checkpoint maths 3 – answers - · pdf filechapter 5 – using and applying...

Checkpoint Maths 3 © 2004, Hodder & Stoughton Educational 1 of 33

SECTION ONEChapter 1 – Algebra 1Exercise 1.11 (a) 43 (b) 35 (c) 76

(d) 62 (e) 123

2 (a) 7 � 7 � 7 � 7 (b) 3 � 3 � 3(c) 9 � 9 � 9 � 9 (d) 6 � 6 � 6 � 6 � 6(e) 11 � 11

Exercise 1.21 25 2 39 3 49 4 53 5 86

6 6 7 83 8 2 9 102 10 38

Exercise 1.31 46 2 36 3 210 4 412 5 314

6 216 7 t4 8 m6 9 p8 10 x16

Exercise 1.41 27 2 33 3 23 4 36 5 54

6 62 7 35 8 t7 9 m3 10 r7

Exercise 1.51 32 � 22 2 42 � 53 3 a2b3 4 pqr2

5 t4u2 6 72 � 43 7 a2b2c2 8 pr2s3

9 u3v 10 55 � t3

Exercise 1.61 5 2 9 3 4 4 15 1 6 x2 7 x 8 19 p 10 1

Exercise 1.71 (a) 16 (b) 121 (c) 272 (a) 81 (b) 1 000 000 (c) 1253 (a) 55 (b) 39 (c) 69

4 (a) 105 (b) 52 (c) 15 (a) 10 (b) 32 (c) 1

6 (a) 32 (b) 54 (c) 87

7 (a) m2 (b) n5 (c) p4

8 (a) 43 � 52 (b) 72 � 82 � 23 (c) 53 � 32

9 (a) a4 (b) 1 (c) c2

10 (a) u3 � w2 (b) u5 � w4 (c) u5v5

11 (a) 24 (b) 1 (c) 312 (a) 2�1 (b) 3�1 (c) 2�2

Chapter 2 – Shape, space andmeasures 1Exercise 2.11 40 km/h 2 75 km/h 3 130 km/h4 14 m/s 5 16 m/s 6 25 m/s7 8 km/h 8 48 km/h 9 120 km/h

10 180 km/h

Exercise 2.21 150 km 2 540 km 3 500 km4 30 km 5 80 km 6 2 km7 120 m 8 2700 m 9 1200 m

10 36 000 m

Exercise 2.31 4 h 2 5 h 3 30 min4 15 min 5 30 min 6 6 min7 5 s 8 5 s 9 0.25 s

10 0.025 s

Exercise 2.41 5 g/cm3 2 2.5 g/cm3 3 20 g/cm3

4 4 t/m3 5 4 t/m3 6 4.5 g/cm3

7 8 g/cm3 8 0.5 g/cm3 9 0.01 g/cm3

10 0.0016 g/cm3

Exercise 2.51 160 g 2 22.5 g 3 2000 g4 6000 g 5 2 g 6 10 g7 120 t 8 4.25 t 9 1200 g

10 1 g

Checkpoint Maths 3 – Answers

27ANSWERS_For_Web_001-033.qxd 29/11/04 9:18 am

Exercise 2.61 28 cm3 2 40 cm3 3 100 cm3

4 8 cm3 5 2 cm3 6 250 cm3

7 100 cm3 8 0.8 m3 9 0.5 m3

10 1 cm3

Exercise 2.71 45 km/h 2 80 km/h3 2.5 h 4 25.5 km5 West to east 613 km/h (3 sf); east to west

520 km/h (3 sf)6 8 g/cm3 7 25 000 m3

8 0.0773 m3 (3 sf) 9 10.8 kg10 1260 km

Chapter 3 – Shape, space andmeasures 2Exercise 3.11 a � 5 cm 2 b � 15 cm 3 c � 20 cm4 d � 13 cm 5 e � 2.5 cm 6 f � 2.6 cm7 g � 7.4 cm 8 h � 12.5 cm 9 i � 3.9 cm

10 j � 10 cm

Exercise 3.21 m � 4 cm 2 n � 5 cm 3 p � 7 cm4 q � 9 cm 5 r � 1.75 cm 6 s � 0.4 cm7 t � 2.1 cm 8 u � 1.5 cm 9 v � 3.2 cm

10 w � 9.6 cm

Exercise 3.31 10 cm 2 13 cm 3 49.5 cm (1 dp)4 7.2 cm 5 125 km 6 65 m7 26 cm 8 375 km 9 184 m (3 sf)

10 2 m

Exercise 3.41 a � 6.5 cm b � 7.4 cm (1 dp)2 c � 13.4 cm (1 dp) d � 14.7 cm (1 dp)3 e � 5.1 cm (1 dp) f � 5.5 cm (1 dp)4 g � 15 cm h � 18.0 cm (1 dp)5 j � 13 cm k � 14.3 cm (1 dp)

l � 15.9 cm (1 dp)

Chapter 4 – Shape, spaceand measures 3Exercise 4.1Pupils’ bearings may differ from these by �2°.

1 085° 2 045° 3 130° 4 245°5 (a) 130° (b) 080° (c) 210°6 (a) 260° (b) 140° (c) 077° (d) 280°

Exercise 4.21 Pupils’ bearings may differ from these by �2°.

(a) 137° (b) 317° (c) 117° (d) 297°

(e)

(f) Bearings and back bearings differ by 180°.

2 (a) 225° (b) 270° (c) 280°(d) 000° or 360° (e) 285° (f) 180°(g) 135° (h) 033° (i) 162°

3

Exercise 4.3Pupils’ answers may vary slightly from those givenhere.1 (a)

2 Section 1 – Chapter 3


Bearing Back bearing

A to B 137° B to A 317°

C to D 117° D to C 297°

E to F 090° F to E 270°

G to H 062° H to G 242°

I to J 043° J to I 223°

Route Bearing Route Back bearing

A to B 080° B to A 260°

B to C 140° C to B 320°

C to D 250° D to C 070°

D to E 264° E to D 084°

E to A 032° A to E 212°

250°

135°

7 km

12 km

A

B

C


(b) 11 km

(c) 11 km on a bearing of 215°

2 (a)

(b) 13.2 km on a bearing of 300°

3 (a)

(b) 11.7 km on a bearing of 061°

4 (a) 308 km(b) 130°(c)

5

6 Pupils’ route, distances and bearings.

Chapter 5 – Using and applyingmathematics/ICT 1Investigation1 Pattern 1 area � 1 unit2

Pattern 2 area � 5 units2

Pattern 3 area � 14 units2

2

3

4 The difference between successive termsincreases by the square of the higher position.

5 Area of 10th pattern � 385 units2

6 Area of nth pattern� n2 � (n � 1)2 � (n � 2)2 � … � 12

ICT activityPupils should find that Pythagoras’ rule holds forany regular shape drawn on the sides of a right-angled triangle.

Review 1A1 (a) 37 (b) 52 (c) 36

2 (a) m3 � r2 (b) p3 (c) x4

3 (a) 4 (b) 1 (c) 1004 65 km/h 5 660 km 6 9.6 g/cm3

7 1.5 g/cm3 8 13 cm 9 6 cm

10 (a) (b) Distance AB � 63.6 km on abearing of 000°

Section 1 – Chapter 5 3


225°

90°

105°

R

S

P

Q

6.5 km

8.5 km7.8 km

170°

270°N

O

M11.2 km

5.8 km

Journey Distance (km) Bearing

Kuala Lumpur to Singapore 308 130°

Singapore to Kuantan 284 348°

Kuantan to Kuala Lumpur 200 242°

Journey Distance (km) Bearing

London to Cambridge 140 010°

Cambridge to Birmingham 184 283°

Birmingham to Cardiff 184 157°

Cardiff to London 280 088°

4

4

3 2 1

Pattern 4:

Pattern 5:

Pattern 6:

