

2

3

4

5

−5

−4

−3

−2

−11 2 3 4 5−5 −4 −3 −2 −1

D(−5, 2)

9

x

y

A

0

B

x

x

x

x

C

D

1

2

3

4

5

−5

−4

−3

−2

−11 2 3 4 5−5 −4 −3 −2 −1

D(−4, −3)

Exercise 28.1H (page 74) 1 £1.99 2 28 miles 3 £25 4 £1.98 5 a) (i) 55 mph (ii) 56.25 mph b) 40, 80, 120 km/h 6 a) 35p b) Australia, Germany, Ireland, Italy, Poland, Spain,

UK, United States c) 16 minutes

Exercise 28.2H (page 76) 1 a) £8.37 b) £1.63 2 a) 75p b) £1.25 3 200 g 4 80 g 5 50 6 750 kg 7 41.6 miles 8 5 km 9 82 miles10 95p11 45p12 205 km

Exercise 29.1H (page 77) 1 a) (i) 2 (ii) 4 b) (i) 7 (ii) 6 c) (i) 11 (ii) 14 d) (i) 2 (ii) 5 2 a) Erica 9, Julia 8 b) Erica 8, Julia 7.5 c) Erica – higher mode and median 3 a) 79 kg b) 87 kg 4 a) 2 b) 2

Exercise 29.2H (page 77) 1 Mean = 23.5 cm, range = 8 cm 2 Mean = 9, range = 8 3 Mean = 30.5, range = 9 4 Mean = 5, range = 7 5 Mean = 54 cm, range = 45 cm 6 Mean = 7, range = 4 7 Mean = 19, range = 5 8 Mean = £22 000, range = £10 000




18

Exercise 29.3H (page 78) 1 a) Catherine: mean 3.9, median 3.5, range 7 Mandy: mean 3.6, median 3.5, range 9 b) They have the same median but Catherine

scored slightly more goals; Catherine was more consistent.

2 a) Variety A: mean 9.6 cm, median 10 cm, range 5 cm Variety B: mean 9.4 cm, median 10 cm, range 6 cm b) There was little difference between them. Variety A was slightly taller on average, measured

by the mean, and had less variation in size. 3 a) Class R: mean 19.4 cm, median 19.5 cm, range

5 cm Class S: mean 17.4 cm, median 17.5 cm, range

5 cm b) The two classes had a similar spread, but

handspans in class R were 2 cm larger than those in class S.

4 ‘Most people pay about £400 for their water’ would be a more reasonable claim, as seven of the given values are in the £400 to £499 range. The mean value of £387 is actually below £400 but the median at £410 and the mode at £430 are above £400.

5 a) 9 b) 4 c) 7 d) 7 e) 8 f) The boys did better because fewer of them

scored lower marks, more of them scored middle and higher marks.


19


Found

ation B

ronze


Exercise 1.1H (page 80) 1 30° 2 70°, 70°, 40° 3

A B

D C

4 a) Equal (or the same size) b) Equal (or the same size)


b)

c)

d)

e)

f)

g)


20 OCR Mathematics for GCSE Specifi cation B © Hodder Education 2010 OCR Mathematics for GCSE Specifi cation B © Hodder Education 2010 20

h)

2 Yes, scale factor 2 3 a) This is not a 3 times enlargement (width is ×3

but height is not). b) This is a 3 times enlargement. 4 The biggest enlargement is 4 times. It will just fit

vertically and have space horizontally.

