checkpoint maths 2 answers pupils’ construction of a regular octagon. 4 (a), (b) pupils’...

Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational 1 of 24

SECTION ONEChapter 1 – Shape, space andmeasures 1Exercise 1.11 (a) 0830 (b) 0535 (c) 0955

(d) 1845 (e) 2330 (f) 1650

2 (a) 1900 (b) 1200 (c) 0005

(d) 2210 (e) 0815 (f) 2015

(g) 0745 (h) 1945

Exercise 1.21 (a) 0840

(b) 0820

(c) 0800

2 (a) 1630

(b) 1606

(c) 1803

3 (a) (b)

4

5

6 (a) 1 hour 2 min

(b) 1620

(c) 1926

(d) 2225

7 Pupils’ own questions and answers.

Chapter 2 – Number 1Exercise 2.11 (a) 14.8 (b) 31.14 (c) 9.66

(d) 100.01 (e) 44.44 (f) 9.1

2 (a) 11.1 (b) 10.9 (c) �15.04

(d) �0.01 (e) �11.7 (f) �10

(g) �12 (h) 0

3 (a) 17.02 (b) 159.36 (c) 43.56

(d) 4 (e) �35.1 (f) �5.1

(g) 18.63 (h) 10

Exercise 2.21 (a) 20 (b) 30 (c) 24

(d) 14 (e) 43 (f) 18

2 (a) 18 (b) 9 (c) 11

(d) 0 (e) 27 (f) 1

3 (a) 15 (b) 18 (c) 2

(d) 35 (e) 15 (f) 6

Checkpoint Maths 2 Answers

Depart Arrive

0523 0631

0715 0823

0904 1012

1028 1136

1445 1553

1622 1730

1809 1917

2017 2125

Depart Arrive

5.23 am 6.31 am

7.15 am 8.23 am

9.04 am 10.12 am

10.28 am 11.36 am

2.45 pm 3.53 pm

4.22 pm 5.30 pm

6.09 pm 7.17 pm

8.17 pm 9.25 pm

Stansted 0500 0715 0915 1040 1315

Luton 0630 0845 1045 1210 1445

Gatwick 0805 1020 1220 1345 1620

Heathrow 0850 1105 1305 1430 1705

London Dubai London Dubai(local time) (local time)

Sunday 0200 1012 1400 2212

Monday 0200 1012 1348 2200

Tuesday 0310 1122 1510 2322

Wednesday 0336 1148 1321 2133

Thursday 0255 1107 1515 2327

Friday 0057 0909 1436 2248

Saturday 0638 1450 1648 0100

D - Ans 4 web - 001-024.qxd 17/8/04 11:13 am

4 (a) (12 � 8) � 2 � 8

(b) 5 � (2 � 4) � 30

(c) 2 � (3 � 4 � 5) � 4

(d) (10 � 4) � (3 � 3) � 36

(e) (9 � 6 � 3) � 2 � 4 � 10

(f) (9 � 6 � 3) � (2 � 4) � 2

5 (a) 20 � 8 � 2 � 6 � 22

(b) (20 � 8) � 2 � 6 � 12

(c) (20 � 8) � (2 � 6) � 1.5

(d) 20 � (8 � 2 � 6) � 10

(e) 20 � 8 � (2 � 6) � 19

6 (a) 8 � 3 � 4 � 6 � 14

(b) (8 � 3) � 4 � 6 � 38

(c) (8 � 3) � (4 � 6) � �22

(d) 8 � 3 � (4 � 6) � 2

Exercise 2.31 (a) 4 (b) 4 (c) 3

(d) 8 (e) 12 (f) 6

2 (a) 13 (b) 37 (c) 12

(d) 12.8 (e) 0.125 (f) 0.5

Chapter 3 – Shape, space andmeasures 2Exercise 3.11 Circumference

2 Radius, radii

3 Chord

4 Diameter

5 Arc

6 Sector

7 Segment

8 Tangent

Exercise 3.21 Pupils’ drawings.

2 Pupils’ drawings.

3 Pupils’ own patterns.

Exercise 3.31 Pupils’ perpendicular bisector constructions.

2 The orientation of pupils’ diagrams may differfrom the ones shown below.

(a) (b)

(d) (e)

(f)

(g)

2 Section 1 – Shape, space and measures 2


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3 Pupils’ construction of a regular octagon.

4 (a), (b) Pupils’ constructions.

(c) Point of intersection is the same distancefrom points A, B and C.

5 Pupils’ constructions.

6 Pupils’ constructions.

Chapter 4 – Handling data 1Exercise 4.11 Primary

2 Secondary

3 Secondary

4 Primary

5 Secondary

Q p.19Pupils’ suggested research.

Q p.19Question (c).

Q p.19Pupils’ own questions.

Q p.19Pupils’ own questions.

Exercise 4.2Pupils’ rewritten questions.

Exercise 4.3Pupils’ own questions. Ensure questions are clear,simple, unbiased and relevant.

Chapter 5 – Using and applyingmathematics/ICT 1InvestigationOnly one possible solution for each number is givenbelow. There are many other correct possibilities.Some solutions have included the use of the factorial(!) which, although not covered in the text, could beintroduced for more able students.