5

5

Area � 30 units2

Area � 55 units2

Area � 91 units2

4 3 2 1

6

6 5 4 3 2 1

Position 1 2 3 4 5 6

Term (total area) 1 5 14 30 55 91

345°

220°radar

A

B

50 km

20 km


Review 1B1 (a) 29 (b) 62 (c) 26

2 (a) p2 � q3 (b) m3 (c) t15

3 (a) 9 (b) 1 (c) 25

4 70 km/h 5 4�12� h

6 0.75 g/cm3 7 270 g

8 QR � 2 cm, QS � 2.1 cm (1 dp) 9 50 cm

10 (a)

(b) Bearing � 234°Distance � 33 km

SECTION TWOChapter 6 – Number 1Exercise 6.11 6.5 � 104 2 7.2 � 107

3 8.4 � 1010 4 7 � 105

5 4.9 � 106 6 8.12 � 105

7 2.4 � 106 8 6.7 � 107

9 4.0 � 106 10 7.0 � 103

Exercise 6.21 1.8 � 105 2 8 � 106

3 2 � 107 4 4.2 � 1010

5 5 � 107 6 1.5 � 107

7 1 � 108 8 6 � 1012

9 9.6 � 108 10 1.6 � 107

Exercise 6.31 6200 2 51 000

3 8 000 000 4 710 000

5 39 100 6 8 000 000 000

7 100 000 8 4500

9 3 800 000 10 9 000 000 000

Exercise 6.41 4.6 � 107 2 1.38 � 109

3 2.9 � 108 4 1.036 � 1010

5 1.558 � 109 6 8.68 � 107

7 5.13 � 1010 8 6.912 � 1011

9 2.304 � 107 10 9.261 � 1012

Exercise 6.51 4.2 � 10�4 2 4 � 10�4

3 8.7 � 10�5 4 5.32 � 10�3

5 8 � 10�7 6 7.6 � 10�4

7 8 � 10�6 8 7.7 � 10�7

9 1 � 10�4 10 5.3 � 10�7

Exercise 6.61 0.000 26 � 2.6 � 10�4

2 0.000 068 � 6.8 � 10�5

3 0.000 000 4 � 4.0 � 10�7

4 0.000 493 � 4.93 � 10�4

5 0.000 000 07 � 7.0 � 10�8

6 0.000 006 41 � 6.41 � 10�6

7 0.004 � 4.0 � 10�3

8 0.54 � 5.4 � 10�1

9 0.000 000 44 � 4.4 � 10�7

10 0.000 36 � 3.6 � 10�4

Exercise 6.75.4 � 10�1, 4.0 � 10�3, 4.93 � 10�4, 3.6 � 10�4, 2.6 � 10�4, 6.8 � 10�5, 6.41 � 10�6, 4.4 � 10�7, 4.0 � 10�7, 7.0 � 10�8

Chapter 7 – Algebra 2Exercise 7.11 a � 5, b � 3 2 c � 3, d � 4

3 e � 2, f � 3 4 g � 3, h � 3

5 j � 6, k � 1 6 l � 5, m � 4

7 n � 2, p � 7 8 q � 1, r � 8

9 s � 4, t � 4 10 u � 7, v � 8

11 a � 2, b � 1 12 c � 4, d � 3



215°

65°

L

B

A

13 km

21 km


13 e � 2, f � 3 14 g � 3, h � 315 j � 5, k � 2 16 l � 2, m � 417 n � 1, p � 3 18 n � 1, p � 319 r � 5, s � 1 20 t � 1, u � 7

Exercise 7.21 a � 2, b � 2 2 c � 3, d � 13 e � 2, f � 3 4 g � 3, h � 25 j � 2, k � 1 6 l � 1, m � 37 n � 2, p � 4 8 q � 4, r � 19 s � 5, t � 3 10 u � 1, v � 4

11 a � 2, b � 2 12 c � 1, d � 313 e � 3, f � 2 14 g � 1, h � 215 j � 2, k � 3 16 l � 4, m � 417 n � 1, p � 3 18 r � 2, s � 719 t � 2, u � 9 20 t � 6, u � 5

Exercise 7.31 a � 2, b � 1 2 b � 1, c � 23 d � 2, e � 3 4 f � 3, g � 25 h � 2, j � 1 6 k � 1, l � 27 m � 2, n � 5 8 p � 3, q � 49 r � �1, s � 1 10 t � 2, u � �3

Exercise 7.4Pupils’ equations.

Exercise 7.51 4 units and 6 units2 12 units and 5 units3 1 unit and 3 units4 4 units and 3 units5 12 units and 15 units6 15 units and 16 units7 1 unit and 3 units8 4 units and 4 units9 20 units and 9 units

10 6 units and 8 units

Exercise 7.61 x � y � 10

x � y � 2 x � 6, y � 4

2 x � y � 26x � y � 2 x � 14, y � 12

3 x � y � 50x � y � 18 x � 34, y � 16

4 x � y � 12x � y � 8 x � 10, y � 2

5 x � y � 60x � y � 20 x � 40, y � 20

6–10 Pupils own problems and solutions.

Chapter 8 – Shape, space andmeasures 4Exercise 8.11 (a) Approx. $72

(b) Approx. $135

(c) Approx. $630

2 (a) Approx. £44

(b) Approx. £25

(c) Approx. £425

Exercise 8.2Pupils’ graphs leading to the following approximatesolutions.

1 112 km

2 25 miles

3 32 km

4 41 miles

5 384 km

6 263 miles

7 112 km/h

8 81 miles per hour

9 Approx. 625 miles per hour

10 297 600 km/s

Exercise 8.31 Approx. 158 °F2 Approx. 49 °C3 Approx. 104 °F4 Approx. 32 °C5 Approx. 37 °C6 Approx. 74 °F7 Approx. 133 °F8 Approx. 38 °C9 Approx. �18 °C

10 Approx. �40 °C




Exercise 8.41 Pupils’ graphs. 2 10 °C or 50 °F

Exercise 8.5Pupils’ graphs showing

1 Approx. €35 2 Approx. €363 Approx. €26 4 Approx. €435 €20 6 €07 Approx. €50 8 Approx. €108

9 If Ayse makes under 286 minutes of calls permonth

10 If Bella makes over 286 minutes of calls permonth

Exercise 8.61 6.25 s 2 40 m3 8.75 s 4 64 m5 81.25 s 6 480 m7 125 s 8 2400 m9 68.75 s 10 28 800 m (28.8 km)

Exercise 8.7Pupils’ graphs leading to the following approximatesolutions.

1 4.2 s 2 60 m3 5.8 s 4 96 m5 54.2 s 6 720 m7 83.3 s 8 3600 m9 45.8 s 10 43 200 m (43.2 km)

Exercise 8.81 7 am

2 (a) 50 km (b) 50 km/h

3 8 am 4 1 hour

5 50 km 6 25 km/h

7 100 km/h 8 5 hours

9 200 km 10 40 km/h

11

12 80 km/h

Exercise 8.91 (a)

(b) 63�13� km/h

2 (a)

(b) 1515

3 (a) 0800

(b) (i) �12� h (ii) 20 km/h (iii) �

12� h

(c) (i) 1 h (ii) 10 km (iii) 10 km/h



0

Mobile phone tariffs compared

Cost

(€)

200 400 600 800 1000 1200

Time (min)

Bella

Ayre

20406080

100120140160

7.00a

m

8.00a

m

9.00a

m10

.00am

11.00

am12

.00pm

50

0

Dist

ance

(km

)

100

Time

first family

Travel graph

150

200

250

second family

0700

0800

0900

1000

1100

1200

1300

1400

1500

1600

1700

50

0

Dist

ance

from

hom

e (k

m)

100

Time

Salesman‘s journey

150

20007

0008

0009

0010

0011

0012

0013

0014

0015

0016

00

50Dist

ance

from

sta

rt (k

m)

0

100

Time

Train journey

150

200

250

300

350

400


(d) The cyclist returning to the starting pointwithout stopping

(e) 10 km/h

(f) 6�23� km/h

Chapter 9 – Shape, space andmeasures 5Exercise 9.11

2

3

4

5

Exercise 9.21 (a) Pupils’ drawings.

(b) Pupils’ measurements.(c) Approx. 0.7 (pupils’ answers may vary).(d) Pupils’ drawings.(e) Ratio � 0.7 each time (answers may vary

slightly).

