answers to homework book 6 - hamilton maths blog · pdf file252 graduated assessment for ocr...

Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007252

Answers to Homework Book 6

STAGE

6

1 Using a calculatoreffectively

Exercise 1.1H (page 1)1 a) 21 b) 20

c) 21 d) 1002 a) 3 b) 20

c) 24 d) 643 a) 8 b) 7

c) 1 d) 104 a) 2 b) 5

c) 6 d) 235 a) 16 b) –5

c) –32 d) 45 6 27·6 7 42·54 8 8·639 6·5

10 24·54

Exercise 1.2H (page 2)1 –1·7 2 –21·243 0·56 4 –1·675 1·37 6 2·457 41·67 8 0·399 7·03 10 39·54

Exercise 1.3H (page 2)1 104·858 2 0·8723 49·215 4 5·8405 7·963 6 22·097 46·53 8 490·9129 4·347 10 2·626

Exercise 1.4H (page 3)1 a) b)

c) d)

e)

2 a) 5 b) 18c) 200 d) 72e) 27

3 a) 0·5 b) 0·2c) 0·625 d) 10e) 0·04

4 a) 1 b) 2

c) 1 d)

e)

Exercise 1.5H (page 3)1 14 m 44 cm2 62 kg 421 g3 38 minutes 44 seconds4 3 m5 4 kg 957 g6 23 hours 40 minutes7 a) 3·5 hours b) 4·25 hours

c) 1·7 hours d) 2·4 hours8 a) 6 minutes 12 seconds

b) 14 minutes 45 secondsc) 8 minutes 48 secondsd) 54 seconds

Exercise 1.6H (page 4)1 17·3 m2 3·3 kg3 1·3 m or 1·30 m4 £1·405 1·76 m6 £15·14

2 Brackets and factors

Exercise 2.1H (page 5)1 21a + 42b2 10c + 15d3 12e – 20f4 21g – 6h5 12i + 6j – 9k6 15m – 6n + 9p7 24r – 18s – 12t8 32r + 16s + 8t9 12u + 20v

10 24w + 18x11 10y + 2z12 12y + 8z13 15v + 1014 21 + 12w15 5 – 15a16 24g – 15

3–5

5––12

3–5

1–2

1–3

1––16

1–––100

1––90

1––12

1–7

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Graduated Assessment for OCR GCSE Mathematics © Hodder Murray 2007 253

Answers to Hom

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STAGE

6

Exercise 2.2H (page 5)1 4(2x + 5) 2 3(x + 2)3 3(3x – 4) 4 5(x – 6)5 8(2 + x) 6 3(3 + 5x)7 4(3 – 4x) 8 4(2 – 3x)9 4x(x + 4) 10 6x(x + 5)

11 4x(2x – 5) 12 3x(3x – 5)

3 Angles

Exercise 3.1H (page 6)1 65°2 a = 143°, b = 74°, c = 126°3 a = 138°, b = 42°, c = 138°4 a = 33° Angles on a straight line add up to 180°.

b = 159° Angles at a point add up to 360°.c = 139° Angles on a straight line add up to 180°.d = 41° Opposite angles at a point are equal.

5 89°

Exercise 3.2H (page 7)1 a = 70° Alternate angles are equal.

b = 82° Corresponding angles are equal.c = 56° Allied angles add up to 180°.

2 d = 59°, e = 80°, f = 41°

3 e.g.

4 a = 69°, b = 33°, c = 78°

5

Exercise 3.3H (page 8)a = 120°, b = 75°, c = 116°, d = 137°, e = 130°, f = 130°, g = 110°, h = 80°

Exercise 3.4H (page 9)1 72°2 70°3 47°4 Exterior angle = 360° ÷ 8 = 45°;

interior angle = 180° – 45° = 135°

5 a) 540°b) 120°

4 Probability

Exercise 4.1H (page 10)1 0·1 2 0·253 0·45 4 0·15 0·3 6 0·217 0·27 8 0·17

5 Translations

Exercise 5.1H (page 12)1

2

3 a) A translation by vector ( )b) A translation by vector ( )c) A translation by vector ( )d) A translation by vector ( )–6

