foundation book answers...1 875 m 2 a) take first left, first left, first right, third left, and the...

Chapter 1: Co-ordinates

Page 5: Finding a square

1 a) D2 b) A3 c) F32 a) B4 b) E3 c) E4 d) D4, E4

Page 7: Finding a point

1 (7, 8)2 (6, 2) (7, 2) (8, 2) (9, 2)

3 1 m 4 1 m long, m wide

5 a) (10, 20) b) (50, 19) c) (30, 32) d) (35, 28)6 a) 10 km b) 20 km c) 30 km

Page 9: Mathematical co-ordinates

1 The Plough (2, 4), (3, 7), (6, 8), (9, 9), (11, 7), (15, 8), (15, 12)

Orion (6, 3), (6, 7), (4, 14), (9, 13), (8, 9), (7, 8), (11, 4)

2 Ask your teacher to check your constellations.3 Square of side 2 units4 Join (2, 1) to (3, 3) to (2, 4) to (1, 3) to (2, 1)

0: Mixed exercise

1 A – (6, 7) B – (2, 6) C – (3, 1) D – (7, 1)E – (7, 5.5) F – (1.5, 5) G – (3.5, 4.5)

2 Letter H

Page 13: Length

1 a) 200 b) 400 2 a) 5000 b) 80003 a) 30 b) 90 4 a) 2 b) 3.5 (3 )5 a) 76 miles b) 138 miles

c) Southampton to Brighton6 a) 60 m b) 100 m 7 Yes (with 6 cm to spare)8 Width 13 cm, depth 8 cm

Page 15: Weight, mass and capacity

1 a) 1000 g b) 0.5 kg c) 2000 ml d) 4 pintse) 1500 g f) 0.14 l

2 a) 20 kg b) 2 c) 2000 d) 50003 1224 a) No (375 kg) b) No (305 kg) c) Yes (295 kg)5 a) 5 b) 25 6 a) 28 b) 7

Page 17: Time

1 a) 2 hours b) 1 minute 30 seconds2 a) 180 seconds b) 75 minutes3 3 minutes 25 seconds4 a) 0435 b) 1740 c) 2120 d) 13505 a) 8.25am b) 2.30pm c) 11.45pm d) 6.15pm6 a) 53 b) Yes c) No

7 a) 30 minutes ( hour) b) 10 minutes

c) Tennis Highlights d) 35 minutes8 a) 0845 b) 0915

Page 19: Money

1 £9 2 £1 3 £156 4 £820 5 £246 6 £8987 £845 8 £10809 Golden Sands: cheaper by £27

Page 20: Mixed exercise

1 a) 40 b) 4000 c) 3 d) 3002 3 kg3 a) 48 b) 2884 a) 2 hours 40 minutes b) 3 hours 5 minutes5 a) 26 minutes b) 21546 £1187 a) £878 b) £531

Chapter 3: Types of number

Page 23: Multiples and factors

1 a) 13, 21, 47 b) 8, 36, 44c) Even numbers end with a multiple of 2, i.e.

0, 2, 4, 6 or 8.d) 3

2 a) 10 b) 15 c) 20 3 94 a)

b) Factors of 18 are 1, 2, 3, 6, 9 and 18.5 a) 3 b) 26 a) (i) 1, 2, 5, 10 (ii) 1, 2, 4, 8, 16 (iii) 1, 7

(iv) 1, 2, 4, 5, 10, 20 (v) 1, 3, 5, 15(vi) 1, 2, 3, 5, 6, 10, 15, 30 (vii) 1, 2, 7, 14(viii) 1, 3, 7, 21 (ix) 1, 2, 3, 4, 6, 8, 12, 16,24, 48 (x) 1, 2, 3, 6, 9, 18, 27, 54 (xi) 1, 2,4, 7, 14, 28 (xii) 1, 2, 3, 4, 5, 6, 10, 12, 15,20, 30, 60

b) 1, 2, 4c) 30 and 60

Page 25: Prime numbers

1 a) No b) Yes c) No d) Yese) No f) No g) Yes h) No

Page 27: Squares, square roots and cubes

1 a) 25 b) 64 c) 81 d) 144 e) 4002 a) 5 b) 7 c) 10 d) 11 e) 203 84 a) 64 b) 81 c) 10

d) Yes, 11 along each side.5 a) 27 b) 64 c) 1256 a) a thousand b) a million c) a billion

12

12

12

Foundation Book Answers

Foundation: Answers © 2007, Hodder & Stoughton Educational 1

18 × 1

9 × 2

6 × 3

3 × 6

1 × 18

8: Mixed exercise

1 a) 12 b) 142 a) 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

b) The first ten multiples of 63 a) Drawings of 8 × 3, 6 × 4, 4 × 6, 12 × 2,

2 × 12, 24 × 1 and 1 × 24b) 1, 2, 3, 4, 6, 8, 12, 24

4 a) 32 b) 60 c) No5 a) 5, 10 15, 20, 25, 30, 35, 40, 45, 50

b) Yes c) Nod) A multiple of 5 ends with a 5 or 0

6 a) 1, 2, 4, 8 b) 1, 5, 7, 35c) 1, 2, 3, 6, 7, 14, 21, 42d) 1, 2, 4, 5, 10, 20, 25, 50, 100

7 418 a) 25 b) 649 a) 25 b) 64 c) 27

d) 1000 e) 2 f) 610 a) 400 b) 729 c) 169

d) 15 e) 14 f) 25

Chapter 4: Symmetry

Page 31: Reflection symmetry1 B, C and D2 a) 2 b) 4 c) 6

d) 1 e) 3 f) 23 a) Many possibilities: ask your teacher to

check your patterns.b) Many possibilities: ask your teacher to

check your patterns.c) Many possibilities: ask your teacher to

check your patterns.

Page 33: Drawing reflectionsAsk your teacher to check your drawings.

Page 35: Rotational symmetry1 A and D2 a) 2 b) 4 c) 3

d) 8 e) 6 f) 43 Ask your teacher to check your drawings.

Page 37: Angles round a point and on a line1 a = 120° b = 80° c = 160° d = 80° e = 160°

f = 140° g = 75° h = 60° i = 72°2 C, H and I A, E and J B, D, F and G

Page 38: Mixed exercise 1 a) i) 2 lines of reflection symmetry

ii) 0 lines of reflection symmetryiii) 1 line of reflection symmetryiv) 4 lines of reflection symmetryv) 0 lines of reflection symmetry

b) i) Rotational symmetry order 2ii) Rotational symmetry order 3iii) No rotational symmetryiv) Rotational symmetry order 4v) Rotational symmetry order 2

2 Check complete drawings3 Check reflections4 a = 110° b = 120° c = 30° d = 60°

Chapter 5: Fractions

Page 41: Equivalent fractions

1 2 3 a) b)

4 a) b) c)

5 a) (i) 8 (ii) 12 (iii) 6

b)

6 a) (i) 10 (ii) 8 (iii) 9 b)

Page 43: Adding and subtracting fractions (1)

1 a) b) c) d)

e) 1 f) g) 1 h)

2 a) b)

3 a) = 1 b) = 1 c) = 1

4 a) 10 b) c) d) e) f)

5 a) b) c) d)

e) f) g) h)

Page 45: Adding and subtracting fractions (2)1 a) 2 b) 2 c) 4 d) 3

e) 3 f) 3 g) 12 h) 3i) 4 j) 14 k) 5 l) 30

2 a) mile b) mile

c) mile d) mile

3 a) � b) � c) � d) �

4 a) b) c) d)

e) f) g) h) = 1

5 a) b) c)

Page 47: Improper fractions, mixednumbers and reciprocals

1 a) 1 b) 2 c) 1 d) 2

e) 1 f) 4 g) 1 h) 4

2 a) b) c) d)

e) f) g) h)

3 3 4 3 5 6 6 5 7 11 8 18 9 2114

12

254

218

1916

194

103

135

138

72

56

12

58

34

12

23

14

45

13

25

138

118

1116

58

1316

58

78

1016

= 58

516

716

1116

58

38

78

58

38

34

38

12

310

1316

14

910

58

34

1124

1324

34

14

512

38

58

+23

13

+14

34

+

38

58

14

18

58

14

34

12

56

34

23

34

12

716

38

2532

1216

34

=1316

38

58

35

13

Answers

2 Foundation: Answers © 2007, Hodder & Stoughton Educational

10 a) (i) (ii) 5 5 � = 1

b) (i) 10 (ii) � 10 = 1c) 1d) A number cannot be divided by zero

11 a) 8 b) 9 c) d)

Page 49: Mixed numbers

1 a) 4 b) 2 c) 1 d) 4 e) 1

f) 2 g) 1 h) 2 i) 2

2 a) 3 miles b) 3 miles

c) 3 miles d) 7 miles

3 3 hours 4 1 kg 5 1 hours

6 a) 4 � b) 1 �

Page 51: Fractions of a quantity

1 a) 6 b) 6 c) 40d) 9 e) 72 f) 40

2 £20 3 6 4 a) £3 b) £95 a) £8000 b) £15 0006 a) 16 cm b) 12 cm 7 £800 000 8 20


1 a) b) c)

d) e) f)

2 a) b) c) d)

3 a) b) c) 0

4 a) b) c) d) 1

5 a) 1 b) 10

6 a) 1 b) 5 c) 3

d) 3 e) 1

7 a) b) c)

d) e)

8 a) 2 miles b) 3 miles c) 5 miles

9 a) 3 b) 1 c) 3 d) 5

e) 3 f) 6 g) 1 h) 1

10 a) 135 litres b) 45 litres c) 90 litres

11 a) b) c)

12 a) b) 6 c) d) 7

Chapter 6: Maps and drawingsPage 55: Maps and scales

1 a) Green family b) Pub or stationc) School d) White family

2 a) West b) North-westc) South-west d) South

3 North-east 4 Shop5 Turn left out of the house. Walk to the end of

the road and turn left. At the end of the road turn left. Take the first right, then the second right, and the station is on the left.

6 Turn left out of the station. Take the second right, first right, first left, first right, first left, and the hotel is on your right.

7 a) 7 cm (± 0.5 cm)b) 70 m (± 5 m)

8 a) Markb) Jessica 17 cm, Mark 6 cm, Ryan 7 cmc) Jessica 170 m, Mark 60 m, Ryan 70 m

Page 57: Scales1 a) 250 m b) 1500 m c) 200 m

d) 75 m e) 237.5 m2 a) 2cm b) 100000cm c) 1000m d) 1km3 a) 4 mm b) 200 m4 56 mm on the map; 2.8 km in real life5 Lounge: 7.5 m by 4.5 m

Dining room: 3.75 m by 3.75 mKitchen: 5.25 m by 2.25 mCloakroom: 3.75 m by 2.25 mBathroom: 3 m by 3 mBedroom 1: 4.5 m by 3 mBedroom 2: 3.75 m by 3 mBedroom 3: 4.5 m by 3.75 m

Page 59: Angles1 a) obtuse angle b) acute angle c) right angle

d) acute angle e) reflex angle f) obtuse angle3 a) 130° b) 30° c) 90°

d) 65° e) 330° f) 110°4 GO FORWARD 5 METRES

TURN LEFT 45°

Page 60: Mixed exercise 1 875 m2 a) Take first left, first left, first right, third left,

and the gallery is just before the third turning on the left.

b) 1 km approximately 3 a)

b) 4340 m = 4.34 km1–7

1–6

5–8

1––16

5––16

1–2

9––16

1–8

1–8

1–8

3–8

1–4

1–8

1–8

11––5

19––10

23––8

15––4

9–2

3––10

3–4

2–5

1–2

1–4

3–4

1–8

1–6

5––16

7–8

1–2

3–4

3–8

2–5

7–8

2–5

1–4

2–3

9––10

3–5

1–4

3–4

14

14

14

12

14

14

12

34

58

34

34

38

516

38

38

12

14

112

34

110

110

15

15

Answers


Stage of race Distance Distance Directionon map in real life

START to A 4 cm 800 m North

A to B 3.5 cm 700 m South-east

B to C 5.8 cm 1160 m East

C to D 2.3 cm 460 m South

D to FINISH 6.1 cm 1220 m North-east

4 Angle ADC = Angle BCD = 70°Angle ABC = Angle BAD = 110°Angle YXZ = Angle YZX = 70°Angle XYZ = 40°

Chapter 7: DecimalsPage 63: Tenths and hundredths

1 A: 3.2 B: 3.5 C: 3.92 0.103, 0.110, 1.02, 10.2, 11.9, 100.13 a) 5.4 b) 2.48 c) 4.13

4 a) b) c) d)

e) 2 f) g) h)

5 a) 0.9 b) 0.71 c) 0.3 d) 0.28e) 2.7 f) 4.23 g) 3.1 h) 1.37

6 A: £1.1m B: £0.7m C: £1.6mD: £0.4m E: £2.4m

Page 65: Halves and quarters

1 a) 2.25 b) 3.5 c) 5.75 d) 1.5e) 3.75 f) 7.25 g) 6.5 h) 1.75i) 0.8 j) 1.6 k) 3.2 l) 2.4

2 a) 4 b) 3 c) 2 d) 8 e) 1 f) 5

g) 4 h) 6 i) j) 1 k) 2 l) 3

3 A: 4.5 B: 4.25 C: 4.75

4

5 A: 6.4 B: 7.8 C: 8.66

Page 67: Adding and subtracting decimals

1 a) £3.55 b) £8.90 c) £6.15d) £8.10 e) £0.12 f) £2.95

2 a) 4.8 b) 7.92 c) 21.03d) 1.89 e) 0.21 f) 1.71

3 £3.01 4 £10.35 5 1.45 km 6 0.7 m (70 cm)

Page 69: Multiples of 10

1 a) 16 b) 30.1 c) 210d) 35 e) 760 f) 3.2

2 1503 a) £2.40 b) £24.00 4 £50 0005 £350.006 a) 7.01 b) 0.73 c) 0.06

d) 6.32 e) 0.826 f) 0.006117 £7 8 £24.50 9 1.5 m

10 a) £4.50 b) £3.50 11 1.6 litres

Page 71: Multiplying decimals1 a) 7.2 b) 6.0 c) 8.88 d) 0.8

e) 0.12 f) 7.28 g) 0.062 h) 95.4

2 Name Height at age 2 (m) Fully grown height (m)Amy 0.85 1.70Jack 0.83 1.66Ryan 0.96 1.92Laura 0.89 1.78

3 Guiseley→Bingley: 4.8 milesBingley→Keighley: 3.0 milesKeighley→Silsden: 4.2 milesSilsden→Addingham: 3.6 milesAddingham→Ilkley: 2.4 milesIlkley→Guiseley: 5.4 miles

4 a) £3.50 b) £8.75c) Yes: 10 sessions would normally cost £17.50.