2 (a) Pupils’ drawings.(b) Pupils’ measurements.(c) Approx. 1.7 (pupils’ answers may vary).(d) Pupils’ drawings.(e) Ratio � 1.7 each time (answers may vary

slightly).

Exercise 9.31 (a) Pupils’ drawings.

(b) Approx. 0.36 (answers may vary slightly).(c), (d)

2 Pupils’ comments.

3 (b) Results will be affected by errors inmeasurements.

Exercise 9.41 0.7 2 1.4 (1 dp) 3 0.6254 0.3̇ 5 3 6 17 0.83̇ 8 1.2 9 0.875

10 0.8

Exercise 9.51 35.0° (1 dp) 2 55.0° (1 dp)3 32.0° (1 dp) 4 18.4° (1 dp)5 71.6° (1 dp) 6 45°7 39.8° (1 dp) 8 50.2° (1 dp)9 41.2° (1 dp) 10 38.7 (1 dp)



adj

opphyp

adj

opp hyp

adj

opp

hyp

adj

opp hyp

adj

opphyp

Angle Length of Length of Opposite �opposite side adjacent side adjacent

20° 3.6 10 cm 0.36

30° 5.8 10 cm 0.58

40° 8.4 10 cm 0.84

50° 11.9 10 cm 1.19

60° 17.3 10 cm 1.73

70° 27.5 10 cm 2.75


Exercise 9.61 4.2 cm (1 dp) 2 3.7 cm (1 dp)3 27.5 cm (1 dp) 4 6.8 cm (1 dp)5 3.3 cm (1 dp) 6 4.9 cm (1 dp)7 53.2 cm (1 dp) 8 17.4 cm (1 dp)9 3 cm 10 12.1 cm (1 dp)

Exercise 9.71 22.0 cm (1 dp) 2 24.2 cm (1 dp)3 3.5 cm (1 dp) 4 11.9 cm (1 dp)5 22.6 cm (1 dp) 6 21.5 cm (1 dp)7 4.0 cm (1 dp) 8 33.3 cm (1 dp)9 25 cm 10 32.0 cm (1 dp)

Chapter 10 – Using and applyingmathematics/ICT 2InvestigationPupils’ own measurements and calculations.

ICT activityPupils’ own conversion graphs.

Review 2A

1 (a) 5 � 106 (b) 2.3 � 107 (c) 4.5 � 104

2 (a) 1.2 � 108 (b) 1.2 � 1010 (c) 2.5 � 107

3 (a) 6.12 � 109 (b) 1.176 � 109 (c) 7.84 � 108

4 (a) 8 � 10�4 (b) 4.16 � 10�6 (c) 7.2 � 10�4

5 (a) x � 3, y � 2 (b) p � 2, q � 1

6 (a) p � 4, q � 3 (b) 12 units and 3 units

7 8.7 cm (1 dp) 8 19.8 cm (1 dp) 9 15.6° (1 dp)

10 (a)

(b) 270 km

(c) 67.5 km/h

Review 2B

1 (a) 1.7 � 107 (b) 7.5 � 105 (c) 8 � 109

2 (a) 2 � 106 (b) 1.8 � 109 (c) 6.4 � 105

3 (a) 6.97 � 107

(b) 2.6 � 107 (1 dp)

(c) 1.5 � 104 (1 dp)

4 (a) 6 � 10�4 (b) 7.3 � 10�5 (c) 8 � 10�5

5 (a) p � 5, q � 5 (b) a � 3, b � 4

6 (a) 4p � 3q � 208p � q � 20

(b) p � 2, q � 4 (c) 20 units

7 17.2 cm (1 dp)

8 6.4 cm (1 dp)

9 53.1° (1 dp)

10 (a) €425

(b) When 1000 units are consumed in a three-month period

SECTION THREEChapter 11 – Number 2Exercise 11.11 a � 9 2 b � 83 c 7 4 d 125 e � 5 6 f 307 g 15 8 h � 79 i � 6 10 j � 10

Exercise 11.21

2



0800

0830

0900

0930

1000

1030

1100

1130

1200

1230

1300

50

0Dist

ance

from

hom

e (k

m)

100

Time

Car journey

150

200

250

300

100

0 1000 2000 3000

Cost

(€)

200

Units used

tariff A

tariff B

Electricity tariffs

300

400

500

600

4 5 6 7 8 9

4 5 6 7 8 9


3

4

5

6

7

8

9

10

Exercise 11.31

2

3

4

5

6

7

8

9

10

Exercise 11.4

1 2 a 5 2 5 b 8

3 4 c 6 4 0 � d 3

5 �3 e 0 6 �4 � f � 3

7 �2 g � 4 8 �6 h 2

9 �8 � i � �1 10 �5 j 4

Exercise 11.51 (a) Lower bound � 7.5, upper bound � 8.5

(b) 7.5 x � 8.5

(c)

2 (a) Lower bound � 44.5, upper bound � 45.5

(b) 44.5 x � 45.5

(c)


(b) 155.5 x � 156.5

(c)


(b) 199.5 x � 200.5

(c)


(b) 2.5 x � 3.5

(c)


(b) 0.5 x � 1.5

(c)

7 (a) Lower bound � �8.5, upper bound � �7.5

(b) �8.5 � x �7.5

(c)


(b) �20.5 � x �19.5

(c)



105 6 7 8 9

0 1 2 3 4 5

7 8 9 10 11 12

5 6 7 8 9 10

5 6 7 8 9 10

0 1 2 3 4 5

0 0.5 1 1.5 2 2.5

1.5 2 2.5 3 3.5 4

4 5 6 7 8 9 10

0 1 2 3 4 5 6

7 8 9 10 11 12 13

1 2 3 4 5 6 7

3 4 5 6 7 8 9

2 3 4 5 6 7 8

�7 �6 �5 �4 �3 �2 �1

�8 �7 �6 �5 �4 �3 �2

�3 �2 �1 0 1 2 3

0 1 2 3 4 5 6

7.5 8 8.5

44.5 45 45.5

155.5 156 156.5

199.5 200 200.5

2.5 3 3.5

0.5 1 1.5

�8.5 �8 �7.5

�20.5 �20 �19.5



(b) �1.5 � x �0.5

(c)

10 (a) Lower bound � �0.5, upper bound � 0.5

(b) �0.5 � x � 0.5

(c)

Exercise 11.61 (a) Lower bound � 4.55, upper bound � 4.65

(b) 4.55 x � 4.65


(b) 8.25 x � 8.35


(b) 17.45 x � 17.55


(b) 6.15 x � 6.25


(b) 0.75 x � 0.85


(b) 2.95 x � 3.05


(b) 1.95 x � 2.05


(b) 4.145 x � 4.155


(b) 7.375 x � 7.385


(b) 0.005 x � 0.015

Exercise 11.71

2 5 min 17.5 s t � 5 min 18.5 s

3

4

5

6

7

8–10 Pupils’ questions.

Chapter 12 – Algebra 3Exercise 12.11 (a)

(b) x � 3, y � 5

2 (a)

(b) x � 2, y � 3



�1.5 1 �0.5

�0.5 0 0.5

12.55 12.6 12.65

4500 5000 5500

11.95 12.0 12.05

235Width

240 245

295Length

300 305

550 600

570 580

0

2

�2

4

6

8

�2 2 4 6 8

y

y � x � 2

y � 2x � 1

x

0

2

�2

4

6

8

�2 2 4 6 8

y

y � x � 1

y � x � 2

x

12


3 (a)

(b) x � 4, y � 4

4 (a)

(b) x � 4, y � 5

5 (a)

(b) x � 2, y � 3

6 (a)

(b) x � 2, y � �2

7 (a)

(b) x � 1, y � 2

8 (a)

(b) x � �2, y � 2



0

2

�2

4

6

8

�2 2 4 6 8

y

y � x

y � 4

x

0

2

�2

4

6

8

�2 2 4 6 8

y

y � x � 3

y � 2x � 3

x

12

0

2

�2

4

6

8

�2 2 4 6 8

y

y � �x

y � �2

x

0

2

�2

4

6

8

�2 2 4 6 8

y

y � 4x � 2

y � �x � 3

x

0

2

�2

4

6

8

�2 2 4

y

y � 2x � 6

y � �2x � 2

x0

2

�2

4

6

8

�2 2 4 6 8

y

y � x � 2

y � �x � 5

x

12


9 (a)