–2

–1–2

3–3

50

0–1–2–3

1

2

3

4

5

1

C

2 3 4 5–2–3 –1 x

y

A

B

D

0–1–2–3–4–5–6

1234567D8

1 2 3 4 5 6 7 8 9 10–3–4 –2 –1 x

y

A

BE

C

131°

131°49°

49°BA

CD

x

x

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6STAGE

4 a) A translation by ( )b) A translation by ( )c) A translation by ( )d) A translation by ( )

6 Fractions

Exercise 6.1H (page 15)1 a) 8, b) 99,

c) 60, d) 15,

e) 70, f) 24,

2 a)

b)

Exercise 6.2H (page 15)1 = = =

2 a) b)

c) d)

3 a) b)

c) d)

e) = f) = 1

g) = h) = 1

4 a) = b)

c) d)

e)

5 a) = b)

c) d)

e)

6 a) b) =

c) d)

e) = 1 f) = 1

g) h) = 1

i) = 1 j) = 1

k) l)

7 a) b)

c)


c) 5 d) 2

2 a) 2 b) 1

c) 3 d) 7

e) 2

3 a) 2 b) 2

c) 2 d) 2

e) 1

4 a) 7 b) 5

c) 5 d) 3

e) 6 f) 4

g) 8 h)

i) 8 j) 3

k) 4 l)

7 Plans and elevations

Exercise 7.1H (page 18)1 Plan

Side elevation

Front elevation

2 Plan

Side elevation

Front elevation

1–2

11––18

7––12

1––28

17––48

13––40

13––18

1––12

9––16

5–8

2–9

7––12

7––10

9––10

1–8

11––24

1–2

7––30

1––10

4–5

17––20

1–4

3–4

5––13

2–3

5–7

47––60

11––24

3––20

19––60

17––24

17––60

77––60

13––55

68––55

1–5

24––20

11––24

19––30

49––30

5––24

29––24

7––16

13––20

5–6

10––12

5–9

9––40

11––24

5––24

3–8

1–4

2–8

13––24

19––30

9––20

7––10

2–3

6–9

2––11

13––11

1–6

2––12

2–9

11––9

5–8

10––16

3––17

5––11

11––15

5–7

2–5

3–8

1––10

3–4

24––36

10––15

6–9

2–3

5–6

3–4

7––12

19––36

4–9

3–4

9––16

1–2

3–8

5––16

2–3

3––10

4–5

1–6

7––11

7–8

–107

10–7

2–9

–8–2



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STAGE

6

3 Plan

Side elevation

Front elevation

4 Plan

Side elevation

Front elevation

5 Plan

Side elevation

Front elevation

6 Plan

Side elevation

Front elevation

7 Plan

Side elevation

Front elevation


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8 Ratio

Exercise 8.1H (page 20)1 a) 4 : 3 b) 2 : 5

c) 7 : 11 d) 1 : 3 : 4e) 3 : 5 : 4

2 a) 2 : 5 b) 1 : 5c) 12 : 5 d) 5 : 2e) 1 : 6

3 2 : 14 4 : 7 : 95 1 : 2 : 5

Exercise 8.2H (page 21)1 a) 1 : 5 b) 1 : 6

c) 1 : 4·5 d) 1 : 2·25e) 1 : 0·6 f) 1 : 20g) 1 : 24 h) 1 : 0·35i) 1 : 25 000

2 1 : 250 0003 1 : 6

Exercise 8.3H (page 21)1 a) 250 ml b) 200 ml2 a) 75 cm b) 9 cm3 a) £600 b) £1004 a) 25 litres b) 210 ml5 a) 50 km b) 16·5 cm6 480 g7 a) 125 ml b) 80 ml8 a) 10 cm b) 3 cm

Exercise 8.4H (page 23)1 Paula £15, Tom £252 £520 : £650 : £7803 £12·604 Sue £14 000, Jane £21 000, Christine £35 0005 Sand 10 kg, cement 2 kg6 1·5 litres7 Copper 150 g, iron 200 g, nickel 100 g8 3 hours 30 minutes9 £2·50