5 a) 2.25 b) 4.84 c) 0.25 d) 23.046 £270 0007 a) 900 b) 249 c) 350 d) 10 000

e) 10 000 f) 18 g) 20 h) 50508 a) (i) 2.5 (ii) 18 (iii) 180 b) Smaller

Page 73: Dividing decimals

1 a) 8.1 b) 70.1 c) 0.661d) 0.28 e) 2300 f) 1.3

2 a) £0.55 (55p) b) £1.98 c) £0.74 (74p)3 £32.97 4 £3.60 5 1.75 m 6 £487 72p (£0.72) 8 No9 a) 600 b) 15 c) 25

d) 1000 e) 1.5 f) 160010 a) (i) 250 (ii) 72 (iii) 222.2 b) Bigger11 a) 2.5 b) 1.8 c) 2.8 d) 4.3 e) 7.2


1 a) b) c) 9 d) 7

2 a) 0.7 b) 2.3 c) 0.47 d) 3.173 a) 36.4°C b) 36.7°C c) 35.9°C4 a) 1.66 cm b) 1.73 cm5 a) 13.9 b) 23.56 c) 5.908

d) 5.5 e) 50.2 f) 17.046 a) £1.62 b) 2.21 c) £2.58

d) £1.25 e) £2.367 a) 710 b) 2160 c) 664 d) 1.68 1.8 m 9 $198

10 a) £1.98 b) £18.02 11 21.2 cm12 a) 12 b) 24 c) 10 d) 4.813 3214 a) 51.84 b) 2.8 c) 24.01 d) 5.4

Chapter 8: ShapesPage 77: Sorting shapes

1 a) 3 sides (triangles) b) 4 sides(quadrilaterals)

c) 5 sides (pentagons) d) 6 sides(hexagons)

e) 8 sides (octagons)f) All sides are the same length and all angles

are equal (regular shapes).

29––––100

1–5

43––––100

3––10

15

45

25

35

14

34

12

14

12

34

14

12

9100

4641

10003

14100

3750

=910

45100

920

=410

25

=31

1007

10

Answers


6 6·25

b) a) c)

6·5 6·75 7

3 4 5

c) a) b)

3·1

3·6 4·2

2 a) E, M, V b) B, D, H, P, R, Vc) B, C, F, I, J, K, L, N, Q, S, T, W, Xd) A, C, K e) B, F, H, N, Q, R, T, V, Xf) F, H, J, N, Q, U

Page 79: Triangles1 a) F b) E c) B d) A

e) G f) D g) C2 FCA, FHC, FGE and EHG are right-angled

scalene triangles.FDA, ADB and DGE are acute-angled scalenetriangles.FHE is an obtuse-angled isosceles triangle.DCB, ADC and FGD are obtuse-angled scalenetriangles.AFG is a right-angled isosceles triangle.CEH is an acute-angled isosceles triangle.

Page 81: Quadrilaterals1 The number of lines of symmetry for each shape

are:a) 4 b) 2 c) 2d) none e) 1 f) none or 1

2 Many possible answers: ask your teacher tocheck your drawings.

3 a) T b) F c) Fd) T e) F f) T

Page 83: Other kinds of shapes1 a)

b) 50 lines of symmetry2 C, F and G

Page 85: Circles1 Clock faces, jam jar lids, drilled holes, buttons,

camera lenses, saucers, and many others.2 Ask your teacher to check your circles.

c) (radius should be 3.5 cm)3 a) about 25 cm b) about 34 cm c) about 22 cm

Page 86: Mixed exercise1 a) D, G, I, P, U, W

b) A, H, L, N, R, S, T, Xa) B, J b) K, Q c) C, F d) M

2 a) I, P b) D, G, W c) U d) D, P3 a) R b) X, N c) L d) T4 F, J, Q5 Get your teacher to check your answer.6 a) 12 b) 1 c) 4 d) 10 e) 10

Rotational symmetry order 2.

Chapter 9: Percentages

Page 89: 25%, 50% and 75%

1

2 C 3 A 4 B 5 C 6 C

Page 91: Finding percentages

1 a) 30% b) 20% c) 50%2 a) 40% b) 20% c) 10%3 a) 16% b) 80% c) 4%4 a) Border 64%; Octo 24%; Tapestry 28%.

b) Border ; Octo ; Tapestry .

c) Border 0.64; Octo 0.24; Tapestry 0.28.

Page 93: Percentage calculations

1 a) 300 b) 120 c) 140d) 72 e) 10 f) 135g) 2 h) 2 i) 60j) 22 k) 100 l) 16

2 £9003 a) £360 b) £840 c) £14404 24 5 £160 6 £352 7 £212 8 £245

Page 95: From fractions to percentages

1 a) 32%, 0.32 b) 55%, 0.55c) 12.5%, 0.125 d) 67.5%, 0.675e) 71.6% 0.716 f) 46.6

.%, 0.46

.

2 a) Knight ; Chequer ; Domino ;

b) Knight 80%; Chequer 48%; Domino 70%

3 a) 47.5% b) 31.25% c) 21.25%4 a) 125 b) 56% c) 52%


1 a) £75 b) £12.50 c) 160d) 520 e) 12 f) £2.25g) £25 000 h) 12 i) 2

2

710

1225

45

725

625

1625

Answers


Equilateral triangle Square Regular pentagon

Regular hexagon Regular octagon

Fraction Decimal Percentage

0.25 25%

0.5 50%

0.75 75%3–4

1–2

1–4

Fraction Decimal Percentage

0.1 10%

or 0.2 20%

0.25 25%

0.7 70%

or 0.8 80%

0.9 90%9––10

4–5

8––10

7––10

1–4

1–5

2––10

1––10

3 57%4 a) 30% b) 50% c) 20% d) 70%

e) 50% f) 80%5 300 ml 6 £680 7 758 a) Homeworld b) Pricebusters

Chapter 10: Statistics

Page 99: Displaying data

1 a) ; b) 20; 6; 10 c) 36

2 a) 8 b) 26c) Ask your teacher to check your bar chartd) Special

3 a)

b) 25 c) 20%d) Not really – each dog’s behaviour must

depend to some extent on the reaction ofthe other dog.

Page 101: Pie charts

1 a) 10%c) Liberal Alliance: 108°

Christian Democrats: 72°Don’t vote: 36°

d) Ask your teacher to check your pie chart.2 b) Greyhounds 72°; Bowling 144°; Skating 36°;

Pub 18°.c) Ask your teacher to check your pie chart.

3 a) 6° c) 25 d) 15 e) 90

Page 103: Line graphs

1 a) Ask your teacher to check your line graph.b) Week 6c) 3.1 kg

2 a) Ask your teacher to check your line graph.b) It increases between July and October and

then gradually decreases.c) July to October

3 a)+ b)

No. of days Tally (a) Frequency (b)0 days 1111 51 day 1111 1111 102 days 1111 1 63 days 1111 44 days 11 25 days 06 days 07 days 111 3

c) 30

d)

e) More of the runners go out every day, ornearly every day, in Summer, probablybecause of better weather or longer daylighthours.

Page 105: Averages and spread

1 a) Mean 3; Median 2; Mode 1b) Mean 30; Median 20; Mode 10c) Mean 13; Median 12; Mode 11d) Mean 103; Median 102; Mode 101e) Mean 22; Median 22; Mode 22.5

2 a) Mean 4.9; Median 5; Mode 6b) It will be full about 1 time in 10

3 a) Mean 12 hours; median 12.5 hours; mode 5 hours; range 23 hours

b) Mean 11 hours; median 11 hours; no mode.The mean and the median are both higherfor the boys than for the girls, so the boyswatch more TV than the girls.

4 a) Mean 13 s; median 13 s; mode 11 s; range 5 sb) Mean 13 s; median 12 s; mode 11 s; range 7 s

The PE staff are perhaps slightly faster: theirmean time is the same as the students buttheir median time is 1 s less. However they areless consistent, with one very slow member.

5 a) Mean £15 667 (to nearest £1); median £11 000; mode £8000; range £57 000

b) £65 000

Page 107: Grouping data

1 Ask your teacher to check your answer.2 a)+ b)

Age Tally (a) Frequency (b)10–19 1111 111 820–29 1111 430–39 1111 540–49 1111 1111 950–59 1111 460–69 111 370–79 11 2

c) They look short of people in the 20–40 agerange, but they have quite a lot of teenagers.

Answers


00 1 2 3 4 5 6 7

123456789

10

Frequency (people)

Number of days

Reaction Play Friendly No Growl Fightsniff reaction

Frequency 6 9 5 4 1

3 a)+ b)

Time Tally (a) Frequency (b)12.0–12.9 111 313.0–13.9 111 314.0–14.9 1111 11 715.0–15.9 1111 1 616.0–16.9 1111 11 717.0–17.9 1 118.0–18.9 111 3

c)

d) The world record for 100 m is under 10seconds. Most of these times (24 out of 50)are between 14 and 20 seconds. They arenot particularly fast. Perhaps the studentsare quite young, or they do not exerciseregularly.

Page 109: Displaying grouped data

1

2 a)

b) A 40≤x<50 B 20≤x<30c) B has younger customersd) A has more variable age

3 a)

b) Male 36≤x<40 Female 28≤x<32c) The females are younger than the males.d) No the male age is more variable.

Page 111: Making comparisons

1 a) Shop A, 6–10. Shop B, 16–20b) Ask your teacher to check your frequency

polygons.c) Fewer items are bought in shop A than in

shop B (lower modal class) but the range isthe same.

d) A is probably a smaller shop because mostpeople just buy a few items. B is probably asupermarket.

2 a) Ask your teacher to check your cumulativefrequency chart.

b) Southbound traffic has longer delays whichcould be helped by setting traffic lights withlonger at green for Southbound traffic.

c) Yes. If this is morning rush hour then thetraffic pattern would be reversed in theevening rush hour.


1 a)

b) Salma £4500, Bob £6000, Carole £7500c) 1° represents £200d) Salma receives £18 000

2 a) 225 b) 110°3

4 a) median 1 mean 2.4 mode 0 range 6

b) Varied performance, but some good results. 5 a)

1–2

Answers


5

4

10 15 20 25 30 35 40 45 50

Time in minutes

8

12

16

Frequency

¥¥

¥

×

×¥

×

¥¥

0123456789

101112

Frequency (people)

12 13 14 15 16 17 18 19 20Time

(seconds)

10

5

20 30 40 50 60 70 80

Age in years

10152025

Frequency

¥

¥¥

¥

¥

¥

¥ ¥ ¥¥¥

¥

¥

AB

2420

4

28 32 36 40 44 48 52

8

12

16

Frequency

××

×¥ ×

×

×

×

××

MaleFemale

×

×

×

×

×

SalmaBobCarole

a) angle b) fraction c)

Sand 120° 1

Cement 60°

Aggregate 180° 1 1–2

1–2

1–2

1–6

1–3

b) No. 6 a)

b)

c) There are certainly 2 underweight and 3overweight students, but we need to knowmore about them.

d)

Chapter 11: Directed numbers

Page 115: Negative numbers

1 –100, –3, –2, 0, 7, 10, 25, 10002 a) Up 1 b) Down 1 c) Down 3

d) Down 2 e) Up 4 f) Down 33 a) £100 b) –£100 c) £04 a) £20 b) –£5 (i.e. £5 loss)5 a) Down 250 m b) Up 200 m

c) Down 300 m d) Up 350 m

Page 117: Adding and subtracting

1 a) 4 b) –4 c) –6 d) 1e) 7 f) –7 g) 3 h) –3i) 3 j) –3 k) 7 l) –7

2 a) –1 b) 100 c) –20 d) –1000

3 London 4°C; Manchester –1°C; Leeds –3°C;Inverness –6°C; Accra 30°C.

4 a) –2 ft b) 0.5 ft c) 3 ft d) 1.5 ft

Page 119: Positive and negative co-ordinates

1 A(2, 2), B(0, 5), C(–2, 2), D(–1, 0), E(–2, –2),F(0, –5), G(2, –2), H(1, 0)

2 The letter M3 a), b) Ask your teacher to check your drawing.

c) When you add up co-ordinate values (withoutthe ‘sign’) you get the number of blocks.