1 44 � 44 2 �44

� � �44

�

3 �4� � �4� � �44

� 4 �4 �

44

� � 4

5 �4� � �4� � �44

� 6 �4 �

44

� � 4

7 4 � 4 � �44

� 8 (4 � 4) � 4 � 4

9 4 � 4 � �44

� 10 �44

4� 4�

11 4! � �4� � �44

� 12 �44

4� 4�

13 4! � �4� � �44

� 14 4 � 4 � 4 � �4�

15 44 � 4 � 4 16 4 � 4 � 4 � 4

17 4 � 4 � �44

� 18 4 � 4 �

19 4! � 4 � �44

� 20 ��44

� � 4� � 4

21 4! � �4� � �44

� 22 4 � 4 � 4 � �4�

23 (4! � 4 � 4) � 4 24 4 � 4 � 4 � 4

25 �4 � �44

��4�26 4! � �

4 �

44

�

27 4! � �4� � �44

� 28 �4�4 � �4� � 4

29 � 4 � 4! 30 4 � 4 � �4� � �4�4�4

4��4�

Section 1 – Using and applying mathematics/ICT 3


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ICT activityPupils’ constructions.

As the vertex is dragged, the shape of the trianglechanges but the circumference of the circle stillpasses through each of the three vertices.

Review 1A1 (a) 1645 (b) 0030

2 0620

3 0900

4 (a) (3 � 4) � 5 � 35(b) (8 � 6) � (7 � 4) � 22(c) 5 � (8 � 3) � 4 � 51

5 Pupils’ construction of a regular hexagon.

6

7 Pupils’ questionnaires.

8 Pupils’ examples of a biased question whichshould not be used.

Review 1B1 1625

2 2040 on Wednesday

3 2300

4 (a) (7 � 8) � (3 � 2) � 3

(b) (7 � 8) � 3 � 2 � 7

(c) 7 � 8 � (3 � 2) � 8.6

5 Pupils’ constructions of a perpendicular bisector.

6 Pupils’ examples.

7 Pupils’ questionnaires.

8 Pupils’ examples of a badly written question, i.e.not clear, not relevant or biased.

SECTION TWOChapter 6 – Number 2Exercise 6.11 (a) One hundred (b) A hundredth

(c) One thousand (d) A thousandth

(e) One thousand (f) A thousandth

(g) A thousandth (h) One thousand

(i) A millilitre (j) One million

2 (a) kg (b) cm

(c) m or cm (d) ml

(e) t (f) m

(g) litre (h) km

(i) litre (j) cm

3 Pupils’ lines and measurements.

4 Pupils’ estimates. Answers may varyconsiderably.

Exercise 6.21 (a) 1 m is 100 cm

so to change from m to cm multiply by 100to change from cm to m divide by 100.

(b) 1 m � 1000 mmso to change from m to mm multiply by 1000.so to change from mm to m divide by 1000.

(c) 1 cm � 10 mmso to change from cm to mm multiply by 10.to change from mm to cm divide by 10.

2 (a) 40 mm (b) 62 mm

(c) 280 mm (d) 1200 mm

(e) 880 mm (f) 3650 mm

(g) 8 mm (h) 2.3 mm

3 (a) 2.6 m (b) 89 m

(c) 2300 m (d) 750 m

(e) 2.5 m (f) 400 m

(g) 3800 m (h) 25 000 m

4 (a) 2 km (b) 26.5 km

(c) 0.2 km (d) 0.75 km

(e) 0.1 km (f) 5 km

(g) 15 km (h) 75.6 km

sector

arc

chord

tangent

4 Section 2 – Number 2


D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

5 1 kg is 1000 gso to change kg to g multiply by 1000to change g to kg divide by 1000.