Exercise 2.1H (page 82) 1 a) 19, 22, 25 b) 59, 52, 45 c) 1.0, 1.2, 1.4 d) 43, 50, 57 e) 43, 49, 55 f) 57, 65, 73 g) 58, 67, 76 h) 46, 51, 56 2 a)

b) 6, 11, 16, 21, 26, 31 3 a)

4, 7, 10, 13, 16, 19 b)

9, 13, 17, 21, 25, 29

c)

10, 16, 22, 28, 34, 40 4 a)

b) Pattern 1 2 3 4 5

Squares 1 5 9 13 17

5 a)

x

x x x

x x x

x

x

x

x

x x x

x x x

x

x

x

x

x

x

x x x

x x x

x

x

x

x

x x x

x x x

x

x

x

x

x

b)Squares 1 2 3 4 5

Crosses 4 6 8 10 12

Exercise 2.2H (page 84) 1 a) 3 6 9 12 b) 26 24 22 20 c) 1 10 100 1000 d) 5 9 13 17 e) 1000 100 10 1 f) 12 6 3 1.5 2 a) Add 3; 15, 18, 21 b) Subtract 1; 96, 95, 94 c) Multiply by 2; 16, 32, 64 d) Subtract 0.5; 4, 3.5, 3 e) Subtract 6; 5, –1, –7 f) Subtract 7; –3, –10, –17 g) Subtract 5; –4, –9, –14 h) Subtract 6; –7, –13, –19 i) Subtract 8; –5, –13, –21 j) Subtract 13; –10, –23, –36 k) Add 4; 21, 25, 29 l) Subtract 5; 2, –3, –8 m) Multiply by 10; 100 000, 1 000 000, 10 000 000 n) Divide by 2; 11

2, 34, 38




21OCR Mathematics for GCSE Specifi cation B © Hodder Education 2010

3 a) 13, 31; Add 6 b) 23, 59; Add 12 c) 76, 58; Subtract 9 d) 91, 75; Subtract 4 e) 37, 52; Add 15 f) 27, –1; Subtract 7

Exercise 2.3H (page 84) 1 a) 4, 11, 18, 25, 32 b) 3, 12, 21, 20, 30, 39 c) 2, 15, 28, 41, 54 d) 63, 65, 67, 69, 71 e) 43, 47, 51, 55, 59 f) 16, 19, 22, 25, 28 2 a) 404 b) 334 b) 1292 d) 899 e) 538 f) 619

Exercise 3.1H (page 85) 1 51° 2 66° 3 52° 4 a = 75° b = 37° c = 35° d = 70° 5 a = 22° Angles in a triangle add up to 180°. b = 75° Angles in a triangle add up to 180°. c = 65° Equal angles in an isosceles triangle. d = 50° Angles in a triangle add up to 180°. e = 60° Angle in an equilateral triangle. f = 125° Angles in a triangle add up to 180°. g = 55° Angles on a straight line add up to

180°. 6 Check students’ sketches. PRQ = 72° 7 111° 8 a) Isoceles b) x = 43°, y = 43°

Exercise 3.2H (page 86) 1 i = 75° Angles in a quadrilateral add up

to 360°. 2 j = 115° Angles in a quadrilateral add up

to 360°. k = 65° Angles on a straight line add up

to 180°. 3 l = 115° Angles on a straight line add up

to 180°. m = 136° Angles in a quadrilateral add up

to 360°. 4 x = 360 � (145 � 82 � 63) = 70° 5 He is wrong because 90 � 45 � 86 � 131 = 352

and the angles of a quadrilateral must add up to 360°.

Exercise 4.1H (page 87) 1 a) (i) –2 (ii) 4 b) (i) 1 (ii) 4 2 a) (i) –3 (ii) 5 b) (i) 2 (ii) 0 and 4 3 a) (i) 20 (ii) 17 b) (–3, –7) and (2, 8)

Exercise 4.2H (page 89) 1 a) 1.7 km b) 50 minutes c) 1635 d) Going 2 a) 1 hour 30 minutes b) 45 minutes c) 1100 d) 180 km 3 a)

Dis

tanc

e fr

om h

ome

(km

)

20

10

5

0

Time of day0900 1000 1100 1200

15

25

1300

b) (i) 1 hour 45 minutes (ii) 44 km

Exercise 4.3H (page 90) 1 a) £40 b) 70 miles 2 a) Sunday b) 120 c) There is no such thing as ‘Monday-and-a-half’;

there is one data value for each day, and the dashed lines are just to show rough trends through the week.