1 a) –2 b) –1 c) –3 d) 5e) –8 f) –4 g) –5 h) –24

2 a) –£3.00 b) –£0.75 c) –£1.253 a) –2°C b) –1°C c) –4°C4 –£8 (or £8 DR)5 a) 3.5 kg b) 3.5 kg c) 1 kg6 a) 1215 b) 17057 a) –£5000 b) £15 000 c) £35 000

d) £50 000

Chapter 12: Ratio and proportion

Page 123: Simple proportion

1 60p2 1→ 70 3 1→ 30

2→140 2→ 603→210 3→ 904→280 4→1205→3506→4207→4908→5609→630

10→7004 Potatoes Apples Bananas

1→0.20 1→0.50 1→0.402→0.40 2→1.00 2→0.803→0.60 3→1.50 3→1.204→0.80 4→2.00 4→1.605→1.00 5→2.50 5→2.00

5 a) 1→2.50 11→27.502→5.00 12→30.003→7.50 13→32.504→10.00 14→35.005→12.50 15→37.506→15.00 16→40.007→17.50 17→42.508→20.00 18→45.009→22.50 19→47.50

10→25.00 20→50.00b) £45.00

Page 125: Ratio and proportion

1 a) 2 b) 102 a) 200 g b) 75 g

Answers


Weight w (kg) Tally60≤w<65 ||65≤w<70 |70≤w<75 ||75≤w<80 ||||80≤w<85 |||| ||85≤w<90 |90≤w<95 |95≤w<100 |

Weight w (kg) Frequency60≤w<65 265≤w<70 170≤w<75 275≤w<80 580≤w<85 785≤w<90 190≤w<95 195≤w<100 1

0

1

2

3

4

5

6

7

8

0 55 60 65 70 75 80 85 90 95 100 105

Weight (kg)

Freq

uenc

y (m

ale

stud

ents

)

3 a) £60 b)

4 a) 4:3 b) 15 c) 75d) Ask your teacher to check your answer.

Page 127: Conversion graphs

1 a) $16 b) $40 c) $80 d) $1282 a) £20 b) £30 c) £90 d) £1003 a) £10 b) 184 Ask your teacher to check your graph.


1 a) 6 gallons b) 36 litres c) 180 litres2 a) 6 b) 43 a) 100 units b) 6 units4 a) 15 b) 6 c) 50

d) 4 e) 10 f) 20g) 8 h) 1000 i) 35j) 35 k) 25 l) 121

5 a) 2:1 b) 1:50 c) 1:4d) 20:3 e) 1:50 f) 3:100 000g) 1:500 000 h) 160:1 i) 2:3

Chapter 13: Formulae

Page 131: Using a formula

1 a) To find the price in £ you multiply theweight by 0.2.

b) P = 0.2 � Wc) P = 0.2 � 12 = 2.4, so 12 kg costs £2.40.

2 a) x y A B1→ 3 1→ 42→ 6 2→ 53→ 9 3→ 64→12 4→ 75→15 5→ 86→18 6→ 97→21 7→108→24 8→119→27 9→12

10→30 10→133 a) 300 pence b) 720 pence c) 10 litres

d) 30 litres e) P = 70 � L

Page 133: More formulae

1 a) £40 b) £562 a) (i) £15 (ii) £50

b) 20 weeks3 a) 8 b) 43 c) 634 75 a) 7 b) 16 c) 31 d) 796 a) £12.50 b) £8 c) £20

Page 135: Collecting like terms1 a) 12a, 1 b) 9p, 1 c) 2q, 1

d) 4y + 3w + 5z, 3 e) r – 7s + 3t, 3f) 6a + 14b, 2 g) 8h + 4k, 2h) 2m + 5n + 8p, 3 i) 9d + 3e, 2 j) 0, 0

2 a) 9a b) 2b c) 3c d) 6de) 6x f) 3y g) 9x h) 4y

3 a) 15x + 5 b) 9y + 17a4 a) 15x + 5y b) 17a + 17 c) 10x + 13y

d) 20p – q – 1 e) 7m + 17n f) 25m + 5ng) 17x + 1 h) 18p + 4qi) 7x + y j) 19x + y k) a + 3bl) 11p + q

5 a) (i) £26 (ii) £181 b) 9a + 6c

Page 137: Using brackets

1 a) 7x b) 13yc) 100n d) 30x

2 a) 3a + 3b b) 5c + 5d + 5ec) 10x + 20 d) 6 + 2y + 2ze) 7f + 21 + 7g f) 2x – 10g) 4x – 4y h) 2p + 2q – 2ri) 8a + 8d + 8

3 a) 13 b) 52c) 8m + 12 d) 52

4 a) 8 b) 40c) 15x – 10y d) 40

5 a) 2x + 5y, 23 b) 3x + 8, 20c) 12x + 30, 78 d) 28 + 4x, 44e) 2y + 5x, 26 f) 8x + 6y, 50g) 6x + 16y, 72 h) 7x + 8y + 56, 108

6 a) 3(x + y + z) b) 3(x + 2y + 3z)c) 3(2a – b) d) 4(2a – b + 4c)e) 6(6p – 2q + 3r) f) 25(4u – v – 3w)

7 a) 21 b) 99c) 40 d) 0

Page 139: Adding and subtracting withnegative numbers

1 a)

b)

c)

d)

e)

f)

g)

13

Answers


, 20 1 2 3 4 5 6

, 2–4 –3 –2 –1 0 1 2

, –2–2 0 2 4 6

,00 2 5

, –2–6 –4 –2 0

, –3–3 –2 0 2

–1

–4

+6

+4

–6

–4

, –3–11 –8 –3 0

+3 +5

+3+2

–5

h)

i)

2 12 – 1 – 4, –1 – 4 + 12 12 – 4 – 1, – 4 + 12 – 1, – 1 + 12 – 4,

3 a) 2x b) –2x c) –10xd) 4y e) 4y f) –4yg) 0 h) y i) –25y

4 a) 4 b) –4 c) –20d) 12 e) 12 f) –12g) 0 h) 3 i) –75

5 a) 5 – 5p b) 3q + 1 c) p – 6d) 6 – 7p e) 3 + 11q f) –p + 3 or 3 – pg) 4p – 3q h) –18q i) 0

6 a) 0 b) 7 c) –5d) –1 e) 25 f) 2g) –2 h) –36 i) 0

Page 140: Mixed exercise 1 a) 16 b) 20 c) 7 d) 5

e) 12 f) 36 g) 50 h) 100i) 11 j) 3 k) 18 l) 18m)15 n) 15

2 a) 3a + 6b, 2 b) 12 – 6x, 2c) 2y – 5z + 4, 3 d) 15c, 1e) p + q + r, 3 f) 99f – 12g, 2g) 3x – 6y + 15, 3 h) 7n – 3m, 2i) 3q + 7p, 2 j) 3r + s, 2

3 a) 6a b) 6a + 1 c) 7x – 8d) 8 – 3x e) 15n – 6 f) k + 3g) 14p – 2x + 7y h) 6a + 3c – 3di) 94d – 51w + 97 j) –17a – 9

4 £3.505 a) 225 minutes b) 222.9 minutes; yes6 a) 2n – 10 b) 14 + 6x

c) 12a + 24 d) 12y + 6ze) 30 – 5a f) 3a + 3b + 3c

7 a) 2x + 17 b) 17 + y c) 8n – 1d) 7d + 5 e) 24a – 5 f) 45 – 6xg) 5x + 9y h) 5p + 3q i) 6p – 60qj) 10r

8 a) (i) 108 (ii) 108b) The expressions are equivalent.c) 0

Chapter 14: SurveysPage 143: Recording data

1 a)

b) Indian c) Yes. There are 20 tallies.

2 a)

b) 30 c) Dragon’s Tail3

Page 145: Stem-and-leaf diagrams

1 a)

b) 30 c) 73 d) 32 a)

b) 21 c) 69 d) 93 a)

b) 6 c) 37 d) 3 e) 144 a)

b) 257 cm, 180 cm c) 245 cm, 150 cmd) Bob’s hollyhocks are shorter and the heights

are more variable. The fertiliser seemseffective.

Page 149: Surveys

1 c) With just two outcomes a bar chart isprobably better.

2 Because some people could not swim.3 a) Boys 39.9 s Girls 37.3 s

b) Boys 39 s Girls 42 s

Answers


, –39–39 –18 0

–21 –18

, 6–55 0 6

+61

Type of food Fish Indian Chinese

Pub& chips meal

Frequency 1 11 2 6

Ride Dragon’s Splashdown Pirate Octopus

Tail Plank

Frequency 12 7 8 3

30 0 0 3 4 4 5 6 7 8 940 2 2 2 2 3 5 5 5 750 1 3 5 7 960 1 2 4 5 570 3

20 1 3 5 5 930 3 5 940 5 6 7 7 7 7 7 7 7 7 750 2 3 7 860 1 3 3 5 8 9

0 6 7 8 910 1 3 3 4 4 4 4 5 6 7 7 7 8 920 2 3 3 4 5 6 7 7 730 1 4 7

Mick 15 0 8 Bob16 417 9

5 0 18 89 6 19 61 0 20 8 8

21 2 4 5 5 79 3 2 22 6 6 8 89 9 4 23 0 08 6 3 24 5

7 6 4 4 0 25

Activity Disco Greyhounds Bowling Skating Pub

Frequency (women) 4 1 3 1 0

Frequency (men) 1 3 5 1 1

4

Page 151: Social statistics

1 a) £7.62 b) £9.902 a) £101.60 b) £132.003 a) 1993 £1.7m, 1994 £3.045m, 1995 £5.28m,

1996 £7.458m, 1997 £9.882m, 1998 £12.707m

Chapter 15: Using symbols

Page 153: Being brief

1 a) 53 b) 85 c) 103 d) 79

e) 108 f) 101 g) x4 h) 4y2

i) 9n3 j) 3a5

2 a) 2 × 2 × 2 b) 6 × 6 × 6 × 6c) d × d × d d) n × n × n × n × ne) 5 × c ×c f) 7 × g × g × g × gg) 10 × z h) 2 × x × x × x × x × x × xi) 2 × m × m × m × m × mj) 8 × u × u × u

3 a) 34 b) 610 c) 48 d) 1017

e) a5 f) v11 g) s5 h) d8

i) x7 j) n8

4 a) 6x b) 20x2 c) 6a3 d) 6g2

e) 6x2 f) 20x2 g) 3p3 h) 7y5

i) 2n4 j) 90m6

5 27 is the biggest.

2 × 7, 72, 27

6 47 is the biggest.