(b) x � �4, y � 5

10 (a)

(b) x � �1, y � 4.5

Exercise 12.21 (a)

(b) x � 1, y � 4

2 (a)

(b) x � 2, y � �1

3 (a)

(b) x � 3, y � 6

4 (a)

(b) x � 1, y � �1

5 (a)

(b) x � 4, y � 4



0

2

�2

4

6

8

�2�4 2 4

y

y � � x � 3

y � �2x � 3

x

12

0

2

�2

4

6

8

�2 2 4

y

y � � x � 4

x

y � �2 x � 2

12

12

0

2

�2

4

6

8

�2 2 4

y

x

2x � y � �2

x � y � 5

0

2

�2

6

8

�2 2 4

y

x

2x � y � 3

x � y � 212

0

2

�2

4

6

8

�2 2 4

y

x

x � 3

3x � y � 3

0

2

�2

�2 2 4

y

x

3x � y � 2

�2x � y � �3

0

2

4

6

8

2 4 6 8

y

x

x � y � 8

4y � x � 12


6 (a)

(b) x � 2�12�, y � �

12�

7 (a)

(b) 0

(c) Pupils’ explanations.

8 (a)

(b) Pupils’ descriptions.

(c) An infinite number.

(d) Pupils’ explanations.

9 (a)

(b) 0

10 (a)

(b) An infinite number.

Exercise 12.31 Graph 1 y � x � 1 x � �3, y � 4

y � 4 � 0

2 Graph 2 y � �12�x � �3 x � 2, y � �2

y � 2x � 2

3 Graph 3 y � �3x � 8 x � 3, y � �1y � �

13�x � 0

4 Graph 4 y � �2 x � 3, y � �2x � 3 � 0

5 Graph 5 y � �2x � 5 No solutiony � 2x � 0

6 Graph 6 y � �34�x � 2 � 0 Infinite number of

4y � �3x � 8 solutions

Chapter 13 – Shape, space andmeasures 6Exercise 13.11 48.6° (1 dp) 2 53.1° (1 dp)

3 44.4° (1 dp) 4 36.9° (1 dp)



0

2

�2

4

�2 2 4

y

x

y � x � �2

y � 12

0

2

�2

4

6

8

�2 2 4

y

x

y � 2x � 3

y � 2x � 2

0

2

�2

4

�2 2 4

y

x

0

2

�2

4

6

8

2

y

x

3x � y � 2

6x � 2y � �4

0

2

�2

4

2

y

x


5 20.5° (1 dp) 6 30°

7 24.2° (1 dp) 8 42.1° (1 dp)

9 27.2° (1 dp) 10 11.5° (1 dp)

Exercise 13.21 3.4 cm (1 dp) 2 8.5 cm (1 dp)

3 6 cm 4 11.5 cm (1 dp)

5 2.7 cm (1 dp) 6 5.8 cm (1 dp)

7 5.8 cm (1 dp) 8 3.7 cm (1 dp)

9 2.9 cm (1 dp) 10 6.3 cm (1 dp)


3 14.9 cm (1 dp) 4 14.6 cm (1 dp)

5 23.1 cm (1 dp) 6 13.7 cm (1 dp)

7 0.7 cm (1 dp) 8 11.7 cm (1 dp)

9 11.3 cm (1 dp) 10 2.1 cm (1 dp)

Exercise 13.41 60° 2 36.9° (1 dp)

3 54.3° (1 dp) 4 41.4° (1 dp)

5 49.5° (1 dp) 6 36.9° (1 dp)

7 53.9° (1 dp) 8 51.0° (1 dp)

9 42.6° (1 dp) 10 71.3° (1 dp)


3 6 cm 4 11.5 cm (1 dp)

5 2.7 cm (1 dp) 6 5.8 cm (1 dp)

7 5.8 cm (1 dp) 8 3.7 cm (1 dp)

9 2.9 cm (1 dp) 10 6.3 cm (1 dp)


3 14.9 cm (1 dp) 4 14.6 cm (1 dp)

5 23.1 cm (1 dp) 6 13.7 cm (1 dp)

7 0.7 cm (1 dp) 8 11.7 cm (1 dp)

9 11.3 cm (1 dp) 10 2.1 cm (1 dp)

Exercise 13.7

Exercise 13.81 a � 53.1°, b � 36.9°, x � 15 cm2 x � 5.6 cm, y � 9.8 cm3 x � 10.9 cm, y � 8.3 cm4 x � 6.7 cm, y � 7.4 cm5 x � 9.7 cm, y � 7.1 cm6 x � 22.2 cm, y � 14.3 cm7 a � 22.6°, b � 67.4°, x � 12 cm8 x � 11.9 cm, y � 15.0 cm9 x � 9.4 cm, y � 23.2 cm

10 a � 53.1°, b � 36.9°, x � 15 cm

Chapter 14 – Shape, space andmeasures 7Exercise 14.11 Pupils’ drawings of a circle with a radius of 6 cm

and centre at X.

2 Pupils’ constructions of the perpendicularbisector of XY.

3

4 (a) Pupils’ constructions of the perpendicular bisector of XY.



Angle x sin x Angle (90° � x) cos (90° � x)

5° 0.087 85° 0.087

10° 0.174 80° 0.174

15° 0.259 75° 0.259

20° 0.342 70° 0.342

25° 0.423 65° 0.423

30° 0.5 60° 0.5

35° 0.574 55° 0.574

40° 0.643 50° 0.643

45° 0.707 45° 0.707

4 cm

10 cmC D

X

Y


(b) The intersection of the perpendicular bisectors of XYand XZ.

5 The intersection of two circles with centres at Land M and radii of 4 cm.

Exercise 14.21 (a), (b)

2 (a), (b)

3 (a)–(d)

4

5 (a), (b)

6 (a), (b)

7 (a)–(d)



X

Y

Z

8 m

3 m

2 m

2 m

4 m

10 m

2 m

8 m

A

B

40 km

30 km

50 km

15 m

10 m10 m X Y

Z

3 m

3 m 7 m

12 m

10 m

3 m

3 m

Alex

James

Sofia

(c)

(b)

(d)

L M

4 cm


8 (a), (b)

Chapter 15 – Using and applyingmathematics/ICT 3ICT activity1 Shortest distance AX � XB � 2236 m

2

Investigation(a) 26.6° (1 dp)(b) 26.6° (1 dp)

Review 3A1 (a) (i) Lower bound � 19.5,

upper bound � 20.5(ii) 19.5 x � 20.5

(b) (i) Lower bound � 99.5, upper bound � 100.5

(ii) 99.5 x � 100.5

2 (a) (i) Lower bound � 15.15, upper bound � 15.25

(ii) 15.15 x � 15.25(b) (i) Lower bound � 0.875,

upper bound � 0.885(ii) 0.875 x � 0.885

3 (a)

(b) x � 2, y � 2

4 x � 3, y � 0

5 (a) One solution, pupils’ explanations

(b) No solution, pupils’ explanations

6 22°

7 Triangle is right-angled as cos 60° � �12

00�

8 p � 9.3 cm (1 dp)q � 8.1 cm (1 dp)

9 (a), (b) Pupils’ constructions of theperpendicular bisector of XY.

10 (a), (b)

Review 3B1 (a) (i) Lower bound � 4.5, upper bound � 5.5

(ii)



6 m2 m

2 m

6 m0

2

�2

�4

4

�2 2 4

y

x

y � 3x � 4

y � � x � 312

0

2

�2

�4

4

6

�2 2 4

y

x

2x � y � 6

x � y � 3

QR

P

8 m

3 m

5 m

4.5 5 5.5


(b) (i) Lower bound � �0.5, upper bound � 0.5

(ii)

2 (a) (i) Lower bound � 9.95, upper bound � 10.05

(ii)

(b) (i) Lower bound � 9.995, upper bound � 10.005

(ii)

3 (a)

(b) x � 2, y � �1

4

x � 3, y � 1

5 (a) Infinite number of solutions, pupils’explanations

(b) No solution, pupils’ explanations

6 63°

7 Not a right-angled triangle as sin 30° � �184�

8 (a) a � 10.9 cm, b � 5.1 cm

(b) c � 34°

9 Pupils’ constructions of the perpendicularbisectors of two of the following: PR, QR andPQ. The point of intersection is the pointequidistant from P, Q and R.