3 a) £4 b) Pay As You Go: 60 minutes, Monthly plan: 80

minutes c) It is cheaper if you use the phone for a short

time (less than 50 minutes a month). You cannot run up a large bill without

realising it. d) It is cheaper if you use the phone for more

than 50 minutes a month.




4 a) £1200 b) £800 c) The interest is £400, or 50%, more with Online

Banking than with Street Cash, not double (100% or more), so the claim is wrong. The diagram is misleading because the vertical scale starts at £5500 and it shows the total value of the investment, not just the interest.

Exercise 5.1H (page 93) 1 a) p + 5 b) q + 2 2 a) x + 7 b) y + 11 3 a) 3p b) 4x 4 a) 2p + 3 b) 3a + 10 5 a) 8 − 2d b) y − 9

Exercise 5.2H (page 94) 1 s = 20r 2 p = 4l 3 c = a ÷ 2 4 e = s ÷ 5 5 t = 40w 6 a = lw 7 c = 30 + 2m 8 C = xy 9 P = 6x10 P = 80n11 K = 1.6m12 P = 4w + 16

Exercise 5.3H (page 95) 1 a) C = 24 b) C = 21 c) C = 42.72 2 a) D = 24 b) D = 6 c) D = 44.1 3 a) E = 144 b) E = 9 c) E = 164.43 4 a) X = 2 b) X = 3.7 c) X = 13.4 5 a) Y = 8 b) Y = 13 c) Y = 8.9 6 a) S = 6.5 b) S = 44 c) S = 5.4 7 a) F = 45 b) F = 1.25

c) F = 57.8

Exercise 5.4H (page 95) 1 a) A = 6 b) A = 6.8

c) A = 12 2 a) B = 17 b) B = 0

c) B = 18 3 a) P = 12 b) P = 8.8 c) P = 17.5 4 a) Q = 15 b) Q = 5.8

c) Q = 0

5 a) R = 2 b) R = 15 c) R = 8 6 a) F = 32 b) F = 27 c) F = 1.19 7 a) C = 38 b) C = 26.85

c) C = 1644 8 a) D = 130 b) D = 13

c) D = 36.9 9 a) P = 14 cm b) P = 27.6 cm10 a) A = 15 cm2 b) A = 7.8 cm2

c) A = 24 cm2

11 a) V = 64 cm3 b) V = 140.608 cm3

c) V = 3.375 cm3

12 a) Area = 15 cm2

b) Area = 2236 mm2

13 a) (i) S = 40 (ii) S = 50 b) Speed = 72 km/h14 a) C = 89a + 75m + 69d b) £9.44

Exercise 6.1H (page 97) 1 Check students’ patterns. Products: 30 × 1, 15 × 2, 10 × 3, 6 × 5 (5 × 6,

3 × 10, 2 × 15, 1 × 30) 2 a) 1, 2, 3, 4, 6, 9, 12, 18, 36 b) 1, 7, 49 c) 1, 3, 5, 15, 25, 75 d) 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 e) 1, 2, 4, 5, 10, 20, 25, 50, 100 3 a) 18, 24, 60 b) 25, 60 c) 24, 60 d) 24 e) 60 4 285, 627 and 969

Exercise 6.2H (page 97) 1 a) (i) 1, 2, 3, 4, 6, 12 (ii) 1, 2, 3, 6, 9, 18 (iii) 1, 2, 3, 4, 6, 9, 12, 18, 36 b) 1, 2, 3, 6 2 1, 3, 5, 15 3 a) 4, 12 b) 35 c) 12, 21 d) 17 4 a) 2, 18 b) 1, 2, 5 c) 15, 18 d) 2, 5, 17 5 a) 1, 3 b) 1, 5 c) 1, 2, 3, 6 6 13, 23, 43, 47 7 Two rows of 12; three rows of 8; four rows of 6; six

rows of 4; eight rows of 3; twelve rows of 2

Exercise 6.3H (page 98) 1 a) 9, 18, 27, 36, 45 b) 16, 32, 48, 64, 80 c) 30, 60, 90, 120, 150 d) 22, 44, 66, 88, 110 e) 14, 28, 42, 56, 70