110, 101, 92, 29 = 83, 74, 38, 65, 56, 47

7 a) 32 b) 26 c) 55 d) x0

8 a) 8 b) 104 c) 49 a) 16 b) 2000 c) 0

Page 155: Using negative numbers

1 a) –5 b) 5 c) –5d) 5 e) –7 f) 3g) –12r h) –14s i) 99t

2 a) 5 b) 17 c) –21 d) 13e) –5 f) 8 g) 24 h) –18i) 999 j) 0

3 a) 9 +m b) 9 –m c) 3 –ad) 3 +2a e) 4 –2n f) 7 +2n

4 a) 4 b) –8 c) 8 d) –45 20356 a) 7 b) 1 c) 10 d) –2

Page 157: Simplifying expressions withnegative numbers

1 a) –8 b) –8 c) 8 d) 24e) –24 f) 20 g) 9 h) 64i) –6 j) 6 k) –6 l) –11m) –10x n) 8x o) 3x

2 a) 9 b) 11 c) –1 d) 0e) 1 f) 19

3 a) 8z + 28 b) 8z – 28 c) –8z – 28d) –8z + 28 e) 60 + 20a f) –60 – 20ag) –60 + 20a h) –7e – 14 i) –4 + 8yj) –4 – 8y

4 a) 16 b) 8 c) –4 d) 3e) 17 f) 11 g) –3 h) 6

5 a) 27 + 2x b) 15 – 2x c) 10n – 10d) 2n + 10 e) 13d + 4 f) a + 30bg) 15 – 10t h) 4 + 6c i) 18

6 a) –10 b) 12 c) –70

Page 158: Mixed exercise 1 a) 45 b) y3 c) 5x2 d) 7a3

e) 15b3 f) x7 g) 3y h) 3p5

i) m j)

2 a) –18 b) 8 c) –3 d) –3e) 3 f) 2 g) 18 h) 8xi) 4 j) –3 k) 5y l) –6m

3 a) 9t2 b) 5s2 c) 6r2 d) 7q2

e) 3p2 f) 5n2

4 a) –1 b) 10 c) –2 d) –85 a) 3a + 6 b) 3b – 2 c) c – 6 d) d

e) –24 f) 5 + 7f g) g – 3 h) 2h – 2i) a + 7b j) –b k) 6x + 3y – 12zl) 0

6 (r – 3p – 3q) or r – 3(p + q), £6.507 a + b – c or a – (c – b), £218 a) 7 b) 7 c) 4 d) 52 e) 52

Chapter 16: Spending moneyPage 160: Bills

1 159 2 271 3 60p 4 72p5 224p (£2.24) 6 480p (£4.80)7 £53 8 £38.509 a) 400 b) 8000p = £80 c) £96

10 a) 663 b) £99.45 c) £141.45

Page 163: Buy now, pay later1 a) £192 b) £42 2 a) £840 b) £1903 a) £384 b) £84 4 a) £648 b) £1485 £208 6 £657 a) £50 b) £18008 a) £550 b) £6600

Page 165: Value added tax (VAT)1 a) £21 b) £1412 a) £31.50 b) £211.503 a) £14 b) £944 a) £157.50 b) £1057.505 Store A, by £4.506 Store X, by £2.37 (to nearest penny)

d4

Answers


Girls Seconds Frequency Boys Seconds Frequency

20–29 4 20–29 2

30–39 6 30–39 5

40–49 3 40–49 3

50–59 1 50–59 2

60–69 1 60–69 1

Mixed exercise

1 243 2 £24 3 £514 a) 513 b) £51.30 c) £66.305 a) £192 b) £436 £120 7 £30 8 £2009 a) £35 b) £1680

10 £35 11 £176.2512 Budget Bernie’s by £10

Chapter 17: Graphs

Page 169: Looking at graphs

1 a) b)

c) Add 3 to xd) y = x + 3a) b)

c) Multiply x by 3d) y = 3xa), b)

c) Subtract 2 from xd) y = x – 2

2 a)

b) It increases by 2 each time.

3 d) H = 150 + 20 Da)

b)

c) (i) £290 (ii) 9 days

Page 171: Gradients and intercepts

1 a)

b), c) Ask your teacher to check your scalesand graph.

d) Gradient = 3 e) Intercept = –42 a)

b), c) Ask your teacher to check your scales and graph.

d) Gradient = e) Intercept = 1

3 a) 1, 5, y = x + 5

b) 2, –2, y = 2x – 2

c) – , 2, y = – x + 2

d) – , –1, y = – x – 112

12

23

23

14

Answers


D

H

0

150

5

250

10

350

15

450

C

1

2

–1–1 1 2 3–2–3

–2

–3

–4

0x

y

0

A

1–1

1

–1

–2

–3

–4

2

3

4

–2–3 2 3 4x

y

–4

x

y

–2

–10

–1

–7

0

–4

1

–1

2

2

3

5

4

8

x

y

–2 –1 0

1

1

1

2

1

3

1

4

212

34

14

12

34

100

O 5D

H

10 15

200

300

400

0 1–1–1

1

2

3

4

5

6

7

–2

–3

–2–3 2 3 4 5 6 7x

y

B

1

123456

2 3 4 5 6x

y

–1–2–3–4–5–6–2–3–4–5–6

Obtaining information

1 a) 25p b) £2.50c) A (2, 5) B (6, 10) C (6, 5)d) AC = 4 miles, BC = £5 e) £1.25 per mile

2 a) £25 b) £350c) A (1, 500) B (6, 1250); AC = 5 thousand,

BC = £750d) £150 e) £1850

3 a) £100 b) £35 per dayc) C = 100 + 35x d) £800

Page 175: Travel graphs: distance and time

1 5 minutes 2 50 minutes3 22.5 minutes (The first 6 miles took 15 minutes

and the last 3 miles took 7.5 minutes.)4 10.45 am 5 120 km6 a) 1 hr 45 mins b) 30 mins7 Ask your teacher to check your graph.

Page 177: Finding the speed from a travelgraph

1 09302 a) 5 km b) 1 hr c) 5 km/h3 a) 7 km b) 1 hr 45 min c) 4 km/h4 4 km/h

Page 179: The gradient of a travel graph

1 a) 12.30 p.m., 1 hours b) 15 minutes

c) 2 hours, she stopped for 1 hour.d) the same speed

2 a) 3.30 p.m., 20 miles b) 15 miles per hourc) He had a break for lunch then went on

more slowly.d) –10 miles per hour. He was going back home.e) They meet 16 miles from home, at 3.54 p.m.

3 a) Ask your teacher to check your graph.b) 50 miles per hour, 48 miles per hour,

70 miles per hourc) At 12.55, about 42 miles from Oxford.


1 a) (i)

(ii), (iii)

(iv) gradient = 1 (v) intercept = 1

b) (i)

(ii), (iii)

(iv) gradient = 2 (v) intercept = –3c) (i)

(ii), (iii)

(iv) gradient = (v) intercept = 2

d) (i)

(ii), (iii)

(iv) gradient = –1 (v) intercept = 5

12

12

Answers


–2.0 –1.0 O 1.0 2.0 3.0 4.0

–1

1

2

3

4

5y

x

x –2 –1 0 1 2 3 4

y –1 0 1 2 3 4 5

x –2 –1 0 1 2 3 4

y –7 –5 –3 –1 1 3 5

–2.0 –1.0 1.0 2.0 3.0 4.0

–8

–7

–6

–5

–4

–3

–2

–1

O

1

2

3

4

5

y

x

x –2 –1 0 1 2 3 4

y 1 1 2 2 3 3 412

12

12

–2.0 –1.0 O 1.0 2.0 3.0 4.0

1.0

2.0

3.0

4.0

y

x

x –2 –1 0 1 2 3 4

y 7 6 5 4 3 2 1

5 x43210–1–2–3

y

1

2

3

4

5

6

7

8

2 b) i) Lights Galoreii) Shadows

3 a) 500 mb) between 1 and 2 minutesc) 300 m per minuted) 100 m per minute

4 a) Ask your teacher to check your answer.b) between 15 and 25 minutesc) between 25 and 30 minutesd) 24 km/hr

5 a) 400 m b) Anwarc) 50 m, 20 seconds

6 a) 2 lengthsb) 50 metresc) Emmad) 75 metres/minutee) 50 metres/minute

Chapter 18: Perimeter and area

Page 183: Perimeter

1 a) 18 cm b) 23 cm2 a) 22 cm b) 38 cm c) 38 cm d) 44 cm3 £3695.20

Page 185: Area

1 a) 35 cm2 b) 55 cm2 c) 32 cm2 d) 55 cm2

2 a) 29 cm2 b) 35 cm2

3 a) 35 cm2 b) 48 cm2

Page 187: Triangles

1 a) 4 cm2 b) 7.5 cm2 c) 5 cm2 d) 8.75 cm2

2 a) 15 cm2 b) 14 cm2 c) 6 cm2 d) 7.5 cm2

3 19.2 m

Page 189: Shapes made of rectangles and triangles

1 a) 1700 m2 b) 1375 m2 c) 2725 m2

2 a) 10.5 cm2 b) 13 cm2 c) 10.25 cm2

Page 191: Circumference

1 a) 25.1 cm b) 37.7 cm c) 31.4 cmd) 42.1 cm e) 60.9 cm

2 a) 6.4 cm b) 13.4 cm c) 5.4 cm3 a) 219.9 cm b) 455 times

Page 193: Area of a circle

1 a) 201.1 cm2 b) 452.4 cm2 c) 78.5 cm2

d) 63.6 cm2 e) 43.0 cm2

2 a) 2.25 cm b) 3.48 cm c) 1.87 cm3 7.57 m2

4 18.8 m2

5 a) 12 b) 38.5 cm2 c) 162 cm2

6 1.78 m


1 a) (i) Area = 32 cm2, perimeter = 28 cm(ii) Area = 91 cm2, perimeter = 54 cm

b) (i) Area = 3200 mm2, perimeter = 280 mm(ii) Area = 9100 mm2, perimeter = 540 mm

2 a) 22 metres, 2200 cmb) £371.25c) 225 000 cm2

3 15 km2

4 a) 4 cm2 b) 64 c) 256 cm2

d) 16 cm by 16 cm e) 256 cm2

5 a) 12.57 m b) 12.57 m2 c) 12.06 m2

6 a) 20 cm2 b) 27 cm2 c) 73.5 cm2

Chapter 19: Three dimensions

Page 197: Drawing solid objects

R and X go with A (cuboid).S and Y go with B (cylinder).P and Z go with C (pyramid).Q and W go with D (cone).

Page 199: Using isometric paper

Ask your teacher to check your drawings forquestions 1 and 2.

2 a) 9 b) 11 c) 22 d) 19

Page 201: Nets

1 A, D2 Ask your teacher to check your net.3 a) Pyramid b) 5 c) 8 d) 54 a) Triangular prism

b) 5 c) 9 d) 6

Page 203: Volume

1 a) (i) 120 m3 (ii) 72 m3 (iii) 60 m3 (iv) 84 m3

b) (i) 120 000 000 cm3 (ii) 72 000 000 cm3

(iii) 60 000 000 cm3 (iv) 84 000 000 cm3

2 a) (i) 48 cm3 (ii) 30 cm3

(iii) 18 cm3 (iv) 42 cm3

b) 48 000 mm3

Page 205: Surface area of a prism

1 a) 114 cm2 b) 232 cm2 c) 125.7 cm2

d) 108 cm2 e) 99.8 cm2

2 556 m2

3 928.3 m2


1 Check net2 Check drawings3 a) 72 cm3 b) 32 cm3

4 b) 5 c) 9 d) 65 a) 5 c) 5 d) 8 e) 56 a) 96 cm3 b) 260 cm3 c) 150.8 cm3

7 Volume

Answers


Chapter 20: Earning money

Page 209: Wages

1 a) £180 b) £90 c) £200 d) £1202 a) 12 b) £603 a) 4 b) 21 c) £844 £48 5 £33.75 6 £312 7 £215

Page 211: Salaries

1 £750 2 £98403 £400 4 Sacha, by £780.5 a) £8400 b) £9200 c) £10 0006 May £850, June £875, July £840, August £765.7 a) £14 000 b) £13 250

Page 213: Simple interest

1 a) £30 b) £600 c) £12d) £1400 e) £120 f) £1687.50

2 a) £84 b) £850 c) £540 d) 80p

Page 215: Tax1 a) £6000 b) £8000 c) £15 0002 a) £3200 b) £3750 c) £26403 a) £13 000 b) £2600 c) £13 4004 a) Telesales £11 500; Marketing £13 000

b) £15005 Yes (net salary is £18 750)


1 a) £350 b) £203.502 £40 3 £331.504

£2585 a) £1072 b) £42006 a) £14 650 b) £15 100 c) £16 0007 a) £1000 b) £1100 c) £1040

d) £31408 £249 a) £81 b) £192 c) £102

10 a) £17 000 b) £4250 c) £15 750d) £1250

Chapter 21: EstimationPage 219: Approximations

1 a) 2000 b) 900 c) 40 d) 0.005 e) 0.0002 f) 0.07

2 a) (i) 57 s, 2 (ii) £64, 2 (iii) 240 miles, 2(iv) 80 km/h, 1 (v) 600 kcal, 1(vi) 2400 m2, 2 (vii) £27 000, 2 (viii) 1, 1

b) (i) 60 s (ii) £60 (iii) 200 miles(iv) 80 km/h (v) 600 kcal (vi) 2000 m2

(vii) £30 000 (viii) 13 Check your answers with your teacher.

Page 221: Decimal places

1 a) 3.1 b) 3.14 c) 3.1422 a) 4.5 b) 4.47 c) 4.4723 a) 1 b) 24 a) Approximately 5.38 to the nearest

hundreth; 5.4 to the nearest tenthb) Approximately 8.72 to the nearest

hundreth; 8.7 to the nearest tenth5 a) 0.167 b) 0.083 c) 0.667 d) 0.4296 5.527 a) 5.8 cm, 2.3 cm b) 13.3 cm2

8 7.869 a) 45.8 m b) 167.3 m2

Page 223: Significant figures

1 a) 77 000 b) 42.2c) 5400 d) 758 000e) 4000 f) 62.0g) 6.7 h) 50 000i) 33.8 j) 0.005

2 a) Approximately 37.73 to 4 significant figures;37.7 to 3 significant figures

b) Approximately 0.2156 to 4 significantfigures; 0.216 to 3 significant figures

c) Approximately 1.444 to 4 significant figures1.44 to 3 significant figures

3 a) 38 b) 0.22 c) 1.44 26 0005 a) 370 m b) 8300 m2

6 a) £90 000 b) £360 0007 a)

b) £39008 34 300

Page 225: Estimating costs

1 a) £3 b) £6 c) £6 d) £82 a) £6 b) £4 c) £24 d) £303 £2500

Answers


Start Finish Hours

Monday 0700 1300 6

Tuesday 0700 1300 6

Wednesday 0700 1300 6

Thursday 0700 1300 6

Friday 0700 1300 6

Saturday 0800 1300 5

Sunday 0900 1300 4

Total 39Day Thursday Friday Saturday

Tickets sold 257 319 348

Income £1090 £1360 £1480

Using your calculator

1 a) 280 m2 b) 400 cm2 c) 48 cm2

2 a) £2000 b) £100 0003 a) 445.60 ringgits b) 4971.20 baht

c) 116.80 Fiji dollars d) 208 Australian dollars4 a) 14 000

b) 160 000, 520 000, 200 000, 240 000, 280 000c) not a typical attendance, e.g. high for a

local derby5 (part iii)

a) 13 b) 3.3 c) 7.4d) 0.75 e) 4.4 f) 23g) 11 h) 1.0


1 a) £18 b) 80 minutesc) 3800 d) 64 000

2 £193 a) Chicken pie £4; Chips £1; Orange £1

b) £6 c) No4 a) 200 b) £6005 a) 8 b) 606 a) 8000, 8000, 12 000, 14 000, 6000

b) 48 000 c) £150 0007 a) i) 30 cm, 50 cm; perimeter 160 cm

ii) 162 cm; 2 cm differenceb) i) 60 cm, 80 cm; perimeter 280 cm

ii) 288 cm; 8 cm difference8 a) 5.3 b) 5.29 c) 5.2929 a) 3.33 b) 3.88 c) 4.64

10 a) 5.7b) She rounded her answers part way through

the calculations and should have left thefull numbers on her calculator, onlyrounding at the very end.