10 (a), (b)

SECTION FOURChapter 16 – Algebra 4Exercise 16.11 (a) x 7 (b) x � �1

2 (a) x �2 (b) x � 1

3 (a) x 2 (b) x �4

4 (a) x � 1 (b) x � 2

5 (a) x � �3 (b) x 1.5

6 (a) x 2.25 (b) x 0

Exercise 16.21 (a) x � �1 (b) x �9

2 (a) x � �2 (b) x 5

3 (a) x �2 (b) x � �14

4 (a) x 12 (b) x 5

5 (a) x � 5 (b) x � 0

6 (a) x � �3 (b) x 4

7 (a) x 4.5 (b) x � 4

8 (a) x � �34 (b) x �36

Exercise 16.31 1 � x 4

2 2 x 4

3 8 � x 9

4 �6 � x �3



�0.5 0 0.5

9.95 10 10.05

9.995 10 10.005

0

2

�2

4

6

�2 2 4

y

y � �2x � 3

y � �1x

0

2

4

2 4 6 8

y

y � x � 4

3y � x � 6

x

7 m

5 m1 m1 m

1 m

1 m

0 1 2 3 4 5

0 1 2 3 4 5

6 7 8 9 10 11

�7 �6 �5 �4 �3 �2


5 x 1, x 2

6 x 2, x � 5

7 x 2.5, x 6

8 x � 1, x 2

Chapter 17 – Algebra 5Exercise 17.11 (a � 2)(a � 4) 2 (b � 3)(b � 4)

3 (c � 3)(c � 5) 4 (d � 3)(d � 8)

5 (e � 1)(e � 3) 6 ( f � 2)( f � 9)

7 (g � 7)(g � 11) 8 (h � 3)2

9 ( j � 10)2 10 (k � 4)2

Exercise 17.21 (a � 2)(a � 3) 2 (b � 4)(b � 5)

3 (c � 1)(c � 4) 4 (d � 8)(d � 9)

5 (e � 5)(e � 7) 6 ( f � 1)( f � 2)

7 (g � 3)2 8 (h � 7)2

9 ( j � 11)2 10 (k � 12)2

Exercise 17.31 (a � 2)(a � 3) 2 (b � 1)(b � 3)

3 (c � 2)(c � 4) 4 (d � 7)(d � 9)

5 (e � 5)(e � 6) 6 ( f � 3)( f � 2)

7 (g � 9)(g � 8) 8 (h � 3)(h � 1)

9 ( j � 6)( j � 2) 10 (k � 4)(k � 4)

Exercise 17.41 (a � 3)2 2 (b � 2)2

3 (c � 2)(c � 2) 4 (d � 4)(d � 4)

5 (e � 3)(e � 5) 6 ( f � 2)( f � 7)

7 (g � 2)(g � 6) 8 (h � 9)(h � 9)

9 ( j � 5)2 10 (k � 3)(k � 3)

Exercise 17.51 a � �2, a � �3 2 b � �3, b � �4

3 c � �9, c � �8 4 d � �1, d � 2

5 e � 5, e � �2 6 f � 6, f � �3

7 g � 2, g � 3 8 h � 4, h � 5

9 j � 6, j � 7 10 k � �3

11 l � �4 12 m � 5

13 n � 8 14 p � 1

15 q � �1 16 r � 7, r � 9

17 s � 1, s � �1 18 t � 3, t � �3

19 v � 5, v � �5 20 w � 11, w � �11

Exercise 17.61 7 cm and 8 cm 2 9 cm and 5 cm

3 6 cm and 9 cm 4 3 cm and 13 cm



9 10 cm and 12 cm 10 12 cm and 13 cm

Chapter 18 – Shape, space andmeasures 8Exercise 18.11 904.8 cm3 2 4.2 cm3

3 179.6 cm3 4 1767.1 cm3

5 134.0 cm3 6 381.7 cm3

7 Mercury � 60 800 000 000 km3

Venus � 929 000 000 000 km3

Earth � 1 090 000 000 000 km3

Mars � 164 000 000 000 km3

Jupiter � 1 520 000 000 000 000 km3

Saturn � 905 000 000 000 000 km3

Uranus � 73 600 000 000 000 km3

Neptune � 59 400 000 000 000 km3

Pluto � 14 100 000 000 km3

Exercise 18.21 8.4 cm 2 6.7 mm

3 4.6 cm 4 1.3 m

5 62.0 cm 6 0.6 cm

7 (a) 6.2 cm (b) Pupils’ predictions.(c) 12.4 cm (d) Pupils’ comments.

8 (a) 4188.8 cm3 (b) Pupils’ predictions.(c) 33 510.3 cm3 (d) Pupils’ comments.



�1 0 1 2 3 4

1 2 3 4 5 6

1 2 3 4 5 6 7

�1 0 1 2 3 4


Exercise 18.31 (a) 216 cm3

(b) 113.1 cm3 (1 dp)

(c) 52.4% (1 dp)

2 (a) 1145.1 cm3 (1 dp)

(b) 763.4 cm3 (1 dp)

(c) 66.7% (1 dp)

3 6.2 cm 4 1466 cm3

5 116.2 cm3 6 8.8 cm

Chapter 19 – Shape, space andmeasures 9Exercise 19.11 18.0 m

2 (a) 3.9 m (1 dp) (b) 3.8 m (1 dp)

3 50 m

4 2.42 km (2 dp)

5 192.0 m (1 dp)

6 (a) 7.8 km (1 dp) (b) 23.4 km (1 dp)

Exercise 19.21 14.00 m

2 7.7 m

3 a � 18.4° (1 dp), b � 9.5° (1 dp)

4 211 m

5 (a) 200 m (b) 317.6 m (1 dp)

6 (a) 46.2 m (1 dp) (b) 9.8 m (1 dp)

7 (a) P: 15 km, Q: 12 km (b) 8.5 km (1 dp)

(c) 25.0 km (1 dp)

8 (a) 7.1 m (1 dp) (b) 7.1 m (1 dp)

(c) 9.2 m (1 dp) (d) 22.5°

Chapter 20 – Using and applyingmathematics/ICT 4InvestigationPupils’ investigations and results.

ICT activityPupils’ investigations on Pythagoras.

Review 4A1 (a) x 4 (b) x � �7

2 (a) 2 � x 5

(b) �2 � x � 3

3 (a) (y � 3)(y � 2) (b) (p � 4)(p � 6)

(c) (x � 4)(x � 4)

4 (a) x � 1, x � �10 (b) x � 2, x � 7

5 (a) �12�(2x � 6)(x � 1) � 48, or equivalent

(b) x � 5 (note x � �9)

(c) Base length � 16 cm, height � 6 cm

6 (a) 2x2 (b) (x � 1)2

(c) 2x2 � (x � 1)2 � 7 (d) x � 2 (note x � �4)

7 (a) 904.8 cm3 (b) 4188.8 cm3

8 13.37 cm

9 (a) 4.8 m (1 dp) (b) 72.5° (1 dp)

10 (a) 16.5 m (1 dp) (b) 8.9 m (1 dp)

Review 4B1 (a) x � 2 (b) x 5.5

2 (a) �5 x 11

(b) x 7, x � 6�12�

3 (a) (x � 8)(x � 1) (b) (r � 8)(r � 7)

(c) (p � 5)2

4 (a) x � 4, x � 9 (b) y � �1, y � 1

5 (a) (x � 6)(x � 1) � 30

(b) x � 4 (note x � �9)


6 (a) 4x2 (b) (x � 6)(x � 2)

(c) 4x2 � 3(x � 6)(x � 2)

(d) x � 6

(e) Square � 12 cm � 12 cm, rectangle � 12 cm � 4 cm



1 2 3 4 5 6

�3 �2 �1 0 1 2 3 4

�8 �4 0 4 8 12

5 6 6 7 7 812

12

12


7 (a) 3050 cm3 (b) 7240 cm3

8 (a) 523.6 cm3 (1 dp) (b) 4188.8 cm3 (1 dp)

(c) 10 cm

9 (a) 3 m (b) 36.9° (1 dp)

10 (a) 11.3° (1 dp) (b) 15 m

SECTION FIVE – REVISIONBook 1Section 11 (a) 7.93 (b) 0.01 (c) 1.10

2 (a) 6800 (b) 37 000 (c) 3 800 000

3 (a) Approx. 15 000

(b) Approx. 400

4 (a) a � 20 (b) b � 4 (c) c � �10

5 (a) Pupils’ drawings of a 52° angle.