6 (a) 2000 kg (b) 7200 kg

(c) 2.8 kg (d) 0.75 kg

(e) 450 kg (f) 3 kg

(g) 6.5 kg (h) 7000 kg

7 (a) 2600 ml (b) 700 ml

(c) 40 ml (d) 8 ml

8 (a) 1.5 litres (b) 5.28 litres

(c) 0.75 litres (d) 0.025 litres

9 138.3 tonnes

10 (a) 720 ml

(b) 0.53 litres

Chapter 7 – Algebra 1Exercise 7.11 (a) a � 2 (b) a � 3 (c) a � 4

(d) a � 6 (e) a � 5

2 (a) b � 7 (b) b � 7 (c) b � 7

(d) b � 5 (e) b � 8

3 (a) c � 4 (b) c � 8 (c) c � 3

(d) c � 4 (e) c � 8

4 (a) d � �2 (b) d � �4 (c) d � �9

(d) d � �11 (e) d � �9

5 (a) e � 2 (b) e � 4 (c) e � 2

(d) e � 4 (e) e � 3

6 (a) f � �3 (b) f � �3 (c) f � �6

(d) f � �4 (e) f � �7

7 (a) g � �4 (b) g � 12 (c) g � 3

(d) g � 4 (e) g � 6

8 (a) h � 2 (b) h � 4 (c) h � 5

(d) h � 5 (e) h � 11

9 (a) k � 6 (b) k � 4 (c) k � 5

(d) k � 4 (e) k � 2

10 (a) m � 9 (b) m � 17 (c) m � 13

(d) m � 1 (e) m � 4

Exercise 7.21 (a) a � �2 (b) a � �3 (c) a � �1

(d) a � �2 (e) a � �2

2 (a) b � �5 (b) b � �2 (c) b � �1

(d) b � �2 (e) b � �3

3 (a) c � �2 (b) c � �5 (c) c � �3

(d) c � �4 (e) c � �3

4 (a) d � �2 (b) d � �3 (c) d � �5

(d) d � �3 (e) d � �3

5 (a) e � 1 (b) e � 3 (c) e � 2

(d) e � 3 (e) e � 2

6 (a) f � �1.5 (b) f � �1 (c) f � �1

(d) f � �3 (e) f � �5

7 (a) g � 1 (b) g � 5 (c) g � 5

(d) g � 14 (e) g � 1

Exercise 7.31 (a) a � 3 (b) a � 4 (c) a � 4

(d) a � 5 (e) a � 1

2 (a) b � 2 (b) b � 3 (c) b � 5(d) b � 3 (e) b � 12

3 (a) c � 3 (b) c � 5 (c) c � 9(d) c � 8 (e) c � 1

4 (a) d � �9 (b) d � �7 (c) d � �4(d) d � �1 (e) d � �5

5 (a) e � �3 (b) e � �2 (c) e � �2(d) e � �3 (e) e � �2

6 (a) f � 8 (b) f � 7 (c) f � 3(d) f � 4 (e) f � 6

7 (a) g � �4 (b) g � 14 (c) g � 3(d) g � 3 (e) g � 5

8 (a) h � 2 (b) h � 3 (c) h � 10(d) h � 3 (e) h � 3

9 (a) j � 8 (b) j � 15 (c) j � 32(d) j � 14 (e) j � 27

10 (a) k � 6 (b) k � 4 (c) k � 6(d) k � 15 (e) k � 16

Section 2 – Algebra 1 5


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Chapter 8 – Shape, space andmeasures 3Exercise 8.11 (a) 18.85 cm (b) 78.54 cm

(c) 125.66 mm (d) 3.14 m

2 (a) 25.13 cm (b) 21.99 cm

(c) 75.40 mm (d) 39.58 m

3 (a) 31.4 cm (b) 35.7 cm

(c) 61.7 cm (d) 121.4 mm

(e) 13.7 cm (f) 100.7 cm

4 (a) 235.6 cm (b) 424 times

5 6.3 cm

6 37.70 m

Exercise 8.21 (a) 28.3 cm2 (b) 176.7 cm2

(c) 2.0 mm2 (d) 918.6 cm2

(e) 167.4 cm2 (f) 0.1 cm2

2 (a) 100.5 cm2 (b) 78.5 cm2

(c) 58.9 cm2 (d) 62.1 cm2

(e) 1.9 cm2 (f) 43.4 cm2

Exercise 8.31 (a) 25 cm2

(b) 19.6 cm2 (1 dp)

(c) 5.4 cm2 (1 dp)

2 11.4 cm2

3 (a) 25.1 cm2 (1 dp)

(b) 21.5% (1 dp)

4 (a) 268 cm2

(b) 81 cm

5 5969 m2

6 Ring 1 � 37.7 cm2

Ring 2 � 62.8 cm2

Ring 3 � 88.0 cm2

Chapter 9 – Shape, space andmeasures 4Exercise 9.11

2

3

4

Exercise 9.21



D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

2

3

4

5

6

Exercise 9.31 2

3 4

5 6

Exercise 9.4The diagrams that follow show only two possiblenets for the three-dimensional shapes in thequestion. Other nets are possible.

1

Section 2 – Shape, space and measures 4 7


D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

2

3

4

5



D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

6

Chapter 10 – Using and applyingmathematics/ICT 2InvestigationPupils will produce a variety of nets. The net usingthe smallest amount of card is shown below:

ICT activity1–7 Pupils generate their own regular polygons and

measure the perimeter and diagonal length ofeach.

8 (a) Pupils’ results should show that, as thenumber of sides of the regular polygonincreases, so the value perimeter � diagonalgets closer to �.

(b) The value perimeter � diagonal gets closer to�, but the results for even and odd-sidedregular polygons differ because theyapproach � differently. This is shown in thefollowing graphs.

The results for odd and even-sided regularpolygons can be combined on a graph asfollows:

Review 2A1 (a) 40 mm (b) 284 mm (c) 850 mm

2 (a) 7200 kg (b) 2.8 kg (c) 50 kg

3 (a) 2300 ml (b) 400 ml (c) 8.9 ml

4 1600 ml

5 (a) a � 4 (b) b � �13 (c) m � �5

6 38.96 cm (2 dp)

7 452.39 cm2

8 18.8 cm2 (1 dp)

Number of sides

Perimeter/diagonal for regular polygons

3.2

3.3

3.4

3.5

3.6

3.1

3.0

2.9

2.8

2.7

2.6

2.50 2 4 6 8 10 12 14

P/D

�

Number of sides

Perimeter/diagonal for odd-sided regular polygons

3.50

3.45

3.40

3.30

3.25

3.20

3.15

3.100 2 4 6 8 10 12 14

P/D

�

Number of sides

Perimeter/diagonal for even-sided regular polygons3.153.10

3.053.00

2.952.90

2.852.80

0 2 4 6 8 10 12 14

P/D

�

56 cm

51 cm

8 820 20

35

Section 2 – Using and applying mathematics/ICT 9


D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

9 Different nets are possible to this one.


Review 2B1 (a) 3500 m (b) 0.75 m (c) 0.28 m

2 (a) 800 g (b) 4100 g (c) 70 g

3 (a) 0.7 litres (b) 20 litres (c) 0.005 litre

4 2.32 litres

5 (a) a � 8 (b) b � �1.5 (c) c � 5

6 42.16 cm (2 dp)