11 a) 8000 b) 765 000 c) 14.8 d) 0.065

Chapter 22: Equations

Page 231: Solving equations (1)

1 a) 2 b) 3 c) 12 a) x = 2 b) x = 3 c) x = 10 d) x = 13 a) x = 3 b) x = 8 c) x = 6 d) x = 13

Page 233: More equations

1 a) x = 3 b) x = 3 c) x = 10 d) x = 22 a) x = 4 b) x = 5 c) x = 3 d) x = 23 a) x = 4 b) x = 5 c) x = 2 d) x = 2

e) x = 3 f) x = 6 g) x = 7 h) x = 24 4 cm5 a) 4a = 20 b) 5 cm

Page 235: Using equations

1 a) n = 54 b) v = 15 c) c = 8d) f = 42 e) x = 10 f) y = 10

2 a) x = 3 b) y = 6 c) z = 5 d) x = 53 a) y = 10 b) x = 2.4 c) x = 2 d) c = 4.1

e) y = 10 f) n = 0.9 g) x = 1 h) n = 78

i) m = 11 j) u = 3 k) t = 10 l) x = 2m)x = 2.5 n) x = 1.3 o) y = 0

4 a) x + 120 = 180 b) 2y + 40 = 180x = 60 y = 70

c) 5z = 180z = 36

Page 237: Solving equations (2)

1 a) h = 8 b) n = 3 c) x = 17

d) y = e) k = 1 f) x = 6

g) x = 10 h) y = 1.2 i) x = –3

2 a) x = 1 b) a = –2 c) x = 2 d) y = 1

e) d = 6 f) x = 4 g) k = 5 h) k = –5

3 a) a = 6 b) t = 7 c) y = 4

d) c = e) x = 0 f) d = –1

4 a) c = 3.75 b) y = 1.286c) x = 0.267 d) p = 3.273e) x = 1.857 f) y = 10g) b = 1.136 h) a = 0.3

5 a) 20 b) 86 c) F – 32 =

F = + 32


1 a) 7 b) 9 c) 9 d) 11 e) 132 a) 473 b) 293

+156 –176–––– ––––629 117

3 a) x = 7 b) x = 33 c) x = 12d) x = 12 e) x = 3 f) x = 14

4 a) x = 10 b) x = 3 c) x = 38d) x = 24 e) x = 10 f) x = 13

5 a) x = 6 b) x = 5 c) x = 2d) x = 0.4 e) x = 11 f) x = 8

6 a) x = 20 b) x = 29 c) x = 101d) x = –24 e) x = 16 f) x = 42

7 a) 1 b) 4 c) 9 d) 1e) 3 f) 0

8 a) 4 b) 3 c) 1 d) 2e) 1 f) 5

9 a) 20 b) 45 c) 36

Chapter 23: Probability

Page 241: Calculating probabilities

1 a) b) c)

2 a) b) c)

3 a) b) c) d)

4

5 a) b)3032

1516

=232

116

=

26

13=

414

27

=214

17

=3

145

14

212

16

=3

1214

=712

36

12

=36

12

=16

95C

95C

12

23

12

12

12

12

Answers


6 a)

b)

Page 243: Working with probabilities

1 a) b) c)

d) e)

2 a) b) c)

3 a) b) c) 120 tickets, £60

d) 3 e) £45f) –£15 (The minus sign shows that it is a loss,

not a profit.)g) No

Page 245: Estimating probabilities

1 a) b)

2 a) b)

3 a) b) 50 c) d) 150

4 a) b)

c) Not really, January probably had most ofthe rainy days.

5 a) b) c) d) 0

Zero is probably a good approximation but it is not impossible that she’ll get 12; it could be her birthday.


1

2 a) = b) =

c) = d)

3 0–0 0–1 0–2 0–3 0–4 0–5 0–61–1 1–2 1–3 1–4 1–5 1–62–2 2–3 2–4 2–5 2–63–3 3–4 3–5 3–64–4 4–5 4–65–5 5–66–6

a) = b) = c) =

4 a) = b) = c)

d) Adds to 1 e) 0

5 a) = 3% b) 97% c) 3% of 50 000 = 1500

6 a) 8% b) 70% c) 30% d) 4% of 12 000 = 480

7 a) b) c) d)

8 a)

b) i)4––25 ii) iii) 0

Chapter 24: Using indices

Page 249: Number patterns

1 a) 1, 2, 3, 4, 6, 12 b) 1, 2, 4, 8, 16c) 1, 3, 5, 15 d) 1, 2, 4, 7, 14, 28e) 1, 5, 25 f) 1, 2, 3, 5, 6, 10, 15, 30g) 1, 2, 3, 4, 6, 8, 12, 16, 24, 48h) 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

2 a) 1, 2, 4, 8 b) 1, 2, 3, 4, 12 c) 1, 2, 43 a) 49 b) 8 c) 400 d) 125

e) 10 f) 900 g) 27 h) 124 7, 11, 13, 17, 195 a) 12 b) 18 c) 306 a) These are 1�20, 20�1, 10�2, 4�5, 5�4.

b) 1, 2, 4, 5, 10, 207 a) 36 b) 100

Page 251: Prime factorisation

1 a) 2 × 7 b) 3 × 5c) 2 × 2 × 7 d) 2 × 2 × 3 × 3e) 2 × 3 × 5 f) 3 × 3 × 3g) 2 × 3 × 3 × 5 h) 2 × 3 × 3 × 7i) 2 × 3 × 5 × 5 j) 2 × 3 × 5 × 7k) 7 × 7 × 11 l) 2 × 2 × 5 × 7 × 11

2 a) 2 b) 3 c) 6 d) 4e) 5 f) 1 g) 9 h) 2i) 7 j) 11 k) 9 l) 14m)6 n) 5 o) 8 p) 20

3 a) 20 b) 30 c) 8 d) 36e) 30 f) 21 g) 54 h) 16i) 70 j) 40 k) 60 l) 90m)12 n) 30 o) 72 p) 30

4 a) 35 b) c) d)

5 a) 8 b) 5 c) 7

37

1535

1435

625

35

25

45

15

15––––120

1–6

1–3

2–6

1–2

3–6

3–4

21––28

1–4

7––28

1–4

7––28

1––52

1––13

4––52

1–2

26––52

1–4

13––52

14

860

215

=⎛⎝⎜

⎞⎠⎟

13

13

23

3040

34

=⎛⎝⎜

⎞⎠⎟

1040

14

=⎛⎝⎜

⎞⎠⎟

67

17

1420

710

=⎛⎝⎜

⎞⎠⎟

620

310

=⎛⎝⎜

⎞⎠⎟

3940

140

5399

395400

7980

=⎛⎝⎜

⎞⎠⎟

5400

180

=⎛⎝⎜

⎞⎠⎟

1820

910

=⎛⎝⎜

⎞⎠⎟

220

110

=⎛⎝⎜

⎞⎠⎟

1020

12

=⎛⎝⎜

⎞⎠⎟

1020

12

=⎛⎝⎜

⎞⎠⎟

220

110

=⎛⎝⎜

⎞⎠⎟

13

Answers


10 1

2

AB C ED

Ice cream ToppingC NC FT NT FR NR F

Number on second spin1 2 3 4 5

1 2 3 4 5 62 3 4 5 6 73 4 5 6 7 84 5 6 7 8 95 6 7 8 9 10

Numberon firstspin

Index notation

1 a) 64 b) 32 c) 81 d) 64e) 216 f) 1296 g) 2.25 h) 15.625

2 a) 500 b) 70 000 c) 8000 d) 200 000e) 650 f) 5800 g) 2 400 000 h) 87 500

3 a) 7�103 b) 3�102 c) 9�104 d) 6�103

e) 8.6�103 f) 5.7�104 g) 7.5�102 h) 2.9�105

4 a) 102 b) 103 c) 106

5 See question 1.

Page 255: Rules of indices

1 a) b) c)

d) e) f)

g) h) i)

j) k) l)

2 a) 49 b) c)

d) 64 e) f) 1

g) 32 h) i) 1 000 000

j) 9 k) l) 1

m) 216 n) o) 4p) 625

3 a) 56 b) 211 c) 64

d) 103 e) 27 f) 106

g) 38 h) 42 i) 104

j) 5–2 k) 33 l) 2m)42 n) 3–2 o) 20

p) 103

Page 257: Calculators

1 a) 7 000 000 000 b) 80 000 000 000c) 250 000 000 000 d) 3 200 000 000 000

2 a) 600 000 000 000 b) 4 000 000 000 000c) 8 000 000 000 000 d) 30 000 000 000e) 15 000 000 000 f) 2 200 000 000 000

3 a) 1.46 � 108 b) 4808 kilowatt hours

Page 259: Brackets

1 a) 19 b) 27 c) 36d) 3 e) 8 f) 11

2 a) 17 b) 23 c) 10 d) 103 a) 15 b) 10 c) 22 d) 34 a) 4 + 5 – 3 = 6 b) (7 + 5)�3 = 4

c) (2 � 6) + 3 = 15 d) (5 + 2)� 2 = 14e) 3�(5 – 1) = 12 f) (3�2) + 2 = 8g) (1�6) – 2 = 4 h) (6�6)�4 = 9i) 8 + 2 – 3 = 7 j) (10 + 8)�2 = 9


1 a) 1, 2, 3, 4, 6, 8, 12, 24 b) 1, 3, 7, 21c) 1, 13 d) 1, 2, 3, 4, 6, 9, 12, 18, 36

2 a) 13 b) 363 a) 64 b) 9 c) 216 d) 2434 a) 300 000 000 b) 3305 a) 4 × 104 b) 4.3 × 107

6 a) 8 × 1011 b) 2.45 × 1010

7 7 000 000 000 0008 a) 22 b) 14 c) 14 d) 28

e) 69 a) 12 b) 24 and 25 May c) 2

10 a) 2 × 3 × 3b) 2 × 2 × 2 × 2 × 3c) 2 × 2 × 5 × 5d) 2 × 2 × 2 × 3 × 5

11 a) 5 b) 4 c) 10 d) 1212 a) 12 b) 24 c) 100 d) 9013 a) 64 b) 1000 c) d) 1

e) 128 f) 6 g) 144 h) 2

i) j) 1296 k) 1 l)

m)15 n) o) 4 p) 1024

14 a) 28 b) 73 c) 56 d) 48

e) 63 f) 44 g) 34 h) 315 a) 6 400 000 b) 0.0002

c) 0.000 000 54 d) 13 60016 a) 2 × 105 b) 1.5 × 10–3

c) 8.3 × 104 d) 2.6 × 10–5

17 a) 8.5 × 105 b) 2.4 × 10–2

c) 3.88 × 1022 d) 4 × 107

e) 2.4 × 106 f) 1.75 × 1016

g) 2.025 × 1015 h) 4 × 106

Chapter 25: Measuring anddrawing

Page 263: Triangles

1 e) 5.0 cm and 6.9 cm2 b) 7.3 or 7.4 cm; 146 or 148 m

Page 267: Using bearings

1 a) A 030°, B 135°, C 315°, D 260°b) A 15 km, B 20 km, C 30 km, D 25 km

2 a) 225° b) 45° c) 280°d) 100° e) 20° f) 200°g) There is a difference of 180° between each

pair of bearings.3 1.8 or 1.9 km and 5.0 or 5.1 km


1 a) AB = 9.8 or 9.9 cm b) XZ = 11.4 or11.5 cm, YZ = 6.6 or 6.7 cm

2 b) ST = 11.4 or 11.5 cm, TP = 9.1 or 9.2 cmc) ST = 285 or 287.5 m, TP = 227.5 or 230 m

3 a) (i) 150° b) (i) 240 km(ii) 330° (ii) 120 km(iii) 95° (iii)180 km

149

164

19

16

164

15

1125

181

110

19

110 000

1216

116

14

181

1100

136

127

18

125

11000

116

Answers


Chapter 26: Using fractionsPage 271: Multiplying fractions

1 a) b) c) d)

e) f) g) h) 7

2 a) 3 b) 4 c) 2 d) 1

e) 12 f) 9 g) 3 h) 7

3 a) 3 b) 3 c) d) 1

e) 1 f) 4 g) 3 h) 7

i) 5 j) 20 k) 4 l) 12

4 27

5 a) (i) 88 cm (ii) 176 cmb) It has doubled (× 2).c) (i) 616 cm2 (ii) 2464 cm2

d) It has quadrupled (× 4).