2 a) 10, 20, 30 or other multiples of 10 b) 21, 42, 63 or other multiples of 21 c) 40, 80, 120 or other multiples of 40 d) 36, 72, 108 or other multiples of 36 e) 90, 180, 270 or other multiples of 90 3 a) 20 and/or multiples of 20 b) 12 and/or multiples of 12 c) 60 and/or multiples of 60 d) 30 and/or multiples of 30 e) 63 and/or multiples of 63 4 a) 36, 56, 60 b) 36, 45, 60, 63 c) 35, 45, 60 d) 35, 56, 63 e) 43, 61 5 Buywise – seven boxes of 8 gives 50 with 6 extra Writewell – five boxes of 12 gives 10 extra. He should buy from Buywise as there are fewer

extra pencils.

Exercise 7.1H (page 99) 1 a) 9 b) 16 c) 49 d) 81 e) 144 2 a) 2 b) 5 c) 6 d) 8 e) 11 3 a) 36 b) 1 c) 100 d) 25 e) 121 4 a) 7 b) 3 c) 9 d) 10 e) 1 5 a) 34 b) 31 c) 42 d) 60 e) 75 f) 289 g) 196 h) 324 i) 10 000 j) 1444

Exercise 7.2H (page 99) 1 28 2 41 3 40 4 27 5 65 6 21 7 110 8 112 9 30810 192

Exercise 7.3H (page 100) 1 a) 9 b) 36

c) 81 d) 121 e) 144 2 a) 64 b) 27

c) 125 d) 8 e) 1000

3 a) 43 b) 74

c) 39 d) 96

e) 27

4 a) 343 b) 8 c) 27 d) 1

e) 125 5 a) 16 b) 1

c) 1024 d) 2401 e) 256

Exercise 7.4H (page 100) 1 a) 121 b) 169 c) 324 d) 441 e) 900 2 a) 1000 b) 1728 c) 4096 d) 8000 e) 19 683 3 a) 4096 b) 248 832 c) 1 048 576 d) 130 321 e) 1 889 568 4 a) 390 625 b) 1 771 561 c) 279 936 d) 19 683 e) 512 5 a) 1 b) 16 384

c) 6561 d) 1 048 576 e) 1 048 576 6 a) 2.5921 b) 3.375

c) 479.61 d) 34 645.976 e) 3048.625 7 a) 2.0736 b) 19.4481 c) 6.859 d) 158.76 e) 97.656 25 8 a) 189 b) 121 c) 46.673 01 d) 16 e) 16.606 08

Exercise 8.1H (page 101) 1 125 cm3 2 120 cm3

3 a) 48.36 m3 b) 182.5 m3

4 240 cm3

5 23 040 cm3

6 80 000 cm3

7 78 125 mm3

8 a) 43 200 cm3 b) 0.0432 m3

9 4 cm10 1 000 000 ÷ 800 = 1250 blocks

Exercise 8.2H (page 102) 1 408 cm3 2 1330 cm3

3 422.55 cm3

4 798 cm3

5 1099 cm3

6 1098.24 cm3

7 100 m3




Exercise 9.1H (page 103) 1 Shape B 2 a) (i) S (ii) P (iii) F b)


2

3

4

5

6

Exercise 9.3H (page 105) 1 a) Shape C b) Shape B c) Shape E d) Shape D There is no net for Shape A.

Exercise 9.4H (page 106)The nets given here are not drawn to size but lengths are marked. Other nets are possible in most cases.