(b) Pupils’ drawings of a 128° angle.

(c) Pupils’ drawings of a 105° angle.

(d) Pupils’ drawings of a 75° angle.

6 (a) Pupils’ constructions.

(b) A � 36°, B � 46°, C � 98°

7

8

9

10

Note: the percentages do not add up to 100%,due to rounding.

Section 21 (a) 7 (b) 20 (c) 13

2 (a) 6.25 (b) 0.25 (c) 0.7

3 23, 29, 31, 37, 41, 43, 47

4 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350

5 60

6 42

7 (a) 18, 22 (b) 53, 62

(c) 54, 45 (d) 36, 49

8 (a) 3n � 1 (b) 5n � 1

9 (a)

(b) Trapezium

10 (a) Frequency table will vary according togrouping.

(b) Pupils’ histograms.

4

2

�2

�4

y

D

C B

A

x�4 �2 20 4

19%

12%

5%

6%7% 10%

22%

France

Spain

PortugalGreece

Egypt

Italy

USA

Other20%

Holiday destinations

Freq

uenc

y

Number of sweets

Sweets in packets

35 36 37 38 39 4002468

10121416

Freq

uenc

y

Number of litres

Milk consumption

1 2 3 4 5 60

10

20

30

40

50

11%

Student‘s travel

24%

56%

bus

carwalk

cycle9%

20 Section 5 – Book 1



Section 31 (a) 360 (b) 22�

12� (c) 49 (d) 64

2 (a) 1�112� (b) �1

96� (c) �5�

58�

3 (a) 60% (b) 62.5% (c) 17% (d) 140%

4 (a) 0.125 (b) 0.8 (c) 0.45 (d) 1.6

5 (a)

(b)

6 (a) y � �12�x � 2 (b) y � �3 (c) y � �x � 1

7 (a)

(b)

8 60°

9 (a) �12

95� (b) �2

65� (c) 0

10 40 000

Section 41 (a) 60 (b) 225 (c) 50

2 (a) 200 (b) 256 (c) 125

3 €105

4 €24 960

5 (a) 4a � 12 (b) �15b � 35

(c) 2bc � 4c (d) 12a2 � 9ab � 3ac

6 (a) a2 � b2

(b) p2 � 2pq � q2

(c) 2mn � 8m � 3n � 12

(d) m2 � 2mn � n2

7

8 Mean � 2.48, median � 2, mode � 1 and 2

9 Mean � 13.4 s (1 dp), range � 1 s

10 Mean � 9.9, median � 10

Section 51 13.5 cm

2 12 : 18 : 30

3 90°, 90°, 135°, 45°

4 (a) 16 (b) �3

5 Pupils’ constructions.

6 42.48 cm2

7 31.5 cm2

8 �16�

4

10

12

�8 �6 �4 �2 0 2 4 6 8

y

x

A

BDC

0

2

�2

�4

�2 2 4

y

x

y � x � 3

0

2

�2

4

6

�2 2 4

y

x

y � 2x

Section 5 – Book 1 21



Book 2Section 11

2 (a) �11.6 (b) �16.8 (c) �20

3 (a) (4 � 2) � 6

(b) (8 � 2) � (5 � 3)

(c) ((5 � 3) � (9 � 2)) � 2

4 (a) 9 (b) 18 (c) 4

5 Pupils’ drawings of a circle with a radius,tangent, minor arc and sector labelled.



8 Pupils’ questions.

Section 21 (a) 89.5 m (b) 700 m (c) 0.45 m

2 (a) 3000 kg (b) 50 kg (c) 0.75 kg

3 (a) 60 ml (b) 4200 ml (c) 8 ml

4 (a) a � 5 (b) b � 5 (c) c � 4

5 (a) 50.3 cm (1 dp) (b) 22.6 cm (1 dp)

6 (a) 37.7 cm (1 dp) (b) 45.2 cm (1 dp)

7 (a) 78.5 cm2 (1 dp) (b) 45.4 cm2 (1 dp)

8 73.3 cm2

9 Pupils’ drawings of the net. One possibility is:

10 Pupils’ drawings of the net. One possibility is:

Section 31 (a) a is less than 8

(b) b is greater than 6

(c) c is not equal to 5

(d) d is less than or equal to 11

2 (a) a � b

(b) 4 � b � 12

(c) b c � d

3 (a)

(b)

(c)

4 (a) x � p � 3 (b) x � y � �12�z

(c) x � �3l �

lm

�

5 (a) y � �32�n � 2m (b) y � �2p � q�

(c) y � �xpq�

6 Pupils’ explanations and diagrams.

7 (a)

(b)

8 (a) 35°

(b) 54°

9 (a) a � 36° therefore angles are 72° and 108°

(b) a � 65°, b � 80°, c � 80°, d � 35°, e � 65°, f � 115°

10 Pupils’ explanations.

10 cm

3 cm

2 cm



Depart 0600 0815 1020 1308 1550 1905

Arrive 0815 1030 1235 1523 1805 2120

6 cm6 cm

5 cm5 cm

4 5 6

8 9 10 11

6 7 8 9 10 11 12


Section 41 2.1%

2 (a) 11.1% profit (b) 3.8% loss

(c) 150% profit

3 (a) 6(a � 2) (b) 3(5a � 6b � 2c)

(c) 7(3x � 8y)

4 (a) 3a(b � 2a) (b) 6x2y(3y2 � 2)

(c) 9ab(4ab2 � 3bz � az)

5 (a) (2x � 3)(a � b) (b) (p � 2q)(4y � z)

6 339.3 cm3

7 4 cm

8 6 cm

9 (a) �135� or �

15� (b) �1

45� (c) �1

75�

10 (a) �12� (b) �1

82� or �

23� (c) �1

22� or �

16�

Section 51 (a) y � �

12�x � 2 (b) y � �x � 1

2 (a)

(b)

3 (a) 4 (b) ��12�

4 72°

5 211°

6 30

7 308 cm2

8 9 cm

9

10 (a)

(b) Class B is more likely to be mixed ability.Pupils’ explanations.

Book 3Section 11 (a) 55 (b) 1 (c) 26

2 (a) a2b3c (b) p6

3 (a) 9 (b) a

4 40 km/h

5 18 km

6 2030 g

7 13 cm

8 5.6 cm (1 dp)

9 10.9 cm (1 dp)

10 Pupils’ scale drawings.

(a) AB � 85 km, BC � 77 km

(b) 135°

Freq

uenc

y

Grouped percentage

Maths test results

0– 20– 40– 60– 80 –100

05

1015202530

Class B

Class AFr

eque

ncy

Grouped height (cm)

Girls’ heights

130– 140– 150– 160– 170 –180

05

1015202530

0

2

�2

�4

4

�2 2

y

2y � 4x � �4

x

0

2

�2

�4

�6

4

�2 2

y

y � 3x � 4

x

Section 5 – Book 2 23



Section 21 (a) 7.5 � 106 (b) 6 � 109

2 (a) 2 � 106 (b) 4.9 � 107

3 (a) 7.84 � 1010 (b) 4 � 106

4 (a) 6.17 � 10�7 (b) 3 � 10�5

5 (a) p � 1, q � 2 (b) m � 8, n � 5

6 x � 2, y � 5

7 35.5 cm (1 dp)

8 19.1 cm (1 dp)

9 68.2° (1 dp)

10 273 K

Section 31 (a) Lower bound � 161.5 s,

upper bound � 162.5 s

(b)

(c) 161.5 h � 162.5

2 (a) Lower bound � 13.85 s, upper bound � 13.95 s

(b)

(c) 13.85 t � 13.95

3 (a) x � 4, y � 0

(b) x � �5, y � 4

4 (a) y � 3

(b) m � �12�

(c)

5 (a)

(b) Pupils’ descriptions.