7 226.19 cm2

8 (a) 345.6 m (b) 5656 m2



SECTION THREEChapter 11 – Algebra 2Exercise 11.11 (a) a is less than 6

(b) b is greater than 5

(c) c is not equal to 10

2 (a) x is less than or equal to 7

(b) y is greater than or equal to 3

(c) z is less than or equal to 10

3 (a) d is greater than 4

(b) e is less than 7

(c) f is not equal to 8

4 (a) m is less than 8

(b) n is greater than 5

(c) f is not equal to 5

5 (a) s is less than or equal to 6

(b) t is greater than or equal to 9

(c) u is not equal to 3

Exercise 11.21 � 2 � 3 � 4 � 5

6 7 � 8 � 9 10 �

Exercise 11.31 a � 10 2 b 7 3 c 5 4 d � 6

5 e � 10 6 f 76 7 g � 12 8 h � 5

9 j 4 10 k � 7

4 cm

4 cm

12 cm

4 cm

4 cm

12 cm

4 cm

10 cm 4 cm

5 cm

10 cm

4 cm5 cm 5 cm

5 cm

5 cm

4 cm

10 Section 3 – Algebra 2


D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

Exercise 11.41

2

3

4

5

6

7

8

9

10

Exercise 11.51

2

3

4

5

6

7

8

9

10

Exercise 11.61 3 � a � 6 2 4 � b � 7

3 6 � c � 9 4 0 � d � 3

5 �2 � e � 1 6 �3 � f � 3

7 �1 � g � 4 8 �3 � h � 2

9 �5 � i � �1 10 �4 � j � 4

Exercise 11.71 11 � a � 18 2 21 � a � 40

3 160 � h � 200 4 14 � t � 28

5 300 � n � 400 6 155 � h � 185

7 7 � n � 11 8 1 � n � 8

9 10 � d � 12 10 40 � n � 50

Chapter 12 – Algebra 3Exercise 12.11 (a) p � m � q (b) q � m � p

2 (a) p � m � d (b) m � d � p

3 (a) s � r � 3t (b) t � �r �

3s

�

4 (a) d � �x �

2c

� (b) c � 2d � x

5 (a) a � �d �

23b

� (b) b � �d �

32a

�

6 (a) r � �p �

35s

� (b) s � �3r

5� p�

7 (a) r � �m2

� � p (b) p � r � �m2

�

8 (a) r � �w5

� � 2p (b) p � �12

��r � �w5

��9 (a) r � w � dt (b) t � �

wd� r�

10 (a) m � �y �

xc

� (b) m � �y �

cx

�

Exercise 12.21 (a) a � c � b (b) b � c � a

2 (a) a � b � c (b) c � a � b–1 0 1 2 3 4

–2 –1 0 1 2 3

–9 –8 –7 –6 –5 –4

–6 –5 –4 –3 –2 –1

2 3 4 5 6 7

2 3 4 5 6 7

1 2 3 4 5 6

7 8 9 10 11 12

2 3 4 5 6 7

2 3 4 5 6 7

2.2 2.3 2.4 2.5 2.6 2.7

0.5 0.6 0.7 0.8 0.9 1.0

2 3 4 5 6 7

2 3 4 5 6 7

2 3 4 5 6 7

2 3 4 5 6 7

2 3 4 5 6 7

2 3 4 5 6 7

2 3 4 5 6 7

2 3 4 5 6 7



D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

3 (a) p � (b) r � �psq�

4 (a) q � r � 3p (b) p � �r �

3q

�

5 (a) p � t � mn (b) n � �t �

mp

�

6 (a) p � �r �

23q� (b) q � �

r �

32p�

7 (a) m � rn (b) n � �mr�

8 (a) d � �vsw� (b) v � �

dws�

9 (a) m � �tnw� (b) w � �

mtn�

10 (a) w � �t �

1mn� (b) m � �

n1

��t � �w1

��

Exercise 12.31 (a) q � r � p (b) q � s � 2r

2 (a) r � 4p � 2q (b) q � 2p � 3s

3 (a) q � �pr

� (b) r � �qps�

4 (a) p � �r �

q3

� (b) r � �q �

p4

�

5 (a) n � r � m (b) n � m � p

6 (a) m � �3p

2� n� (b) p � �

3x2� q�

7 (a) x � �uyv� (b) p � ��

rqs�

8 (a) q � �2p

6� 5� (b) p � �

6q2� 5�

9 (a) z � �3x �

47y

� (b) y � �3x �

74z

�

10 (a) r � �8

2�

pq

� (b) q � 2pr � 8

Chapter 13 – Shape, space andmeasures 5Exercise 13.11 a � 130° 2 b � 140°

3 c � 135° 4 d � 70°

5 e � 62° 6 f � 55°

7 g � 90° 8 h � 144°

9 i � 154° 10 j � 35°

Exercise 13.21 a � 110° 2 b � 145°

3 c � 55° 4 d � 95°

5 e � 100° 6 f � 125°

7 g � 106° 8 h � 150°

9 i � 90° 10 j � 60°

Exercise 13.31 Pupils’ drawings and measured angles.