1 a)

4 cm

4 cm

3 cm

3 cm3 cm

3 cm

6 cm

b)

2 cm 2 cm 2 cm

2 cm

2 cm

5 cm

2 cm

c)

7 cm1 cm

1 cm1 cm

2 cm

2 cm

2 a) and c) 3 40 cm3

4 a) (i) K (ii) I b) MN 5

2 cm

3 cm

2 cm

2 cm

2 cm

3 cm

4 cm

6

6 cm

4 cm

1 cm1 cm

1 cm1 cm




7 Any 6 of these arrangements.

no no

yesyes

noyes

yes yes

yes yes noyes

Exercise 10.1H (page 108) 1 a) 3 b) 6 c) 1 d) 24 e) 18 f) 17

g) 514 h) 1470 i) 5638 j) 400 2 a) (i) 1070 (ii) 1100

(iii) 1000 b) (i) 23 630 (ii) 23 600

(iii) 24 000 c) (i) 8910 (ii) 8900 (iii) 9000 d) (i) 26 790 (ii) 26 800 (iii) 27 000 e) (i) 46 950 (ii) 47 000 (iii) 47 000 3 a) 2 000 000 b) 5 000 000 c) 3 000 000 d) 4 000 000 e) 1 000 000 4 a) 28 000 b) 27 600 5 £9

Exercise 10.2H (page 108) 1 a) (i) 80.9 (ii) 80.93 b) (i) 5.1 (ii) 5.12 c) (i) 4.4 (ii) 4.40 d) (i) 0.0 (ii) 0.03 e) (i) 649.0 (ii) 649.00 2 a) 0.83 b) 30.3 c) 4.90 d) 22.10 e) 1.36 3 26.9 cm2

4 38.81 cm2

5 £78.98

Exercise 10.3H (page 109) 1 a) 900 b) 300 c) 8000 d) 800 e) 900 f) 40

g) 6 h) 70 i) 100 j) 600 000 2 a) 7 b) 7 c) 50 d) 0.6 e) 0.9 f) 4000 g) 600 h) 0.06 i) 0.008 j) 0.0004

3 a) 19 b) 790 c) 7800 d) 79 000 e) 90 f) 0.31 g) 0.057 h) 0.0047 i) 0.031 j) 0.99 4 a) 7.39 b) 72.5 c) 19 100 d) 236 e) 17 900 f) 8.24 g) 67.1 h) 0.893 i) 0.0490 j) 2.72 5 600 people 6 a) 3 m b) 300 cm

Exercise 10.4H (page 109) 1 20 � 40p = 800p = £8 2 £20 � 4000 = £80 000 3 4 � 8 = 32 cm2

4 a) 30 � 5 = 6 cm b) Estimate is smaller than the actual length

because the numerator is reduced and the denominator is increased.

5 3 � 0.2 = 15 6 a) 6 � 7 = 42 b) 30 � 6 = 5 c) 50 � 30 = 1500 d) 8000 � 200 = 40 e) 300 � 0.3 = 90 f) 20 � 20 = 400 g) 900 � 200 = 4.5 h) 5 � 6 � 10 = 300 7 Number of tiles = 5 � 6 � 0.3 = 100

Exercise 11.1H (page 110) 1 a) 180 ml b) 75 ml 2 a) 200 g b) 600 g c) 1000 g or 1 kg 3 a) 24 cm b) 5 cm 4 a) 6 buckets b) 3 buckets 5 a) 20 litres b) (i) 3 litres (ii) 15 litres 6 a) 1500 g b) 1

2 teaspoon 7 2 : 1 8 a) 6 cm b) 180 cm

Exercise 11.2H (page 111) 1 300 g 2 a) £4000 b) £4500 3 a) 50 cm b) 24 cm 4 24 cm 5 108 cm 6 a) 150 g b) 13 people 7 a) 662 b) 6951

Exercise 12.1H (page 112) 1 a) 6112 b) 6811 c) 6517 2 a) 0229 b) 0425 c) 0722




In questions 3 and 4, points may be marked anywhere within the square or on the bottom or left-hand grid line.