(c) None

(d) There are no solutions because the lines donot intersect.

6 (a) 9 cm (b) 10.4 cm (1 dp)

7 (a) 54° (b) 24.9°

8 Yes, because cos 60° � �13

50�

9 (a), (b)

(c)

(d)

15 m

A B10 m

4 mA B10 m

6 m

15 m

A B10 m

0

2

�2

�2

�4

4

6

2 4

y

x

y � 3x � 2

y � 3x � 2

0

2

�2

4

6

�2 2 4 6

y

y � x � 2

y � x � 5

x

12

13.85 13.9 13.95

161.5 162 162.5




10 (a), (b) Perpendicular bisector of XY ending atthe point of intersection of two circleswith radii 8 cm and with centres at Xand Y.

Section 41 (a) x 6 (b) x � �5

2 (a) x �2

(b) 3 x � 12

(c) x �3

3 (a) (x � 5)(x � 3) (b) (x � 7)(x � 3)

4 (a) x � 1, x � �6 (b) x � 4

5 (a) (x � 1)(x � 2) � 28

(b) x � 5 (note x � �6)

(c) Length � 7 cm, width � 4 cm

6 (a) �12�(4x � 8)(�

12�x � 1) � 100

(b) x � 8 (note x � �12)


7 4188.8 cm3 (1 dp)

8 700 cm3

9 (a) 266.3 m (1 dp) (b) 8

10 (a) 3.8° (1 dp) (b) 40.07 m

SECTION SIX - EXTENSIONChapter 21 – Number 3

Exercise 21.11 3000 2 1200 3 3504 500 5 2500 6 9007 20 8 11 9 360

10 560

Exercise 21.21 160 2 112 3 3604 220 5 64 6 647 76 8 70.4 9 2

10 600

Exercise 21.31 50 2 €6000 3 1254 44 5 3200 6 €150 0007 €7500 8 120 9 €360

10 €350

Exercise 21.41 (a) 60 (b) 210 (c) 20 (d) 120

2 (a) 800 (b) 300 (c) 360 (d) 134

3 (a) 175 (b) 560 (c) 220 (d) 110

4 €84 5 6 years

6 25% 7 150%

8 €5000 9 40

10 100%

Chapter 22 – Algebra 6Exercise 22.11 x � �1, x � 2 2 x � �2, x � 33 x � �3, x � �1 4 x � �1, x � 15 No solution 6 x � 1

Exercise 22.21 (a)

�5 �4 �3 �2 �1 0

2 4 6 8 10 12 13

�5 �4 �3 �2 �1 0



8 cm

X

Y

x 0 1 2 3 4 5

y 6 2 0 0 2 6


(b)

(c) x � 2, x � 3

2 (a)

(b)

(c) x � �2, x � 2

3 (a)

(b)

(c) x � �12�, x � 4

4 (a)

(b)

(c) x � �2, x � 3

5 (a)

(b)

(c) x � �3

6 (a)

(b)

(c) x � 1.3, x � 2.7

7 (a)

(b)

(c) x � 0, x � 1�13�

8 (a)

0

2

�4

�6

�8

1 2�1

y

x

0

5

10

15

1 2 3 4

y

x

0

2

4

6

8

10

1�1�3�4�5�6 �2

y

x

0�2

�4

�6

2

4

6

1�1�3 �2 2 3 4

y

x

0�2

�4

2

4

6

8

1�1�2 2 3 4 5

y

x

10

2

�2

�4

4

�1�2�3 2 3

y

x

0 1�2

2

4

6

8

2 3 4 5

y

x



x �3 �2 �1 0 1 2 3 4

y �6 0 4 6 6 4 0 �6

x �6 �5 �4 �3 �2 �1 0

y 9 4 1 0 1 4 9

x 0 1 2 3 4

y 14 2 �2 2 14

x �1 0 1 2

y �7 0 1 �4

x �1 0 1 2 3 4

y �7 �3 �1 �1 �3 �7

x �3 �2 �1 0 1 2 3

y 5 0 �3 �4 �3 0 5

x �1 0 1 2 3 4 5

y 7.5 2 �1.5 �3 �2.5 0 4.5


(b) (c) No solution

Exercise 22.31 (a) (x � 5)(x � 2) � 20

(b)

x � 1.2, x � �8.2(c) Length � 6.2 cm, width � 3.2 cm

2 (a) Area A � m2 cm2, area B � (2m � 2)2 cm2

(b) (2m � 2)2 � 3m2

(c) m � 0.5, m � 7.5

(d) 13 cm3 (a) 6x2 (b) 6(x � 2)2

(c) 6(x � 2)2 � 12x2

(d) x � 4.8 cm

4 (a) 4x2 (b) �12�(2x � 4)x (c) 4x2 � x(x � 2)

(d) x � �23�

(e) Square side length � 1�13� cm

Triangle base length � 5�13� cm,

triangle height � 1�13� cm

5 (a) �(r � 5)2 � 3�(r � 1)2

(b) r � 9.2

(c) X: radius � 8.2 cm, Y: radius � 14.2 cm

6 (a) 6(x � 1)2 (b) 2x2 � 4x(x � 3)(c) 6(x � 1)2 � 4x2 � 8x(x � 3)

(d)

x � 0.4

(e) Approx. 5.9 cm2

0

5

�5

�10

�15

10

�1 1�2�3

y

x

0�10

�20

�30

�40

�50

�2 2 4 6 8 10

y

r

0

5

1

�1

2

3

4

�0.5�1 0.5 1 1.5

y

x

0

50

40

30

20

2 3 41�1

y

x

0

10

�10

4 6 82

y

m

0

10

�10

�20

42�2�4�6�8

y

x

0

�2

�6

�8

1 2 3 4�1

y

x




Chapter 23 – Shape, space andmeasures 10Exercise 23.11 � � 2 � � 3 � � 4 � �5 � � 6 � � 7 � � 8 � �Exercise 23.21 4 units to the right and 4 units vertically

upwards2 1 unit to the right and 0 units vertically3 2 units to the right and 9 units vertically

downwards4 6 units to the left and 5 units vertically upwards5 8 units to the left and 2 units vertically

downwards6 0 units horizontally and �

12� unit vertically

downwards7 4 units to the left and 0 units vertically8 �

12� unit to the right and 10 units verticallydownwards

Exercise 23.3

1 (a) � � (b) � � (c) � � (d) � �(e) � �

2 (a) � � (b) � � (c) � � (d) � �(e) � � (f) � � (g) � � (h) � �

3

Exercise 23.4

1 (a) � � (b) � � (c) � � (d) � �2 (a) � � (b) � � (c) � � (d) � �3 (a) � � (b) � � (c) � � (d) � �

(e) � � (f) � � (g) � �(h) Same magnitude but opposite direction,

resulting in change of sign.

(i) Same magnitude but opposite direction,resulting in change of sign.

4 � � 5 � �6 � � 7 � �8 � �

Chapter 24 – Handling data 1Exercise 24.11 (a) Class A

Class B

100

89

5�3

0�2

�1�4

23

�2�3

3�3

�33

�6�2

9�1

�16

�54

�30

0�5

81

�64

�3�5

5�1

42

A

B

E

C

D

03�

12�

0�7

�8�9

4�6

4�2�

12�

82

�4�1

41

�32

�50

1�3

4�1

32

00

�60

0�8

�2�7

6�3

�42

51

23



Grouped percentage Frequency Cumulative frequency

0 � x 20 1 1

20 � x 40 3 4

40 � x 60 16 20

60 � x 80 8 28

80 � x 100 2 30


0 � x 20 0 0

20 � x 40 0 0

40 � x 60 25 25

60 � x 80 4 29

80 � x 100 1 30


(b)

(c) Median class A � 56%, median class B � 48%

(d) IQR class A � 16%, IQR class B � 12%

(e) Pupils’ comparisons of both classes, forexample class A results more spread outthan class B.