2 Pupils’ drawings and measured angles.


4 Pupils’ own observations leading to: verticallyopposite angles are equal.

Exercise 13.41 Pupils’ drawings and measured angles.



4 Pupils’ own observations leading to:corresponding angles are equal.

Exercise 13.51 a � 40° b � 140°

2 c � 60° d � 120°

3 e � 40° f � 140°

4 g � 48° h � 132°

5 j � 144° k � 36°

6 l � 70° m � 110°

7 n � 80° o � 100° p � 100° q � 80°

8 r � 43° s � 137° t � 137° u � 43°

9 v � 35° w � 145° x � 145° y � 35° z � 145°

10 a � 36°

s�qr



D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

Chapter 14 – Handling data 2Exercise 14.11 Pupils’ own explanations should accompany

each answer.

(a) Likely to be a positive correlation.

(b) No correlation.

(c) Likely to be a positive correlation.

(d) Likely to be a negative correlation, thoughthere will be exceptions for vintagemotorcycles.

(e) Different correlations possible – checkexplanation for justification.

(f) Likely to be a negative correlation.

(g) Up to adulthood there is a positivecorrelation. However, once adulthood isreached there is no correlation.

(h) Likely to be a positive correlation.

2 (a)

(b) Strong/moderate positive correlation.

(c) Pupils’ explanations.

(d)

(e) About 11 km

3 (a)

(b) Very little/no correlation. Pupils’explanations.

4 (a)

(b) Pupils’ explanations.

(c) Pupils’ explanations.

(d)

Chapter 15 – Using and applyingmathematics/ICT 3InvestigationPupils will each produce a table of results and agraph of their results. Answers to questions willdepend on class results.

8070 9060504030Female life expectancy (years)

Correlation between male and femalelife expectancy in different countries

3545556575

Mal

e lif

e ex

pect

ancy

(yea

rs)

0 10 20 30 40 50 60 70Adult illiteracy rate (%)

Correlation between adultilliteracy and infant mortality

Infa

nt m

orta

lity

per 1

00

20

4060

80

100

120

0 2 4 6 8 10 12 14Hours of sunshine

Rainfall comparedwith hours of sunshine

Rain

fall

(mm

)

12345678

0 2520 3015105Distance (km)

Distance from schoolplotted against travel time

45

5152535

Tim

e (m

in)

0 2520 3015105Distance (km)

Distance from schoolplotted against travel time

45

5152535

Tim

e (m

in)

Section 3 – Using and applying mathematics/ICT 3 13


D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

ICT activityPupils produce their own angle booklets.

Review 3A1 (a) (b) (c) � (d)

2 (a) c � b � a (b) b � �x �

3w

�

(c) q � �pmn� (d) t � �

2(mnw

� 5)�

3 (a) p � 70° q � 70° r � 110°

(b) s � 104° t � 38° u � 38°

4 b � 100° c � 80° d � 35° e � 105°f � 40° g � 35° h � 80°

5 (a) (b)

6 (a) Likely to be a positive correlation; pupils’explanations.

(b) Likely to be a negative correlation (with theexception of vintage cars); pupils’explanations.

(c) Many factors may affect this. For a givenpainter at a particular point in time, though,it is likely to be a positive correlation. Pupils’explanations.

Review 3B1 (a) x 50% (b) 21 � x � 55

2 (a)

(b)

3 (a) r � �q �

3p

� (b) r � �12

��5 � �mt��

(c) v � �t(n

m� 2)� (d) p � �

15

��r � �23q��

4 (a) r � 30° q � 150°

(b) p � 57° q � 57° r � 87° s � 93°

5 a � 130° b � 130° c � 50° d � 65° e � 65°f � 115° g � 115° h � 65° i � 65°

6 (a) Weak negative correlation

(b) Strong positive correlation

7 (a) Likely to be a negative correlation; pupils’ explanations.

(b) Likely to be a positive correlation; pupils’ explanations.

(c) Likely to be no correlation; pupils’ explanations.

SECTION FOURChapter 16 – Number 3Exercise 16.11 (a) €30 (b) €160 (c) €90

(d) €60 (e) €450

2 (a) 3 years (b) 4 years (c) 5 years

(d) 6 years (e) 3�12� years

Exercise 16.21 (a) 5% (b) 6% (c) 8%

(d) 7�12�% (e) 4�

12�%

2 (a) €400 (b) €800

(c) €466.67 (d) €850

Exercise 16.31 €20 loss 2 €6 loss 3 €3 profit

4 €5 loss 5 €1400 loss

Exercise 16.41 70% 2 50% 3 75% 4 25%

5 50% 6 60% 7 25% 8 75%

9 75% 10 70%

Exercise 16.51 62.5%

2 60%

3 50%

4 30%

5 33.3% (1 dp)

0.7 0.8 0.9 1.0 1.1 1.2

4 5 6 7 8 9

14 Section 4 – Number 3


D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

6 28.6% (1 dp)

7 40%

8 35%

9 42%

10 37.5%

Chapter 17 – Algebra 4Exercise 17.11 (a) 2(2a � 5) (b) 5(2a � 3) (c) 3(3a � 7)

2 (a) 3(2b � 1) (b) 5(2b � 1) (c) 5(5b � 2)