6 36 lbs

Page 273: Dividing fractions

1 a) 1 b) c) d)

e) f) g) h)

2 a) 12 b) 6 c) 16 d) 30

e) f ) 1 g) 10 h) 1

i) j) 7 k) 2 l) 3

3 a) 10 b) 204 405 286 a) 39 b) 26 c) 46

Page 275: Fractions to decimals

1 a) 0.6 b) 0.375 c) 0.45 d) 1.25e) 0.32 f) 0.0625 g) 3.5 h) 2.6

2 a) 1.3·

b) 0.1·

c) 1.16·

d) 0.4·

3 a) 1

Page 277: Fractions to percentages

1 a) 20% b) 35% c) 36% d) 37.5%e) 78% f) 82.5% g) 34% h) 62.5%

2 a) 30% b) 40% c) 20%3 a) Karen 50%, b) Marie 33 %

c) Jo 22.9% approximately

4 a) £120 000 b) 28 % c) 31 %

5 20%

Page 279: Making comparisons

1 a) 0.8 b) 0.44 c) 0.375d) 0.6

·e) 0.16

·f) 0.583

·

2 0.09, 0.83, , ,

3 A4 a) Northhill 79.5%; Heartland 54.9%;

Southdown 78.8%b) The Heartland centre is less successful than

the other two.5 a) A 4.5% B 4.9% C 4.6%

b) Ac) Breakdown or older machine


1 a) 4 b) c) 4

d) 9 e) f) 10

g) 5 h) 5 i)

j) 11 k) l) 3

2 a) b) c) 8

d) 5 e) 10 f) 4

3 a) 80%b) Parkside (71.7%)c) Eastwood (62.9%)

4

5 3.04, 3.3, , ,

6 a) UK £10 m, USA £8 m, Germany £6 m

b) UK , USA , Germany

7 a) 30 b)

8 a) 56% b) 87.5% c) 83. .3%

d) 74.2%9 a) £160 000 b) 20%

c) 52.5% d) £40 000, 25%10 a) Oakington b) Waterbeach

c) Waterbeach11 a) Ben £1200, Jo £1440, Guy £1080,

Tanya £1080b) 30%

Chapter 27: Angles and shapes

Page 283: Parallel lines

1 a) a, d, e b) b, c, f2 a = 76° b = 104° c = 76° d = 108°

e = 72° f = 108° g = 108° h = 72°i = 56° j = 56° k = 76°

3 a) a = 69° b = 62° c = 49° b) 180°

Page 285: Angles and triangles

1 a) a = 70° b) b = 110°c) c = 70° d) d = 80°, e = 100°e) f = 70°, g = 60° f) h = 15°, i = 35°, j = 55°g) k = 70°, l = 60°, m = 50°h) n = 80°, o = 100°, p = 50°, q = 40°

2 a)(i) a = b = 70°, x = y = 110°, (ii) isoscelesb)(i) a = b = c = 60° (ii) equilateral

16

14

13

512

278

103

11

58

49

512

110

58

34

14

34

2532

18

23

12

12

1316

58

1720

2125

56

23

13

13

35

12

34

34

45

78

14

516

34

12

19

25

110

14

14

12

1316

12

78

34

34

34

78

38

14

12

34

13

12

35

23

12

12

12

1564

35

14

58

320

316

16

Answers


Quadrilaterals

1 a = 55° b = 85° c = 80° d = 135°e = 37° f = 117° g = 65°

2 a = 105° b = 42° c = 33° d = 42°e = 43° f = 69° g = 27° h = 66°i = 66° j = 59° k = 59° l = 55°m = 54° n = 72° p = 54° q = 89°r = 89° s = 37°

Page 289: Interior angles of polygons

1 b) 720°, 1080°, 1440°, 1800°2 a) 120° b) 135° c) 144° d) 150°3 a) 72° b) 54° c) 108°4 d) They should all be 5 cm. The six triangles

are all equilateral.

Page 291: Exterior angles of polygons

1 hexagon 60°, octagon 45°, decagon 36°,dodecagon 30°.

2 a) They all add up to 180°.b) The interior and exterior angles make up a

straight line, so they must add up to 180°.3 a) 9 sides – 40°, 25 sides – 14.4°, 100 sides – 3.6°

b) 9 sides – 140°, 25 sides – 165.6°, 100 sides – 176.4°

4 a) irregular pentagon b) equilateral c) 60°d) 150° e) 360°

Page 293: Tessellations

1 Ask your teacher to check your patterns.2 These pentominoes tessellate.

These do not.


1 a) 30° b) 102° c) 37° d) 137°e) 49° f) 115° g) 115° h) 65°i) 92° j) 92° k) 88° l) 88°m)92° n) 96° o) 96° p) 84°q) 43° r) 35° s) 30° t) 68°u) 95° v) 70° w) 15°

2 1620°3 (i) a) 2880° b) 160° c) 20°

(i) a) 3240° b) 162° c) 18°4 Ask your teacher to check your answers.

Chapter 28: Using decimals

Page 297: Tenths and hundredths

1 a) 7.4 m b) 14.68 m2 Barcelona 1.7 m, Munich 1.2 m, Dublin 1.0 m,

Vienna 1.5 m

3 a) 2 b) 4 c) 3 d) 5

4 a) 3.9 b) 2.19 c) 5.03 d) 0.109

58 b) a) c) 9

6 £2.397 a) 1.08 m b) 1.78 m

Page 299: Multiplication and division

1 a) 17 b) 170 c) 1700d) 0.32 e) 0.032 f) 0.0032

2 a) 3 b) 0.8 c) 16.2 d) 3.123 a) 5 b) 8 c) 6.5 d) 204 a) £32.50 b) £325 5 £186 a) 86 °F b) 68 °F 7 £4.748 £12 9 a) 1.50 m b) 165 cm


1 a) 1.65 m b) 1.78 m

2 a) b) 5 c) 1 d) 6

3 a) 2.3 b) 3.17 c) 6.07 d) 0.1414 £2.165 12.7 cm6 a) 9.62 m2 b) 11.7 m7 a) £7.50 b) £0.50 (= 50 pence)8 £6.589 a) 10 b) 15

10 a) 76.8 cm b) 22.6 cm11 £16.8012 a) £1 500 000 b) £1313 a) 28.09 b) 2.9 c) 46.24 d) 3.914 a) 0.8 b) 0.625 c) 0.35 d) 0.83315 5, 5.01, 5.02, 5.1

Chapter 29: Sequences

Page 303: Patterns

1 a) 8, 10, 12 b) 20, 25, 30 c) 7, 9, 112 a)

1, 3, 5, 7, 9, 11

b)

(i) 1, 2, 3, 4, 5, 6(ii) 4, 6, 8, 10, 12, 14

c)

1, 4, 9, 16, 25, 363 a) 8, 12, 16 b) 20 c)

371–––––1000

83––––100

2–5

7––10

2371000

7100

91100

310

Answers


More sequences

1 a) 10, 12, 14 Add 2b) 17, 21, 25 Add 4c) 6, 5, 4 Subtract 1d) 96, 88, 80 Subtract 8e) 2.5, 3, 3.5 Add 0.5f) 1, –1, –3 Subtract 2

2 a) 60 b) 15 c) 1053 a) EVENS 26–32, EVENS 34–40, EVENS 42–48

b) ODDS 49–63, ODDS 65–79, ODDS 81–95c) ODDS 65–79

4 4 September, 18 September, 2 October, 16 October

5 2008, 2012, 2016

Page 307: Finding n

1 a) Add 5 b) 212 a) Subtract 5 b) 83 a) £60, £70, £80,… b) £100

c) Ask your teacher to check your arrow diagram.d) Amount saved = £50 + £10 � weeks after

birthday.A = 50 + 10 � N

e) 8 weeks

Page 309: More number sequences

1 a) 8, 16, 32 Multiply by 2b) 40, 80, 160 Multiply by 2c) 27, 81, 243 Multiply by 3d) 10000, 100000, 1000000 Multiply by 10

2 a) 100, 50, 25 Divide by 2b) 100, 10, 1 Divide by 10c) 8, 4, 2 Divide by 2

3 a) 4 mm b) 1, 2, 4, 8, 16, 32

c) 1, , , , , d) m2

4 a) 2 b) 4 c) 5 years


1 a)

1, 4, 9, 16These are square numbers

2 0945, 10001230, 14000915, 1000

3 27, 81, 243, 729, 2187

4

Term (n) = 2n5 a) 8

b) 4, 8, 12, 16, 20 …c) 1 ➝ 4

2 ➝ 83 ➝ 124 ➝ 16

d) 4e) Number of pages = 4 × n

Chapter 30: Using percentagesPage 313: Percentages, decimals and fractions

1 a) (i) B (ii) A (iii) Cb) 10% approximately

2 a) 12.5% b) 50% c) 37.5%3 a) 20% 44% 36%

b)

c) 0.2 0.44 0.36

Page 315: Percentage calculations

1 a) 200 b) 240 c) 150d) 66.5 e) 55.2 f) 1125g) 128 h) 227.5

2 a) £24 b) £50 c) £2883 a) £8400 b) £4.504 £2255 a) £1575 b) £1520

Page 317: Proportions

1 a) 0.75 75% b) 0.25 25%

c) 0.34 34% d) 0.6 60%

e) 0.86•

86.6•% f) 0.24 24%

g) 0.95 95% h) 0.7•

77.7%2 a) 41 b) 0.585... or about 59%

c) tennis d) badminton3 a) about 58% b) about 32%

c) about 57%d) Ask your teacher to check your answer.

925

1125

15

18

132

116

18

14

12

Answers


Mixed exercise

1 a) 40% b) 30% c) 30%2 46%3 a) 450 b) 176 c) 10.54 £72.255 £57 2006 Sporting Life (by £1.50)7 a) 80% b) 28% c) 62.5% d) 64.4%8 60%9 a) 33 % b) 3

10 a) 20b) A 30%; B 40%; C 20%; D 10%

Chapter 31: Co-ordinates andgraphs

Page 321: More co-ordinates

1 a) (2, 6) b) (7, 5) c) (7, 2) d) (6, 4)e) (7, 6) f) (2, 8)

2 (5, 2)3 B(2, 4), D(5, 8)4 B(5, 11), D(9, 17)5 (10, 11)6 a) (0, 0, 0) b) (0, 0, 2) c) (1, 0, 0)

d) (3, 0, 0) e) (2, 1, 0) f) (2, 1, 3) g) (4, 0, 2) h) (3, 1, 3) i) (0, 1, 2)

7 C(6, 0, 0), D(9, 3, 12), E(2, 2, 9), F(9, 9, 12)

Page 323: Using co-ordinates

1 (3, 0), (–1, 2) or (–5, –5)2 (0, 3), (8, –1) or (–12, –5)3 a) (5, 9) c) rectangle4 a) (–5, –6) d) rhombus5 a) (8, 2) d) square6 a) (6, 1) c) rectangle

Page 325: Equations and graphs

1 a) (0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), (9, 10)

b)

c) The y co-ordinate is the same as the x co-ordinate add 1. y = x + 1

2 a) (i) (0, 3), (1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9), (7, 10)

(ii)

(iii)The y co-ordinate is the same as the x co-ordinate add 3. y = x + 3

b) (i) (0, 6), (1, 5), (2, 4), (3, 3), (4, 2), (5, 1),(6, 0)

(ii)

(iii)The x co-ordinate add the y co-ordinate is 6.x + y = 6

3 a)

b) Ask your teacher to check your graphs. They should meet at (3, 3).

Page 327: Curved graphs

1 a)

b) Ask your teacher to check your graph.c) 0.5 s and 3.5 s. The ball is 10 m above the

ground both on the way up and on the waydown.

d) If the graph were extended, the ball wouldseem to continue falling below the ground.

2 a)

b)

c) 2.25d) 1.4, 3.6

3 a)

1–3

Answers


x

y

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9

10

x

y

0

3

1

4

2

5

3

6

4

7

5

8

6

9

7

10

x

y

6

0

5

1

4

2

3

3

2

4

1

5

0

6

x

y

8

10

7

9

6

8

5

7

4

6

3

5

2

4

1

3

0

2

t

20t–5t 2

h

0

0

0

0

1

20

–5

15

2

40

–20

20

3

60

–45

15

4

80

–80

0

x

–4

+5x

–x2

y

0

–4

0

0

–4

1

–4

5

–1

0

2

–4

10

–4

2

3

–4

15

–9

2

4

–4

20

–16

0

5

–4

25

–25

–4

0

1

–11 2 3 4 5

–2

–3

–4

2

y

x

x

x3

–2xy

–2

–8

+4

–4

–1

–1

2

1

0

0

0

0

1

1

–2

–1

2

8

–4

4

b)

c) 1.4, 0, –1.4d) Rotational symmetry about O.