3

70

71

72

73

74

75

40 41 42 43 44 45 46 47 48 49 50

76

77

78

79

80

P

R

Q

4

20

21

22

23

24

25

20 21 22 23 24 25 26 27 28 29 30

26

27

28

29

30

T

S

U

5 a) (i) 25 km (ii) 15 km (iii) 12.5 km b) (i) 8 cm (ii) 14 cm (iii) 7 cm 6 a) (i) 7731 (ii) 7232 (iii) 7740 b) (i) South-east (ii) Vicarage Road c) Rectory Gardens d) Go north along Broad Street. Turn right down

Rectory Gardens to the end. Turn right down High Street. Turn first left into Friar Street. The book shop is on the left.

e) Green Road 7 a) (i) 40 km (ii) 76 km (iii) 51 km (iv) 106 km (v) 28 km (vi) 50 km b) 33 cm

Exercise 12.2H (page 114)Allow ±1° in all answers that involve drawing. The diagrams are not full size. The measurements given are correct for the suggested scale. 1 A 045° B 122° C 255° D 328° 2

25°

123°

114°5 cm

5 cm

5 cm

Not fullsize

N

C

A

B

O

3 090° 4 225° 5 165° 6 330° 7

85°

5 km

N

BA

8 a) 084° b) 264° c) 122° d) 302° 9

40°

5 miles

6 miles

N N

A

B




10 a)

105°6 cm

10 cm

N

A

Not fullsize

C

B

b) (i) 214° (ii) 10.2 km

Exercise 13.1H (page 116) 1 x = 7 2 x = 6 3 x = 2 4 x = 1.6 5 x = 1.5 6 x = –2 7 x = 5 8 x = 2.5 9 x = 4 10 x = 211 x = 5 12 x = 1.513 x = 4.5 14 x = 0.815 x = 2.5

Exercise 13.2H (page 116) 1 x = 3 2 x = 9 3 x = 2 4 x = 6 5 x = 4 6 x = 3 7 x = 4.5 8 x = –1 9 x = 4 10 x = 7

11 x = 223 12 x = 4.5

13 x = 1.5 14 x = 415 x = 3.5

Exercise 14.1H (page 117)A range is given for each answer. Anything in the range is acceptable. 1 150 to 170 m2 2 3600 to 4000 m2

3 650 to 750 m2

4 75 000 to 90 000 m2

5 90 to 110 m 6 1100 to 1500 m 7 a) 12 to 15 km b) 575 to 675 km2

Exercise 15.1H (page 119)A range of 2° is acceptable in the drawing. All the pie charts need to be labelled. 1

Purple

24°

Orange

36° Green

48°

Yellow

84°

Red

108°

Blue

60°

2

30°

15°Eating

Homework

Playingand

watchingTV

Travel

School

Sleeping

120°

90°

90°

15°

3

78° 108°

84°42°30°

Horse 18°

Dog

CatOther

Bird

Rabbit

4

60°

90°165°

30°

15°

Black

Blonde

BrownRed

Other




5

80°

136°88°

56°

Entertainment

Travel

Accommodation

Foodanddrink

6

18°

100.8°

93.6°68.4°

79.2°

Train

Walk

BusCycle

Car

Exercise 15.2H (page 121) 1 School lunch 20, Sandwiches 6, Chips 4 2 a) 1

4 b) 0–9 14; 10–19 20; 20–29 35; 30–39 28;

40–49 37; 50–59 45; 60–69 65; 70 andover 31 (all ±1)

3 0.77 million or £777 000 (± £5000) 4 a) 36 ± 1 b) 6 ± 1 5 a) The Daily Mail b) The Sun, Magazines and Other newspapers c) 12 (±1)