10 72

9 Solving equations

Exercise 9.1H (page 24) 1 x = 32 x = 53 x = 44 x = 105 x = 6

Exercise 9.2H (page 24)1 x = 8 2 x = 33 x = 7 4 x = 25 x = 5 6 x = 67 x = 8 8 x = 39 x = 11 10 x = 1·5

11 x = 3 12 x = 313 x = 5·5 14 x = 4·515 x = 3·5

Exercise 9.3H (page 25)1 x = 3 2 x = 43 x = 2 4 x = 105 x = 3 6 x = 17 x = 1 8 x = 39 x = 3 10 x = 3

11 x = 4·5 12 x = 513 x = 2 14 x = 215 x = –3

10 Powers and indices


c) 26 d) 53

2 a) d 7 b) m6

c) t7 d) a4

3 a) a4b2 b) c4d5

c) r3s2t4 d) m2p3t2

4 a) 36x3 b) 6a3

c) 6y3 d) 40a4

5 a) 52 + 32 b) 23 + 32

c) 62 – 22 d) 73 – 53

Exercise 10.2H (page 27)1 a) (i) 5 (ii) –3

b) (i) 5 (ii) –7c) (i) 3 (ii) 3d) (i) 10 (ii) 15e) (i) 11 (ii) 11

2 a) A = 2·5 b) B = 7c) C = 8 d) D = 12e) E = 47 f) F = 0·5

11 Circles

Exercise 11.1H (page 28) 1 a) 25·1 cm b) 53·4 cm

c) 123·2 cm d) 364·4 mme) 16·0 m f) 19·9 mg) 44·0 cm h) 72·3 cm



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2 a) 490·1 mm b) 245·0 mmc) 27·6 m d) 17·3 m

Exercise 11.2H (page 28)Students may give answers to a different accuracyfrom these answers.

1 a) 908 cm2 b) 1662 cm2

c) 14 103 cm2 d) 5809 mm2

e) 17 203 mm2 f) 3217 cm2

g) 10 568 cm2 h) 58·1 cm2

2 a) 254 cm2 b) 616 cm2

c) 3632 cm2 d) 1134 mm2

e) 4778 mm2 f) 2642 cm2

g) 1662 cm2 h) 32·2 cm2

12 Scatter diagrams


2

Exercise 12.2H (page 30)1 The data in question 1 show positive

correlation.The data in question 2 show negativecorrelation.

2 a)

b) Positive correlationc) (i) 63 (ii) 70

3 a)

b) No correlationc) Nothing

0

2530354045505560657075808590

14 18 22Temperature (°C)

Rain

fall

(mm

)

26 30

0

40

45

50

55

60

65

70

75

80

85

40 45 50 55 60English

Geo

grap

hy

65 70 75 80 85

0

2

4

6

8

10

12

14

16

18

20

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

y

0

20

22

24

26

28

30

32

34

36

38

40

42

2 4 6 8 10 12 14 16 18 20 x

y


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13 Rotations

Exercise 13.1H (page 32)1 a)

b)

2 a)

b)

3 a)

b)

Exercise 13.2H (page 34)1 a), c)

b) Rotation 90° clockwise about (5, 5)c) Rotation 180° about (0, 3)

2 a), b)

c) Rotation 180° about (–3, 1)

3 a) Rotation 90° clockwise about (0, 0)b) Rotation 90° anticlockwise about (4, 5)c) Rotation 180° about (0, 3)d) Rotation 90° anticlockwise about (0, 0)