1 a) (–2, 5) d) Square2 a)

b)

3 a) (6, –3) d) Rhombus4 a) (i) Board to water b) 1 second

(ii) Down in water c) 2 metres(iii) Surfacing d) 5 seconds

5 a) Changed directionb) Red

Green

c) Red: x co-ordinate plus y co-ordinate =eightx + y = 8

Green: y co-ordinate = x co-ordinate minusfoury = x – 4

6 a)

b)

c) –3.56d) ± 2.65

Chapter 32: Using statistics

Pages 330–331: Revision exercise

1 a) or for 1, or for 3

b) 70 points c) 20 teams2 a) Ask your teacher to check your frequency

table.b) 20 c) 30

3 Ask your teacher to check your charts and table.4 a) 0 b) 1.5 c) 1.5 d) 55 a) 5 b) 26° C c) 15 °C6 a) 20 b) 1 c) 15 d) 40

e) 2

Page 333: Pie charts

1 a) 90°, 120°, 150°b) Children £150 000 Adult £90 000

Teenage £120 000

c) 33 %

2 a) Ask your teacher to check your pie chart.b) 50%

3 a) 15 b) 15 c) 6d) Every time one team wins, another team

loses.4 a) 15°

b) Ask your teacher to check your pie chart.c) 50

Page 335: Mean, mode, median and range

1 a) Mode 14, median 10, mean 11, range 6b) Mode 4, median 4, mean 4, range 6c) Mode 2, median 2, mean 2, range 4d) Mode 23, median 23, mean 23, range 4e) Mode 0, median 3.5, mean 2.6, range 6

13

Answers


x 0 1 2 3 4 5 6

y 8 7 6 5 4 3 2

x 6 7 8 9 10

y 2 3 4 5 6

x –3 –2 –1 0 1 2 3

x2 +9 +4 +1 0 +1 +4 +9

–5 –5 –5 –5 –5 –5 –5 –5

y +4 –1 –4 –5 –4 –1 +4

1 2 3 4 x–1–2–3–4 0

1

2

3

4

–1

–2

–3

–4

–5

y

y

x0

1

–1–1 1 2–2

–2

–3

–4

2

3

4

x 0 1 2 3 4 5 6 7 8 9 10

y 8 7 6 5 4 3 2 1 0 –1 –2

2 a) 30 b) (i) 4 (ii) 3 (iii) 3 (iv) 63 a) Ask your teacher to check your frequency

tables.b) Mount Pleasant Street 1.8, Mandela Avenue 3c) Mount Pleasant Street 6, Mandela Avenue 6d) Ask your teacher to check your answer.

Page 337: Grouping data

1 a)

b) Ask your teacher to check your bar chart.c) Ask your teacher to check your answer.

2 a) Add up the lengths of the calls. The mean is 560––––20 = 28 minutes.

b) 560––––7 = 80 minutes (or 1 hour)

c) Ask your teacher to check your frequency chart and frequency polygon.

d) 15 � x < 203 a) Ask your teacher to check your tally chart.

b) Ask your teacher to check your frequencytable.

c) Ask your teacher to check your frequency chart and frequency polygon.

d) £2000 � x < £3000 and £4000 � x < £5000

Page 339: Scatter diagrams

1 a) no correlationb) positive correlationc) negative correlationd) negative correlatione) positive correlationf) no correlation

2 a) Ask your teacher to check your scatterdiagram.

b) Positive correlation. The more pages they type, the more mistakes they make.

c) Mandy

Page 341: Mean, median and mode of grouped data

1 a) 6–10 kg b) 8 kg c) 430 kg d) 8.6 kg2 a) £51 000 – £60 000 b) £105 500

c) = £49 206

3 a) 90–94 mins b) 92.25 minsc) 92.5 mins (approx 25 mins added to total)d) modal class still 90 – 94 mins

Page 343: Line of best fit


b) 19.5 Nc) 5.3 kg


b) Strong positive correlationc) Ed is wrong. Should be 67.5e) 0.133 g


b) 7.78 hours, 58 visitorsc) 57


1 a) 700 m b) 12° Cc)

d)

e) 14° C f) 1130–1180 m2 a) Boys: mode 6 nights

range 7 nightsGirls: mode 4 nights

range 4 nightsb) Boys higher average nights out, but more

varied.

c)

3 a) mean:2range:5

b) mean: 2.5range: 2

c) Girls pass more quickly.4 a) 30

b) discrete

£7036500143

Answers


0 300 600 900 1200 15005

10

15

20

Tem

p (¡

C)

Height (m)

Number of plants 0 � x < 4 4 � x < 8 8 � x < 12 12 � x < 16growing

Description Very low Low Medium High

Frequency 7 2 3 8

Tem

p (°

C)

c)

d) Ask your teacher to check your answers.e) 75 ≤ t < 80

5 a)

b) Negative correlationc) No

Chapter 33: Using formulae

Page 347: Using brackets1 a) p = 2(l + w) b) t = 3(a + b)2 a) 12 cm b) (i) p = 4a3 a) 14 cm b) (i) p = 2x + 2y4 a) 2a + 2b b) 2a + b c) 6a5 a) 48 cm b) 48 cm, cube

Page 349: Multiplying out brackets1 a) n2 + 6n b) n2 – 2n

c) n2 + n d) n2 – ne) 2n2 + 10n f) –8n – 4g) 2x2 – 3x h) –7p2 + pi) 15a2 + 6a j) –2c2 – 5ck) 12k + 20k2 l) 25x3 – 5xm) –a3 + 4a2 n) –4b4 – 28bo) 3x4 – 18x2

2 a) n2 + 6n + 8 b) n2 + 7n + 6c) n2 + 2n – 15 d) n2 + 3n – 28e) n2 – 10n + 16 f) 2n2+ 11n + 12g) 3x2 + 19x + 6 h) 4x2 + 3x – 10i) 3x2 – 5x – 28 j) 5a2 + 14a – 3k) 4b2 – 11b + 6 l) 6c2 + 29c + 28m) 16d2 – 2d – 3 n) 6t2 – 35t + 36o) 20y2 – 9y – 77 p) 1 + 5y + 6y2

q) 12 + 5s – 2s2 r) 14 – 19u – 3u2

s) 4b2 – 5b – 6 t) –12d2 + 31d – 20u) 25 – 9f 2

3 x2 + 8x + 164 a) x2 + 10x + 25 b) x2 – 12x + 36

c) 9x2 + 6x + 1 d) 16x2 – 24x + 95 a) n2 + 6n b) 13n2 – 3n

c) 10x2 + 30x + 25 d) 6p2 + 5pe) 2x2 + 11x – 6 f) –9g) 3c2 – 2 h) –n + 10i) 49x2 – 34x + 22 j) 24x

6 a) n(n + 1) b) (n + 3)nc) (n + 1)(n + 2) d) (n + 1)(n – 1)e) n(n + 1)(n + 2) f) n(n + 2) + (n + 1)

Page 351: More formulae1 a) 14 b) 12 c) 302 a) 16 b) 33 a) 14 b) 12 c) 30 d) 104 a) 6(x + 2) b) 722

5 a) (i) a3 cm2 (ii) 6a2 cm2

b) volume = 8 cm3 surface area = 24 cm2

6 a) ab + 2a2 b) 147 a) 3h b) 128 a) 0 b) –2 c) 0 d) 4

Page 353: Changing the subject of aformula

1 a) x = y – 4 b) x = y – 20 c) x = y – ad) x = y – 3 e) x = y – 13 f) x = y – cg) x = y + 5 h) x = y + 11 i) x = y + bj) x = 6 – y k) x = 1 – y l) x = d – y

2 a) x = y b) x = 10y c) x =

d) x = 4y e) x = 10y f) x = by

g) x = y h) x = y i) x = y

j) x = y k) x = y l) x = y

m) x = p n) x = o) x = (l + m)

p) x = s2

3 a) t = b) t = c) t =

d) t = 4 – c e) t = f) t =

g) t = h) t = i) t = 3 p

4 a) u = v – at b) l = c) x =

d) x = e) x = (a – b) f) x = (a – b)2

5 a) x = or – y

b) x = or – r

c) x = d) x = or a –

6 a) l = b) h = c) R =

d) d = e) r = f) P =

g) T = h) R = i) P =

Page 355: Expanding two brackets1 a) 6a b) 6c2

c) 20y2 d) –6xe) –12x f) 15x

2 a) x2 + 4x + 3 b) y2 + 7y + 10c) 12 + 7x + x2 d) 30 + 11y + y2

e) x2 + x – 2 f) y2 + y – 6g) x2 – 4x – 12 h) y2 – 4y – 5i) x2 – 9x + 14 j) y2 – 7y + 12k) x2 – 8x + 15 l) y2 – 11y + 30

4A–––π100I––––PT

100I––––PR

100I––––rc––

2πc–π

V–I

V––lb

A–b

y–4

4a – y–––––

48 – s–––––

4

V––12

V – 12r––––––12

p–2

p – 2y––––––

2

v – u––––a

V + 9y––––––

4p – 2b––––––

2

n + 3x––––––7

x + c––––5

s – a––––2

6 – z––––2

p – 6–––––

2y – 4––––

3x + 3––––

2

q–2

b–a2––11

5–4

b–a3–5

4–3

y–a

12

Answers


Time t 65 � t < 70 70 � t < 75 75 � t < 80 80 � t < 85 85� t < 90(seconds)

Frequency 4 7 10 4 5(No of runners)

3 a) 400 + 20 + 20 + 1 = 441b) 900 + 30 + 30 + 1 = 961c) x2 + 2x + 1 d) 1681

4 a) a2 + 6a + 9 b) x2 + 10x + 25c) a2 – 6a + 9 d) x2 – 10x + 25e) 4y2 + 4y + 1 f) 9x2 + 12x + 4

5 a) 6x2 + 19x + 10 b) 6x2 – 19x + 10c) 6x2 + 11x – 10 d) 6x2 – 11x – 10

6 a) xy + x + y + 1 b) ad + 2a + 3d + 6c) xy – x – y + 1 d) ck – 10c + 4k – 40e) ax + 4a – 3x – 12 f) xy – x + 10y – 10

7 a) (x + 1)(x + 2) b) x2, 2x, x, 2c) x2 + 2x + x + 2 = x2 + 3x + 2d) C and B

Page 356: Mixed exercise1 a) 11 b) 10 c) 122 a) 35 b) 12 c) 273 a) 1 b) 9 c) 254 a) 21 b) –21 c) –1 d) 15 a) (i) 3 (ii) 8

b) M =

6 £60£C = 30 + 0.3M

7 a) 5a + 5b b) 2x – 2y c) 3x + 9y8 a) 3(a + b) b) 4(x – y) c) 2(x + 3y)9 a) £7 b) £15 c) £25

10 a) Bb) Yes. 4 × 6 + 12 = 36

Chapter 34: Equations andinequalitiesPages 358–359: Revision exercise

1 a) 10 b) 15 c) 9d) 4 e) 12 f) 8g) 3 h) 5 i) 24j) 18

2 a) 28 b) –8 c) –3d) –1 e) 3x f) –3xg) –3y h) –6c

3 a) 3a + 6b b) 4m – 6n + 3pc) 2b + 7c – 5d d) 2a + 5b – 3ce) 8f + 7g – 4h f) 4r + 5s – 6t

4 a) 32 b) 42 c) 3d) 3 e) 4 f) 3g) 3 h) 4

5 a) 5x + 10 b) 6x – 18 c) 10 – 2xd) 45 – 18x e) 12x + 8 f) 35x – 15g) 20x – 8y h) 9x – 12y

6 a) 9a b) m c) 4bd) 5b – a e) 4f + 7g f) 3r

7 a) 5x – 1 b) 5 c) 2x – 1d) y – 1 e) 3r + 3 + 2y f) b + 9g) 3s + 7 h) t + 5

8 a) x + 6 b) 12b – 23 c) 12a – 23d) 14x + 47 e) 16b f) 23s – 22g) 0 h) 4

Page 361: Solving equations

1 a) 6 b) 4 c) 11 d) e) 1

f) 6 g) 8 h) 30 i) 16

2 a) 4 b) 2 c) 2 d) 1e) 7 f) 5 g) 5 h) –5

3 a) 10 b) 5 c) –2 d) 2e) 0 f) –2

4 a) –8 b) –14 c) –13 d) 15e) 4 f) 2 g) –3 h) 5

5 a) –7 b) –17 c) –1 d) –1e) –2 f) 2 g) –1 h) –3

Page 363: Trial and improvement

1 a) 1 and 2, 1.6 b) 4 and 5, 4.4c) 3 and 4, 3.4 d) 9 and 10, 9.0e) 4 and 5, 4.8 f) 5 and 6, 5.7