Exercise 16.1H (page 124) 1 a) 3

4 = 68 = 912 = 30

40

b) 45 = 8

10 = 1215 = 36

45

2 a) 34 = 15

20 b) 1521 = 57

c) 12 = 11

22 d) 1860 = 3

10

e) 1618 = 89

3 a) 45 b) 5

6

c) 34 d) 1

2

e) 35 f) 1

3

g) 58 h) 3

4

i) 411 j) 2

5


2 b) 313

c) 218 d) 15

9

e) 345 f) 13

7

g) 157 h) 51

2

i) 314 j) 32

3

2 a) 97 b) 13

8

c) 152 d) 11

4

e) 175 f) 14

5

g) 299 h) 29

6

i) 418 j) 13

3

3 a) 145 b) 12

3

c) 116 d) 1

4

e) 112 f) 2

5

g) 123 h) 11

3

i) 1 211 j) 11

3

Exercise 16.3H (page 125) 1 a) 8, 78 b) 99, 7

11

c) 60, 16 d) 15, 45 e) 70, 3

10 f) 24, 23

2 a) 516

38

12

916

34

b) 49

1936

712

34

56


3 = 69 = 1015 = 24

36 2 a) 3

4 b) 110

c) 38 d) 2

5 3 a) 5

7 b) 1115

c) 511 d) 3

17

e) 1016 = 58 f) 11

9 = 129

g) 212 = 16 h) 13

11 = 1 211

4 a) 69 = 23 b) 7

10

c) 920 d) 19

30

e) 1324




5 a) 28 = 14 b) 3

8 c) 5

24 d) 1124

e) 940

6 a) 59 b) 10

12 = 56 c) 13

20 d) 716

e) 2924 = 1 5

24 f) 4930 = 1 19

30

g) 1124 h) 24

20 = 115

i) 6855 = 1 13

55 j) 7760 = 1 17

60

k) 1724 l) 19

60 7 a) 3

20 b) 1124

c) 4760

8 415


2 b) 16

c) 0

2 23 or 46

3 a) 815 b) 7

15 c) 0

4 a) 13 or 39 b) 2

3 or 69 5 1

150 6 a) 1

5 or 210 b) 3

10

c) 12 or 5

10 7 a) 9

30 or 310 b) 8

30 or 415

c) 1330

8 a) 111 b) 2

11 c) 0

9 a) 2652 or 12 b) 4

52 or 113

c) 1252 or 3

13 10 a) 12

72 or 16 b) 1572 or 5

24 c) 45

72 or 58 d) 1872 or 14


Number Letter

1 A

1 B

2 A

2 B

3 A

3 B

2 Gill Chloe

R R

R T

R G

T R

T T

T G

G R

G T

G G

3 a)

b) 836 = 29

4 1st Course 2nd Course

Soup SB

Soup LB

Soup C&MP

Melon SB

Melon LB

Melon C&MP

1 2 3 4 5 6

0 1 2 3 4 5

1 0 1 2 3 4

2 1 0 1 2 3

3 2 1 0 1 2

4 3 2 1 0 1

5 4 3 2 1 0

1

2

32nd dice

1st dice

4

5

6




5 a) 116 b) 4

16 = 14 6 a)

b) (i) 120 (ii) 4

20 = 15 (iii) 10

20 = 12 (iv) 620 = 3

10 7 a)

b) (i) 12 (ii) 312 = 14

8 16

Exercise 18.1H (page 129) 1 Square, rectangle, parallelogram, rhombus 2 Rectangle 3 Square, rhombus 4 Kite 5 Isosceles trapezium 6 a) Trapezium b) Kite c) Parallelogram d) Rectangle 7

8 Isosceles tapezium

Exercise 19.1H (page 130) 1 4a 2 2a 3 abc 4 y2

5 3p � 4r 6 2c 7 5x � 4y 8 7a � 2b 9 4a � b 10 2y � 3s11 a3b2 12 12xy13 10x 14 3ab � 3ac15 6ab 16 3x � 2y17 6a � 3b 18 a � 2b19 2a2 � 9a 20 4p � 3q � 421 10a

Exercise 19.2H (page 130) 1 5p � q 2 5x2 � 4x 3 Cannot simplify 4 2ab � 3ac 5 7x � 3y � 6z 6 3a2 � 5ab � 4b2

7 6a � 3b 8 6 � a � b � c 9 9ab � 6ac10 –2a2 � ab11 7a2 � 3ab

Exercise 20.1H (page 131) 1 a) Mean 8.8, median 8, mode 7 b) Mean 14.7, median 15, mode 11 c) Mean 74.5, median 73.5, mode 73 2 a) Mean 3139 (3138.8), median 3147, range 1168 b) 7 3 Greg is, on average, faster, as his mean and

median are greater, but Pete is more consistent as his range is less.