0–1–2–3–4–5

123456

1 2 3 4 5 6–1–2–3–4–5–6–7 x

y

A

B

–6

0–1–2–3–4

1234567

1 2 3 4 5 6 7 8–1–2–3–4–5–6 x

y

B

A

T

0

1234567

1 2 3 4 5 6–1–2–3–4–5 x

y

0

1234567

1 2 3 4 5 6–1–2–3–4–5 x

y

0–1–2–3–4–5

123456

1 2 3 4 5 6–1–2–3–4–5 x

y

–6

–6

0–1–2–3–4–5

123456

1 2 3 4 5 6–1–2–3–4–5 x

y

–6

–6

0–1–2–3–4–5–6

123456

1 2 3 4 5 6 7–1–2–3–4–5 x

y

0–1–2–3–4–5

123456

1 2 3 4 5 6 7–1–2–3–4 x

y

–5



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STAGE

6

14 Multiplying anddividing fractions

Exercise 14.1H (page 37)1 2 2 3

3 4 2

5 6 24

7 8

9 10

11 12

13 14

15 16

17 18

19 1 20

21 22

23 24

25 1 26

15 Decimals

Exercise 15.1H (page 38)1 a) £9·60 b) £6·03

c) £14·25 d) £3·29e) £5·31

2 a) 13·02 b) 97·55c) 108·95

3 a) 13·03 b) 31·74c) 172·33

4 a) £6·34 b) £20·01c) £164·92 d) £70·74

5 5·68 m6 5·37 seconds7 £7·11


c) 3260 d) 1252 a) 2·14 b) 1·725

c) 0·623 d) 0·005 143 a) 17·2 b) 993

c) 19 500 d) 28·74 a) 1·62 b) 5·847

c) 0·183 d) 0·006 41

Exercise 15.3H (page 40)1 a) 4·8 b) 1·15

c) 920 d) 3e) 0·028

2 a) 24·91 b) 24 910c) 0·2491 d) 2·491e) 249 100

3 a) 2·4 b) 1·4c) 1·5 d) 7·2e) 0·04 f) 0·56g) 35 h) 24i) 0·12 j) 0·06k) 0·49 l) 0·04

4 a) 5·04 b) 15·08c) 34·83 d) 20·8e) 125·8 f) 243·2

5 £80·706 a) 1·35 kg b) £2·977 £2·168 £5·30

Exercise 15.4H (page 41)1 a) 4·1 b) 18·1

c) 3·1 d) 41·4e) 1·09

2 a) 3·64 b) 8·435c) 2·325 d) 14·64e) 16·13

3 a) 0·4 b) 0·375c) 0·75 d) 0·65e) 0·175

4 a) 0·875 b) 0·07c) 0·556 d) 0·182


c) 4 d) 18e) 30 f) 40g) 30 h) 50i) 80 j) 160k) 3·1 l) 95

2 a) 59 b) 29·25c) 26 d) 52e) 47 f) 63g) 17·6 h) 10·8i) 316 j) 5·7k) 2·7 l) 6·3

1–9

17––25

27––28

7––32

7––10

3––28

20––99

1–8

5–6

14––45

5––48

10––21

1–3

5––12

1–2

2–3

2–5

1–2

1––20

3––20

1––18

8––11

3––20

1–3

1–7


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16 Linear graphs


2

3

4

5


2

0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10 x

y

x + 2y = 10

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 x

y

x + y = 10

0–2

2

4

6

8

10

1 2 3 4–2 –1 x

y

y = 6 – 2x

0–2–4–6–8

2

4

6

8

10

1 2 3 4–2 –1 x

y

y = 3x – 2

0–1–2–3

1

2

3

4

5

6

y = 2x + 3

7

8

9

1 2 3–3 –2 –1 x

y

0–1–2–3–4–5–6

1

2

3

4

5

6

y = 2x

1 2 3–2–3 –1 x

y

0–1–2–3–4–5

1

2

3

4

5

y = 4

x = 2x = –4

y = –3

1 2 3 4 5–2–3–4–5 –1 x

y



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6

3

4

5

17 Real-life graphs

Exercise 17.1H (page 44)1 a) AB and CD

b) 11:50c) 16 miles

2 a) Imran walked 1 kilometre in 20 minutes.He stopped for 5 minutes and thentravelled the remaining 9 kilometres in 9 minutes. (Perhaps he got a lift or caught a bus.)

b) 32 minutesc) 6 minutesd) 0·25 kilometres per minute

3 a) 8:30 a.m.b) 8°Cc) Between about 12:30 p.m. and 1:00 p.m.d) 5 hours

4

18 Drawing triangles andother shapes

Exercise 18.1H (page 47)1 a) Check students’ drawings.

b) Angle A = 63°2 a) Check students’ drawings.

b) AB = 5·4 cm3 a) Check students’ drawings.

b) BC = 7 cm4 a) Check students’ drawings.

b) Angle YXZ = 44°5 a) Check students’ drawings.

b) BD = 13·3 cm

Exercise 18.2H (page 49)1 Check students’ drawings.