3 (a) 5(3c � 5) (b) 4(3c � 2) (c) 8(a � 3)

4 (a) 4(2 � d) (b) 2(3 � 2d) (c) 6(3 � 2d)

5 (a) 2(3a � 2b) (b) 7(c � 2d) (c) 4(3a � 4b)

6 (a) 4(6p � 7q) (b) 6(a � 5b) (c) 7(3d � 2e)

7 (a) 3(2a � 3b � 4c) (b) 2(4a � b � 2c)

(c) 3(2p � 3q � 5r)

8 (a) 4(3m � 4n � 9r) (b) 7(a � 2b � 5c)

(c) 8(8p � 4q � 2r)

9 (a) 3(3a � b � 6c) (b) 4(6p � 8q � 3r)

(c) 3(a � b � c)

10 (a) 6(a � 2b � 3c) (b) 7(p � q � r)

(c) 15(2p � 4q � r)

Exercise 17.21 (a) x(2a � 3b � 4c) (b) b(7a � 8c)

2 (a) q(3p � 4 � 5s) (b) n(2m � 3r � 5p)

3 (a) x(4a � 3x) (b) b(4a � 3b)

4 (a) p(6p � 5q) (b) m(7n � 2m)

5 (a) x(x � a) (b) p(qr � p)

Exercise 17.31 (a) 2y(2x � 3z) (b) 3q(3p � 4r)

2 (a) 5m(3n � 2p) (b) 7c(2b � 3c)

3 (a) 6p(q � 5p) (b) 5x(3x � 2y)

4 (a) 4xy(3x � 2y) (b) 5ab(2b � 5a)

5 (a) 7a(x � 2y � 3z) (b) 3x2(10a � 2b � 3c)

Exercise 17.41 (a) 3(3m � 5) (b) 2(8 � 3p)

2 (a) 2(2p � 3) (b) 6(3 � 2b)

3 (a) 3(2y � 1) (b) 2(2a � 3b)

4 (a) 3(a � b) (b) 4(2a � 3b � 5c)

5 (a) a(3b � 4c � 5d) (b) 2p(4q � 3r � 2s)

6 (a) b(b � c) (b) 2a(2a � 5b)

7 (a) ab(c � d � e) (b) m(2m � 3)

8 (a) 3ab(c � 3d) (b) 5a(a � 2b)

9 (a) 2ab(4a � 3b) (b) p2(2q2 � 3r2)

10 (a) 12(a � 2) (b) 21(2a � 3)

11 (a) 11a(1 � b) (b) 4a(1 � 4 � 2b)

12 (a) 5b(a � 2c � 3b) (b) 2b2(4a � 3)

13 (a) a(a �1) (b) b(1 � b)

14 (a) b2(1 � b) (b) a(a2 � a � 1)

15 (a) p(p2 � 2p � 3) (b) m(7m2 � 9m � 4)

16 (a) 3a(2a2 � a � 4) (b) 5a(a2 � 2a � 5)

17 (a) 28ab(2a � b) (b) 12b(6a � 3c � 4d)

18 (a) 2a3(2b � 3c) (b) 7m2n(2mn � 3)

19 (a) 6ab(ab � 2) (b) 3c2(1 � 5c)

20 (a) 5a(b � c) (b) 13bc(b � 2c)

Exercise 17.51 (a) (a � b)(c � d) (b) (p � q)(r � s)

2 (a) (m � n)(p � q) (b) (a � c)(b � d)

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

4 (a) (a � 4)(b � c) (b) (a � 3)(b � c)

5 (a) (p � q)(m � n) (b) (p � q)(n � m)

6 (a) (a � b)(c � d) (b) (r � t)(s � v)

7 (a) (x � y)(w � v) (b) (a � b)(a � c)

8 (a) (x � y)(z � x) (b) (p � r)(q � p)

9 (a) (m � n)(n � r) (b) (p � r)(x � y)

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



D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

Exercise 17.61 (a) (3a � b)(b � c) (b) (2p � q)(3r � s)

2 (a) (x � y)(z � y) (b) (4a � b)(2c � b)

3 (a) (r � 2s)(3t � r) (b) (2m � 3n)(q � 2m)

4 (a) (5f � g)(f 2 � h) (b) (ab � c)(d � c)

5 (a) (2gh � i)(jk � i) (b) (a � b)(c � b)

Chapter 18 – Shape, space andmeasures 6Exercise 18.11 (a) 24 cm3 (b) 150 cm3 (c) 40 cm3

(d) 4000 cm3 (e) 1500 cm3

2 (a) 120 cm3 (b) 120 cm3 (c) 270 cm3

(d) 4000 cm3 (e) 3861 cm3

3 (a) 339.3 cm3 (1 dp) (b) 2827.4 cm3 (1 dp)

(c) 954.3 cm3 (1 dp) (d) 924.7 cm3 (1 dp)

(e) 155.0 cm3 (1 dp)

Exercise 18.21 224 cm3

2 225 cm3

3 3200 cm3

4 1500 cm3

5 3930 cm3 (3 sf)

Exercise 18.31 8 cm

2 (a) 5 cm (b) 6.5 cm

3 (a) 9 cm (b) 81 cm2

4 10 cm

5 1.51 cm (2 dp)