4 Jenny did better overall, shown by a higher mean, median and mode. She also had a lower range, showing she had a smaller range of marks and therefore had no low marks.

5 Spearman scored higher on average, shown by a higher mean and median. However Johnson had a higher range, suggesting that his highest score was greater than Spearman’s.

6 a) Alice: median 15.5, range 18 Bob: median 15.5, range 25 b) On average, they did about the same. Bob’s scores were more variable, showing that

Alice was more consistent. 7 Seashore: mean = 8.96, median = 8.7, range = 5.9 Cliff Top: mean = 2.88, median = 2.0, range 9.8 Seashore is, on average, more sunny, as shown by

a higher mean and median. Cliff Top has more variable amounts of sun, as

shown by a higher range.

Exercise 21.1H (page 133) 1 –2 2 3 3 2 4 –2 5 –1 6 7 7 2 8 0 9 –3 10 311 –5 12 –113 –1 14 –1115 –5 16 –717 –1 18 –119 –3 20 –2

1 2 3 4 5

2 3 4 5 6

3 4 5 6 7

4 5 6 7 8

5 6 7 8 9

1

2

32nd spinner

1st spinner

4

1 2 3 4 5 6

T

Hcoin

Dice




Exercise 21.2H (page 133) 1 3 2 –1 3 2 4 1 5 –2 6 –1 7 1 8 0 9 510 –411 a) –4°C b) (+) 3°C

Exercise 21.3H (page 134) 1 6 2 –40 3 12 4 –24 5 –35 6 –21 7 20 8 –4 9 –5 10 –511 4 12 513 –5 14 –815 –3 16 –217 –18 18 –319 6 20 –15

Exercise 21.4H (page 134) 1 –26 2 10 3 1 4 24 5 –3 6 –9 7 4 8 1 9 –2110 –1


3, 1725 , 7

10 , 72%, 0.84

2 16.9%, 725 , 0.29, 30%, 13

3 825 is 32% so more support Manchester United.

4 Aftab (65%) answered more correct than Jamil (63%).

5 320 = 0.15, 16 = 0.167, so Welton had rain on

more days. 6 Purslane Academy (0.354); Bridge Grammar School

(0.34); Denby High School (0.323)

Exercise 22.2H (page 135) 1 14 2 4.2 3 252 m 4 £1071

5 282 km 6 £3.24 7 7.98 8 £1440 9 £6210 £38611 Iain paid £6210, Clare paid £6080. Iain paid £130

more.

Exercise 23.1H (page 136) 1 a) Rotation symmetry of order 2 about the centre b) No rotation symmetry (rotation symmetry of

order 1) 2 a) Order 2 b) Order 6 c) Order 1 d) Order 2 e) Order 2 f) Order 4 g) Order 1 h) Order 1 i) Order 8 j) Order 5 k) Order 3

Exercise 23.2H (page 137) 1 Rotation symmetry of order 4, no line symmetry 2 No rotation symmetry (rotation symmetry of order 1)

3 Rotation symmetry of order 4

4 Rotation symmetry of order 2, no line symmetry 5 No rotation symmetry (rotation symmetry of order 1)




6 Rotation symmetry of order 6

7 No rotation symmetry (rotation symmetry of order 1)

8 No rotation symmetry (rotation symmetry of order 1)

Exercise 23.3H (page 138) 1 Check students’ diagrams 2 Check students’ diagrams 3

4





1Foundation Initial and

Foundation Bronze

Series Editor:Brian SeagerHoward Baxter Mike Handbury John Jeskins Jean Matthews Colin White

OCRMathematics

Homework Book Answers

GCSE Bfor

I S BN 978-1-444-13678-4

9 7 8 1 4 4 4 1 3 6 7 8 4

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