Exercise 18.3H (page 49)1 a), d) and e)2 Various nets are possible, such as in this

diagram.

5

5

3 33 3

3 3

4 4

4 4 44

0

5

15

25

10 20 30 40 50Time (seconds)

Hei

ght

(m)

60 70 80 90 100 x

y

0–1–2–3–4–5

1

2

3

4

1 2 3 4–2 –1 x

y

2y = 3x – 4

0

1

2

3

4

1 2 3 4 5 6 x

y

2x + 6y = 12

0

1

2

3

4

5

1 2 3 4 5 x

y

3x + 4y = 12


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3

4 Sketch of net for pyramid, such as in thisdiagram.

19 Area and perimeterExercise 19.1H (page 51)

1 a) 6 cm2 b) 5 cm2

c) 6 cm2 d) 10 cm2

e) 4·25 cm2 f) 7 cm2

g) 8·1 cm2 h) 17·01 cm2

2

Area = 10·5 cm2

Exercise 19.2H (page 52)1 a) 12 cm2 b) 10·8 cm2

c) 6·48 cm2 d) 22·68 cm2

2 a) x = 4 cm b) y = 3·2 cmc) z = 3·5 cm

Exercise 19.3H (page 53)1 a) 9 cm2 b) 13·5 cm2

c) 11 cm2 d) 18 cm2

2 a) x = 4 cm b) y = 5 cm

Exercise 19.4H (page 54)1 a) 24·6 cm b) 14·9 cm

c) 21·2 cm2 a) (i) 12 m (ii) 7·16 m2

b) (i) 18·4 m (ii) 13·48 m2

c) (i) 20·8 m (ii) 22·26 m2

3 a) 20 cm2 b) 26 cm2

c) 15·5 cm2

4 a)

b) 28·5 squares

5 a)

b) 33 squares

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5

B

C

D

E

A

6 7 8 x

y

0

1

2

3

4

5

6

7

8

1 2 3 4 5B

C

D

A

6 7 8 9 x

y

0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 x

y

14 cm

14 cm

12 cm12 cm

12 cm12 cm

12 cm

12 cm

12 cm

12 cm

Not full size

4 cm 4 cm

4 cm 4 cm4 cm4 cm

4 cm

4 cm

4 cm



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20 Volume and surface areaExercise 20.1H (page 56)

1 a) 125 cm3 b) 150 cm2

2 a) 150 cm3 b) 190 cm2

3 a) 72 m3 b) 60 m2

4 a) 360 cm3 b) 324 cm2

5 a) (i) 60 cm3 (ii) 336 cm3

b) (i) 94 cm2 (ii) 292 cm2

6 43 to 44 cm2

Exercise 20.2H (page 57)1 408 cm3 2 1330 cm3 3 422·55 cm3 4 798 cm3

5 1099 cm3 6 1098·24 cm3

21 Organising dataExercise 21.1H (page 58)

1 a) 0 5 61 1 2 2 7 82 1 2 3 3 3 4 7 8 8 93 1 1 2 4 7 7 7 7 74 1 2 3 7

Key: 4 2 represents 42

b) (i) Median = 28(ii) Mode = 37

2 a) Men Women2 1 7 2 33 7 9 3 3 74 7 7 7 8 4 0 1 2 4 95 1 2 7 8 5 1 2 2 2 3 46 1 1 2 2 4 5 9 6 1 1 2 3 4 4 77 3 4 6 7 7 1 78 1 2 8 2 4

Key: 3 7 represents 37

b) Median: men = 61, women = 533

3 15 6 916 1 2 2 3 3 4 5 5 6 7 8 8 9 917 0 0 2 2 3 3 3 4 4 4 5 5 6 6 7 7 8 8 8 9 918 0 0 1 2 2 4 4 5 5 6 819 1 4