Chapter 19 – Handling data 3Exercise 19.11 Independent 2 Independent

3 They are mutually exclusive events.

Exercise 19.21 �3

16�

2 �58�

3 (a) �15� (b) �

25� (c) �2

25� (d) �

35�

Exercise 19.31 �2

75� 2 �2

85�

3 �255� or �

15� 4 �2

15�

5 �225� 6 �2

25�

7 �235� 8 Mutually exclusive

9 �225� 10 �2

15�

11 �12

75� 12 �

12

55� or �

35�

13 �22

55� or 1 14 �

22

05� or �

45�

15 �285� 16 �

12

35�

17 �12

25� 18 �2

75�

19 �245� 20 �2

35�

Exercise 19.41 �3

16� 2 �3

16�

3 �346� or �

19� 4 �

23

06� or �

59�

5 �316� 6 �

13

16�

7 �118� 8 �

13

66� or �

49�

9 �118� 10 �

13

66� or �

49�

Exercise 19.51 �

18�

2 �112�

3 �19

96�

4 �916�

5 �38�

6 �122� or �

16�

7 �49

66� or �

24

38�

8 �966� or �1

16�

9 0 (it is impossible to throw a red face on thedodecahedron)

10 �99

66� or 1

16 Section 4 – Handling data 3


D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

Chapter 20 – Using and applyingmathematics/ICT 4Investigation1 (a) 8 cm2 (b) 40 cm3

(c) 32 cm2 (d) 320 cm3

2 (a) Small triangular cross-section � 21 cm2

Enlarged triangular cross-section � 84 cm2

(b) Volume of small prism � 168 cm3

Volume of enlarged prism � 1344 cm3

3,4 Pupils investigate the relationship between scalefactor of enlargement and its effect on the areafactor and volume factor of enlargement.If the scale factor of enlargement is n, the areafactor of enlargement is n2 and the volume factorof enlargement is n3.

ICT activityThe screenshot below shows an example of theformulae that can be used:

Pupils prepare a report based on their findings.

Review 4A1 €2600 2 4.2%

3 66.7% (1 dp) 4 600%

5 (a) 4(4a � 3) (b) x(4x � 1)

(c) 2bc(3b � 1 � 2c)

6 (a) (2c � a)(3b � c) (b) (4p � q2)(2p � r)

7 251.3 cm3 (1 dp)

8 (a) Pupils’ examples. (b) Pupils’ examples.

Review 4B1 7 years

2 66.5%

3 (a) 4(2p � q) (b) 7r(2r � 3)

(c) 3t(2t2 � 3t � m)

4 (a) (r � 3s)(2t � r) (b) (4ab2 � c)(a � d)

5 48 cm3

6 8.9 cm

7 (a) �140� or �

25� (b) �1

20� or �

15� (c) �1

60� or �

35�

8 (a) �46� or �

23� (b) �

26� or �

13� (c) �

29�

SECTION FIVEChapter 21 – Algebra 5Exercise 21.11 Pupils’ tables of sets of co-ordinates leading to

y � 2x

2 Pupils’ tables of sets of co-ordinates leading to y � �

12�x � 1

3 Pupils’ tables of sets of co-ordinates leading to y � x � 2

4 Pupils’ tables of sets of co-ordinates leading to y � �

12�x � 3

5 Pupils’ tables of sets of co-ordinates leading to y � �x

6 Pupils’ tables of sets of co-ordinates leading to y � ��

12�x � 3

7 Pupils’ tables of sets of co-ordinates leading to y � 4

8 Pupils’ tables of sets of co-ordinates leading to x � �3

9 Pupils’ explanations.

Exercise 22.21 Sloping

2 Sloping

3 Vertical

4 Sloping



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5 Horizontal

6 Vertical

7 Sloping

8 Horizontal

9 Sloping

10 Sloping

Exercise 21.31

2

3

4

5

6

7 y

x–4 –2

2

4

6

20 4

2y = x + 6

y

x– 2

2

4

–2

–4 20 4

x = –2

y

x–2

2

4

–2

20 4 6

y – x = –1

y

x–2

2

4

–2

20 4

y = 3

y

x–2

2

4

–2

20 4

12y = x + 1

y

x–2

2

4

–2

20 4 6

y = 2x – 3

y

x–4 –2

2

4

6

–2

20 4

y = x + 2

18 Section 5 – Algebra 5


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8

9

10

Exercise 21.4Pupils’ own line graphs accompany questions 1–10.