2 3.1413 1.3254 a) x2(x + 1) = x3 + x2 b) 4 litres = 4000 cm3

c) x = 15.5; 15.5 cm by 15.5 cm by 16.5 cm5 (8.87 – 2)m = 6.87 m

Page 365: Using inequalities

1 a) x > 6 b) x � 0 c) x < 3d) x � –4

2 a) x is less than 10b) p is greater than 20c) q is greater than or equal to 10d) y is less than 11e) x is less than or equal to 24f) b is greater than or equal to –5

3 a) 2 < 7 b) 13 > 4 c) –3 > –10d) 13 > –2 e) 5 > –4 f) –2 < 2

4 a) s � 50 b) p � 89 c) n � 10d) n � 8 e) c < 350 f) m � 50g) w < 3 h) d � 200

5 a) 7 > 2 b) 4 < 13 c) –10 < –3d) –2 < 13 e) –4 < 5 f) 2 > –2

Page 367: Number lines

1

2 a) w � 60 b)

3

12

12

P + Q––––––2

Answers


-3 -2 -13 4 5

5 6 7 2 3 4

-1 0 1 -1 0 1

5 6 7 5 6 7

-2 -1 0

a) b)

c) d)

e) f)

g) h)

i)

2.9 3 3.12.7 2.8 2.9

3 4 5 6000 7000 8000

1900 2000 2100 0.115 0.12 0.125

59 60 61

a) b)

c) d)

e) f)

4

5 0 < x < 12 or 1 � x � 11, and x is a wholenumber

6 a) Yes b) No – too shortc) No – too youngd) No – too young and too short

Page 369: Solving inequalities

1 a) x < 7 b) x � 7 c) x � 10d) x � 5 e) x < 2 f) x > 5g) x � 4 h) x � 5 i) x > 3j) x � 2 k) x � 1 l) x � 1

2 a) 13, 17, 19, 23, 29b) 36, 49c) 2, 3, 4, 6d) 6, 9, 12, 15, 18

3 a) £(3x – 100)b) 3x – 100 > x, x > 50

4 56 > 14w, w < 45 a) x � 15 b) x � 3

c) x > 4 d) x < 8e) 4 � x � 10 f) 9 � x > 4g) 5 < x < 9 h) 2 � x � 14i) 3 < x � 10 j) x > 7k) x � 6 l) x > 3


1 a) 7 b) 2 c) 2d) 3 e) 2 f) 5g) 1 h) 3

2 a) 2 b) 5 c) 2d) 3 e) 2 f) 2g) 6 h) 1

3 a) 3 b) 3 c) 2d) 5 e) 3 f) 2

4 7x – 12 = 23, x = 55 a) –6 b) –5 c) –17

d) –1 e) –4 f) –2

6 a) x is greater than 3

b) x is less than or equal to 2

c) x is greater than or equal to 5

d) x is less than –1

e) x is greater than –1 and less than 3

f) x is greater than or equal to 2 and less thanor equal to 5

7 25 000 ≤ m ≤ 49 9998 a) x � 7 b) x � 4 c) x � 6

d) x � 5 e) x � 7 f) x � 4g) x � 9

Chapter 35: Ratio and proportion

Page 373: Simplifying ratios

1 a) 2:1 b) 1:5 c) 4:1 d) 2:3e) 3:1 f) 3:1 g) 2:5 h) 5:8

2 a) 1:3 b) 200:1 c) 4:1 d) 2:5e) 1:6 f) 4:3 g) 2:5 h) 8:3

3 copper 300 g, zinc 150 g4 Milton £36, Spencer £245 Ceri £7500, Andrea £12 5006 a) (i) 2:3 (ii) 4:1 (iii) 2:1

b) 5:3 c)

Page 375: Unitary method

1 4 litre box2 6 pack3 9 pack4 750 g box5 the garden centre6 2.5-litre tin7 1300 m.8 35 s9 54 km

10 11 78011 a) (i) 64 (ii) £51.20

b) (i) 36 (ii) £53.64c) the smaller tiles

Page 377: Changing money1 a) 9 b) 90 c) 5402 a) 220 b) 1100 c) 5500

38

Answers


2 3 4

)

-1 0 1 2 3

-2 -1 0 1

65 70 75

)

-3 -2 -1 0

)

-4 -3 -2 -1

)

-2 -1 0 1 2 3 4

0 1 2 3 4 5

)

c)

d)

e)

f)

g)

h)

a)

b)

0 1 2 3 4 5 6 7 8 9 10 11 12

7–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

7–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

7–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

7–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

7–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

7–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

3 a) 2.28 b) 22.80 c) 34.204 a) £20 b) £2.275

6 Keyring (€7) and vase (€8)

Page 379: Distance, speed and time

1 a) 100 km b) 105 km c) 1980 km d) 20km

2 a) 56 km/h b) 64.8 km/hc) 84 km/h

3 a) 2 h b) 3 h c) 1h 40 min

d) 2 h 6 m 36 s4 a) 1240 b) 80 km/h

c) 64 km/h d) 35 minutes

Page 380: Mixed exercise1 1002 a) 50 ml b) 50 ml3 a) 3:2 b) 2:14 a) 1:2 b) 3:2 c) 2:5 d) 3:1

e) 4:1 f) 1:20 g) 3:4 h) 4:55 a) 1:50 b) 8 cm c) 3:5 m

(or 3 m 50 cm)6 a) Helen £40; Clare £60

b) Helen £100; Clare £407 a) 500 g tub b) 120 tablets

c) 10 kg potatoes8 Motor School £12.50; Learn to Drive £129 a) 128 b) 224 c) £12.50 d) £69

10 a) 22.5 km b) 720 km/h c) 45 minutes

Chapter 36: Area and volume

Page 383: Parallelograms and trapezia

1 a) 24 cm2, 20 cm b) 38 cm2, 30 cmc) 40 cm2, 35 cm d) 20 cm2

e) 112.5 cm2 f) 126 cm2

2 a) 42 cm2 b) 92 cm2

c) 63 cm2 d) 60 cm2

3 10 000 cm2 (or 1 m2)

Page 385: Cuboids

1 a) 504 cm3 b) 270 cm3 c) 180 cm3

d) 240 cm3

2 a) 2 gcm–3 b) 3 gcm–3

c) 5 gcm–3 d) 11.5 gcm–3

3 72 000 cm3 (or 72 litres)4 12.5 cm5 162 cm3

6 50 m

Page 387: Volume of a prism

1 a) 45 cm3 b) 100 cm3 d) 18 cm2

e) 62.8 cm3 d) 30 cm3 e) 35.3 cm3

2 870 m3

3 795

Page 389: More about prisms

1 a = 1.99 cm b = 4 cm c = 2 cmd = 2.44 cm e = 15.92 cm f = 6 cm

2 a) 150.5 cm2 b) 146 cm2 c) 108 cm2

d) 98.7 cm2 e) 84.9 cm2

3 a) 8.84 cm b) 3.26 cm4 2.78 m


1 a) 672 cm3 b) 300 cm3

2 a) 4800 cm3 b) 25 cm3 a) A = πr2

V = πr2lb) A in cm2

V in cm3

c) Area 25π m2

Volume 1000π m2

4 a) 96 cm3 b) 260 cm3 c) 150.8 cm3

5 a) 254 cm3 b) 5.3 cm6 a) 5250 mm3 b) 36.6 mm7 0.71 m3 (707 000 cm3)

Chapter 37: Transformations

Page 393: Revision exercise

1 Ask your teacher to check your drawings.

2 Ask your teacher to check your drawings.

3 a) C, D, G, I b) E, F, H

c) (i) Translation

(ii) Reflection in x = –3(iii) Rotation, centre (–3, –3) 90° clockwise

4 Ask your teacher to check your graph.e) An octagon. (Note it is not quite regular.)

Mirror symmetry in x axis, y axis, y = x andy = –xRotational symmetry about origin, order 4

Page 395: Translations using columnvectors

1 a) b) c) d)

e) f) g) h)

2 a) Ask your teacher to check your drawings.

b)

c) Ask your teacher to check your drawings.

d) e) f) 71

⎛⎝

⎞⎠

––71

⎛⎝

⎞⎠

24

⎛⎝

⎞⎠

53–

⎛⎝

⎞⎠

–70

⎛⎝

⎞⎠

36–

⎛⎝

⎞⎠

––25

⎛⎝

⎞⎠

04

⎛⎝

⎞⎠

–23

⎛⎝

⎞⎠

––53

⎛⎝

⎞⎠

42

⎛⎝

⎞⎠

51–

⎛⎝

⎞⎠

15

⎛⎝

⎞⎠

34

12

Answers


5K

£0.33

4K

£0.26

3K

£0.20

2K

£0.13

1K

£0.06

100K

£6.66

75K

£5.00

50K

£3.33

20K

£1.33

10K

£0.66

Reflection

1 Ask your teacher to check your drawings.2 Ask your teacher to check your drawings.3 a) (1, 3) (–1, 4) (–2, 2)

c) (3, 1) (4, –1) (2, –2)e) (–3, –1) (–4, 1) (–2, 2)

Page 399: Rotation

1 Ask your teacher to check your drawings.2 a) Reflection in y = x

b) Rotation through 90° clockwise about (2, –1)

c) Reflection in x =

d) Translation

e) Rotation through 180° about (–5, 0)f) Reflection in y = –x

g) Translation

h) Reflection in y = 2i) Rotation through 90° clockwise about (0, 3)

Page 401: Enlargement

1 B, G2 Ask your teacher to check your enlargements.3 Ask your teacher to check your enlargements.

Page 403: Scale factors less than 1

1 a) 54 cm b) 4.5 cm c) 27 cm d) 12 cm

2 Ask your teacher to check your diagram.

3 a) 2 b) c) 3 d)

4 a) Scale factor , centre (0, 1)

b) Scale factor , centre (3, 4)

Page 405: Similar shapes

1 a) 4/3 or 1.33 b) 2.25 c) 0.3752 a) B, D, E b) 30 cm3 a) A and F, B and D, C and E.


1 (i) a) 0 b) 2 c) 6 d) 0(ii) a) 3 b) 2 c) 6 d) 4

2 a) b)

3

4 P – NoQ – Yes, scale factor 2R – Yes, scale factor 3S – No

5

6

Chapter 38: Locus

Page 409: Simple loci

1 a)

b)

12

13

12

13

––

56

⎛⎝

⎞⎠

–17

⎛⎝

⎞⎠

12

Answers


3 cm

A B

D C

2 cmA B

D C

c)

d)

e)

f)

2 Ask your teacher to check your diagram.3 Ask your teacher to check your diagram.4 Ask your teacher to check your diagram.5 Ask your teacher to check your diagram.

Page 411: A point equidistant from twofixed points

2 c) It is the centre of the circle.3 Ask your teacher to check your diagram.4 Ask your teacher to check your diagram.

Page 413: A point equidistant from twolines

2 b) It is the same distance from all three sides.It is also the centre of a circle which justtouches all three sides of the triangle.

3 a) b), c) d) Ask your teacher to check yourdiagrams.

4 Ask your teacher to check your diagram.


1

2

3

4

5

Answers


cm1

A B

D C

A B

D C6 cm

5 cm

3 cm2 cm

A B

D C

1 cm

1 cm

A B

D C

4cmX

S

T

perpendicularbisector of ST

B A

Cbisector ofangle B

X Y

2cm

3cm

M

N

8cm

perpendicularbisector of MN

6

7

8

9

10

11

12

13

14

Answers


Y

4cm

X 5cm

Z

Y

XZ

perpendicularbisector of XZ

2cm

Y

XZ

2cm

3cm

Y

XZ

3cm

4cm

5cm

Y

XZ

bisectorof angle X

1cm

Y

XZ

perpendicularbisector of YZ

bisector ofangle Y

SPEAKER SPEAKER

STAGE

20m

10m

perpendicular bisectorof line connectingthe speakers

Jed would like to beanywhere alongthis line

SENSOR

SENSOR

8m8m

Ab)

Aa)

Chapter 39: Pythagoras’ rulePage 417: Finding the hypotenuse

1 a) 8.06 cm b) 8.49 cm c) 13.60 cmd) 13.45 cm e) 8.16 cm f) 9.17 cm

2 192 m 3 28.6 km4 a) 3 units b) 2 units c) 3.61 units5 a) 5.39 units b) 4.24 units

c) 5.10 units d) 4.47 units

Page 419: Finding one of the shorter sides

1 a) 6.24 cm b) 8.94 cm c) 4.47 cmd) 8.02 cm e) 4.08 cm f) 7.07 cm

2 2.44 m3 a) 5.66 cm b) 11.3 cm2

4 a) 3 cm b) 6 cm2 c) 2.4 cmd) AN = 3.2 cm, CN = 1.8 cm

5 33 cm

Page 420–421: Finishing off

1 a) a = 10.2 cm b) b = 9.71 cmc) c = 6.36 cm

2 a) 25 = 5 units b) 32 (or 4 2) units

c) 29 units3 27.5 km4 4.04 m or 404 cm5 Yes6 a) 7.28 m b) 1.88 m

c) 2.31 m d) 2.98 m7 a) 34 (17 each side) b) 28 c) 9528 Yes. Diagonal of box is 51.2 cm.

Answers


foundation book answers...1 875 m 2 a) take first left, first left, first right, third left, and the...

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