Key: 19 4 represents 194 cm


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Exercise 21.2H (page 59)1 a) (i) 5 (ii) 9 (iii) 4·16

b) (i) 100 (ii) 6 (iii) 100·875c) (i) 1 (ii) 6 (iii) 1·64d) (i) 1 (ii) 7 (iii) 2·09

2 £8·203 1·3275

Exercise 21.3H (page 62)1 a)

b) 75 � w � 80c) 75 � w � 80

2 a) 5 b) 40c) 30% d) 8 � t � 9 minutes

e)

3

4

22 Enlargement


2

3

4 a) 4 b) 3c) 3 d) 2

5 a) No: the width of the smaller square hasbeen enlarged by scale factor 2, the lengthhas not.

b) No: the width of the shape has beenenlarged by scale factor 3, the length byscale factor 2.

6 a) (i) 2 (ii) (–1, 4)b) (i) 3 (ii) (9, 5)

7 Enlargement, scale factor 3, centre the origin

Exercise 22.2H (page 67)1 a), b)

c) An enlargement with scale factor 3, centrethe origin

0

2 B

A

4

6

2 4 6 x

y

O

0

1234567

1 2 3 4 5 6 7 8 9 10 11 12 x

y

10

0

20

30

40

5 10 15Time (minutes)

Freq

uenc

y

20 25 30

5

0

10

15

3 4 5 6Height (cm)

Freq

uenc

y

7 8 9

Time (t minutes) Frequency

5 � t � 6 3

6 � t � 7 9

7 � t � 8 10

8 � t � 9 13

9 � t � 10 5

10

0

20

30

40

50

60 65 70 75Weight (kg)

Freq

uenc

y

80 85 90



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6

2 a), b)

c) An enlargement with scale factor 2, centre (3, 2)

3 a), b)

c) An enlargement with scale factor , centre the origin

4 a), b)

c) An enlargement with scale factor , centre (1, 2)

5 a) An enlargement with scale factor 2, centrethe origin

b) An enlargement with scale factor , centrethe origin

c) An enlargement with scale factor 3, centre(0, 3)

d) An enlargement with scale factor , centre(0, 3)

23 Transformations


2

3 a)

b)

c)

0–1–2–3

1

2

3

1

C

BA

D

2 3–2–3 –1 x

y

0

–2

2

4

2

A

DC

B

4–2 x

y

1–3

1–2

1–3

0

1

2

3

4

5

6

7

1 2 3

A

B

4 5 6 7 x

y

2–5

0

1

2

3

4

5

6

7

8

1 2 3

A

B

4 5 6 7 8 x

y

0

2

B

A

4

6

2 4 6 x

y


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4 a) A reflection in the line y = 2b) A reflection in the line y = xc) A reflection in the line x = 3·5

5 a) A reflection in the line y = 0·5b) A reflection in the line y = –xc) A reflection in the line y = 1·5


2

3

4 a) A rotation of 180° about the originb) A rotation of 90° clockwise about (2, 1)c) A rotation of 90° clockwise about (1, 0)

5 a) A rotation of 90° anticlockwise about theorigin

b) A reflection in the line x = 2c) A rotation of 180° about (1, 0)d) A rotation of 90° clockwise about (1, –1)e) A reflection in the line y = –1

6

7 a) A translation by vector ( )b) A translation by vector ( )c) A translation by vector ( )d) A translation by vector ( )

8 a) A reflection in the y-axisb) A rotation of 180° about the originc) A rotation of 90° anticlockwise about the

origind) A translation by vector ( )

9 a) A translation by vector ( )b) A reflection in the line x = –1c) A rotation of 90° anticlockwise about the

origin

d) A translation by vector ( )e) A rotation of 180° about the point (1, 2)

f) A translation by vector ( )g) A rotation of 180° about the point (3, 1)

h) A translation by vector ( )–30

03

2–3

1–2

8–1

–6–2

–1–2

3–3

50

0

–2

2

4

C

2 4 6–2 x

y

6

B

A

D

0–1–2–3

1

2

3

1 2

B

DA

C

3–2 –1 x

y

0–1–2–3

1

2

3

4

1 2

B

D

A

C

3–2–3 –1 x

y

0–1–2–3–4

1

2

3

4

1 2 3 4–2–3–4 –1 x

y

–5 5


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