2 (a) Boys

Girls

(b)

(c) Median height for boys � 155 cm, median height for girls � 146 cm

(d) IQR boys � 15 cm, IQR girls � 12 cm

(e) Pupils’ comparisons, for example similarspread, but boys’ median height isapproximately 10 cm taller than girls’.

3 (a) Motorway

Smaller roads



Grouped height (cm) Frequency Cumulative frequency

120 � x 130 3 3

130 � x 140 5 8

140 � x 150 9 17

150 � x 160 20 37

160 � x 170 12 49

170 � x 180 1 50

Grouped height (cm) Frequency Cumulative frequency

120 � x 130 6 6

130 � x 140 9 15

140 � x 150 23 38

150 � x 160 8 46

160 � x 170 3 49

170 � x 180 1 50

5

10

15

20

25

30Class A cumulative frequency graph

0

20 40 60 80 100

Percentage

Cum

ulat

ive

frequ

ency

5

10

15

20

25

30Class B cumulative frequency graph

0

20 40 60 80 100

Percentage

Cum

ulat

ive

frequ

ency

10

20

30

40

50

Cumulative frequency, height : boys

0

100

110

120

130

140

150

160

170

180

Height (cm)

Cum

ulat

ive

frequ

ency

10

20

30

40

50

Cumulative frequency, height : girls

0

100

110

120

130

140

150

160

170

180

Height (cm)

Cum

ulat

ive

frequ

ency

Grouped time (min) Frequency Cumulative frequency

20 � t 30 10 10

30 � t 40 3 13

40 � t 50 2 15

50 � t 60 0 15

60 � t 70 3 18

70 � t 80 1 19

80 � t 90 0 19

90 � t 100 1 20

Grouped time (min) Frequency Cumulative frequency

30 � t 40 1 1

40 � t 50 18 19

50 � t 60 1 20


(b)

(c) Motorway median � 30 min, small roadsmedian � 46 min

(d) IQR motorway � 25 min, IQR small roads � 5 min

(e) Pupils’ conclusion, for example median timesfor motorway are lower, but there is a largerrange in times for the motorway.

4 (a) Resort A

Resort B

(b)

(c) Median resort A � 25.5 °C, median resort B � 23 °C

(d) IQR resort A � 7.5 °C, IQR resort B � 1 °C

(e) Pupils’ conclusion, for example mediantemperature of resort A is slightly higherthan B, but resort B has a more consistenttemperature than A.



2

4

6

8

10

12

14

16

18

20

Cumulative frequency : motorway times

0

10 20 30 40 50 60 70 80 90 100

Time (min)

Cum

ulat

ive

frequ

ency

2

4

6

8

10

12

14

16

18

20

Cumulative frequency : Small road times

0

10 20 30 40 50 60 70 80 90 100

Time (min)

Cum

ulat

ive

frequ

ency

Grouped max. dailyFrequency

Cumulative temperature (°C) frequency

18 � t 20 0 0

20 � t 22 0 0

22 � t 24 28 28

24 � t 26 3 31

26 � t 28 0 31

28 � t 30 0 31

Grouped max. dailyFrequency

Cumulative temperature (°C) frequency

18 � t 20 6 6

20 � t 22 3 9

22 � t 24 3 12

24 � t 26 5 17

26 � t 28 5 22

28 � t 30 9 31

4

8

12

16

20

24

28

32

Cumulative frequency : resort A

018 20 22 24 26 28 30

Temp (°C)

Cum

ulat

ive

frequ

ency

4

8

12

16

20

24

28

32

Cumulative frequency : resort B

0

18 20 22 24 26 28 30

Temp (°C)

Cum

ulat

ive

frequ

ency


5 (a)

(b)

(c) Approx. 320

(d) Approx. 190

(e) Approx. 38%

Chapter 25 – Using and applyingmathematics/ICT 5InvestigationPupils’ results and conclusions.

ICT activityGraphs plotted in the form y � (x � a)2 producetranslations of the graph y � x2. a � 0 produces atranslation to the right, a � 0 produces a translationto the left. (x � 4)2, (x � 2)2, x2, (x � 2)2, (x � 4)2

Variations in a and b produce diagonal translationsof the graph y � x2. (x � 6)(x � 2), (x � 4)(x), (x � 2)(x � 2), (x)(x � 4)

Review 6A1 €217 000 (3 sf)

2 (a) 187.5 (b) 6400 (c) 66�23�

3 (a)

(b) x � �3.5, x � 2.5

4 (a)

(b) x � �2

5 (a) �12�x(x � 1) (b) �

12�(2x � 4)(x � 3)

(c) �12�(2x � 4)(x � 3) � 2x(x � 1)

(d) x2 � 3x � 6 � 0

(e)

(f) x � 4.3 (note x � �1.3)

6 (a) 3 units to the right and 6 units verticallyupwards

(b) 4 units to the right and 2 units verticallydownwards

0

�5

�10

�1 1 2 3 4�2�3

y

x

0

1

2

3

4

5

6

�1�2�3�4

y

x




0 � x 10 26 26

10 � x 20 44 70

20 � x 30 56 126

30 � x 40 62 188

40 � x 50 80 268

50 � x 60 126 394

60 � x 70 245 639

70 � x 80 148 787

80 � x 90 131 918

90 � x 100 82 1000

100

200

300

400

500

600

700

800

900

1000

Mathematics exam results :cumulative frequency

0

10 20 30 40 50 60 70 80 90 100

Percentage score

Cum

ulat

ive

frequ

ency

0

�5

5

�10

�1 1 2 3�2�3�4

y

x


7

8 (a)

(b)

(c) Approx. 45 min

(d) Approx. 15

(e) Approx. 8.55 am

Review 6B1 €42 900 (3 sf)

2 (a) 236.4 (1 dp)

(b) 10

(c) 0.56 (2 dp)

3 (a)

(b) x � �1, x � 1.5

4 (a)

(b) It has no solution because the graph does notintersect the x axis.

5 (a) 3(x � 3)(x � 2)

(b) (x � 1)(x � 5)

(c) 3(x � 3)(x � 2) � 4(x � 1)(x � 5)

(d) x2 � 9x � 2 � 0

(e)

(f) x � �0.23

(g) Cuboid A � 3 � 1.77 � 2.77, cuboid B � 1 � 0.77 � 4.77

0

5

10

�5

�10

�15

�20

�5�10

y

x

0�1

1

2

3

4

5

6

�1 1 2�2

y

x

0�1

1

2

3

4

�2

�3

�4

1 2�2

y

x

A

D

B

C



Time (min) Frequency Cumulative frequency

0– 2 2

10– 5 7

20– 8 15

30– 4 19

40– 14 33

50– 15 48

60–70 2 50

5

10

15

20

25

30

35

40

45

50

Travelling time : cumulative frequency

0

10 20 30 40 50 60 70

Time (min)

Cum

ulat

ive

frequ

ency


6 (a) 1 unit horizontally to the right

(b) 3 units horizontally to the left and 5 unitsvertically upwards

7 (a) � � (b) � � (c) � �8 (a)

(b)

(c) Approx. 56% (d) Approx. 40%

(e) Approx. 46%

SECTION SEVEN –CHECKPOINT QUESTIONSNumber1 2.167 � 106

2 42.749̇3 5.95 � 1019

Algebra1 x � 6, y � 4

2 x � 4, x � �3

3 (a) 6000 litres

(b) 20 minutes

(c) 50 litres/minute

(d) 270 minutes

Shape, space and measures1 (a) 064°

(b) Pupils’ bearing diagrams.

(c) (i) 9.5 cm (ii) 95 km

2 (a) 3.54 m

(b) 31°

�50

4�5

74

Section 7 – Checkpoint questions 33


Percentage Frequency Cumulative frequency

0– 7 7

20– 15 22

40– 38 60

60– 14 74

80–100 26 100

10

20

30

40

50

60

70

80

90

100

Exam results : cumulative frequency

0

10 20 30 40 50 60 70 80 90 100

Percentage

Cum

ulat

ive

frequ

ency


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