1 Gradient � 1 2 Gradient � 2

3 Gradient � �12� 4 Gradient � 2

5 Gradient � ��12� 6 Gradient � 4

7 Gradient � ��13� 8 Gradient � �3

9 Gradient � 0 10 Gradient � infinite

11 Pupils’ own observations.

Exercise 21.51 (a) y � x � 1 (b) Gradient � 1

(c) y intercept � 1

2 (a) y � 3x � 1 (b) Gradient � 3

(c) y intercept � �1

3 (a) y � �12�x � 2 (b) Gradient � �

12�


4 (a) y � 4x � 4 (b) Gradient � 4


5 (a) y � �x � 3 (b) Gradient � �1


6 Pupils’ observations.

Exercise 21.61 (a) Gradient � 2 y intercept � 1

(b) Gradient � 3 y intercept � �1

(c) Gradient � �12� y intercept � �3

(d) Gradient � 1 y intercept � 0

(e) Gradient � 1 y intercept � ��12�

(f) Gradient � �3 y intercept � 4

(g) Gradient � �1 y intercept � 4

(h) Gradient � �1 y intercept � 0

2 (a) Gradient � 2 y intercept � 4


(c) Gradient � 3 y intercept � 0

(d) Gradient � �2 y intercept � 4

(e) Gradient � �3 y intercept � �1

(f) Gradient � 1 y intercept � 1

(g) Gradient � 5 y intercept � �4

(h) Gradient � �2 y intercept � 4

3 (a) Gradient � 1 y intercept � 2


(c) Gradient � 3 y intercept � 1

(d) Gradient � 1 y intercept � 0

(e) Gradient � 4 y intercept � �8

(f) Gradient � 3 y intercept � �3

(g) Gradient � 0 y intercept � 4

(h) Gradient � �12� y intercept � �3

y

x–4 –2

2

4

–2

20 4y + x = –1

–4

y

x–2

2

4

6

–2

20 4

y = –2x + 2

y

x–4 –2

2

4

6

–2

20 4

y = –x + 3



D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

Chapter 22 – Shape, space andmeasures 7Exercise 22.11 a � 40° 2 b � 43°

3 c � 30° 4 d � 45°

5 e � 25°, f � 35° 6 g � 27°, h � 27°, i � 36°

Exercise 22.21

2 The number of sides is always 2 more than thenumber of triangles.

3

Exercise 22.31 a � 75°

2 b � 70° c � 120°

3 d � 104°

4 e � 48° f � 84° g � 132°h � 132° i � 48° j � 48°

5 k � 108° l � 108°

6 m � 120° n � 60° p � 120° q � 60°r � 60° s � 120° t � 120°

Chapter 23 – Shape, space andmeasures 8Exercise 23.11 150 cm2

2 138 cm2

3 288 cm2

4 108 cm2

5 703.7 cm2 (1 dp)

6 155.5 cm2 (1 dp)

7 480 cm2

8 262 cm2

Exercise 23.21 9 cm

2 3 cm

3 (a) 11.3 cm (1 dp) (b) 2226 cm2

4 (a) 13 cm (b) 450 cm2

5 2 mm

Chapter 24 – Handling data 4Exercise 24.11 Discrete 2 Continuous

3 Discrete 4 Continuous

5 Continuous 6 Continuous

7 Discrete 8 Continuous

9 Continuous (usually) 10 Discrete

Exercise 24.2Pupils’ examples.

20 Section 5 – Handling data 4


Number Name Number Total sum ofof sides of polygon of triangles interior angles

3 triangle 1 180°

4 quadrilateral 2 2 � 180° � 360°

5 pentagon 3 3 � 180° � 540°

6 hexagon 4 4 � 180° � 720°

8 octagon 6 6 � 180° � 1080°

9 nonagon 7 7 � 180° � 1260°

10 decagon 8 8 � 180° � 1440°

12 dodecagon 10 10 � 180° � 1800°

Number of 3 4 5 6 8 9 10 12sides

Sum of the 180° 360° 540° 720° 1080° 1260° 1440° 1800°interiorangles

Size of each 60° 90° 108° 120° 135° 140° 144° 150°interiorangle

Size of each 120° 90° 72° 60° 45° 40° 36° 30°exterior angle

D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

Exercise 24.31

2

3

4

5

6

7

8

9

Exercise 24.41

Temperature (°C)

Mean annualtemperatures in two cities

– 20–

– 10– 0– 10–

20–

30–

40 –

50

5

0

10

15

20

25

30

Freq

uenc

y

city A

city B

Distance (km)

Distances travelled to school

7 –8

0– 1– 2– 3– 4– 5– 6–

10

0

2030

40

50

6070

Freq

uenc

y

Temperature (°C)

Temperatures in 50 towns in July

15– 20– 25– 30– 35 – 40

2018

20

468

10121416

Freq

uenc

y

0

Height (cm)

Heights of students

130–

140–

160–

170–

180

– 19

0

150–

10

20

30

40

Freq

uenc

y

Mark (%)

Maths test results

10–0– 30– 50– 70– 90 –100

2468

1012

Freq

uenc

y

0Scores

Scores in a golf competition

90 –95

85–80–75–70–65–

2018

2468

10121416

Freq

uenc

y

Section 5 – Handling data 4 21


Mass (kg) 0– 1– 2– 3– 4– 5– 6– 7– 8– 9– 10–11

Frequency 0 1 2 4 3 5 8 4 2 1 0

Time (secs) 8– 10– 12– 14– 16– 18– 20– 22–24

Frequency 0 3 14 8 1 2 2 0

Number of books 0– 10– 20– 30– 40– 50–60

Frequency 8 14 26 20 8 4

Points scored 0– 10– 20– 30– 40– 50– 60– 70–80

Frequency 0 1 3 5 11 6 4 2

D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

2

3 Pupils’ sketches of frequency polygons.


5

Pupils’ explanations. ‘On average’, pupils atschool A travel less distance to school than thoseat school B.






Chapter 25 – Using and applyingmathematics/ICT 5InvestigationPupils’ calculations based on their packaging.

1 Pupils’ observations based on their results.

2 Pupils’ examples.

ICT activityPupils’ analyses of test results.

Review 5A1 y � x � 2

2 (a)

(b)

3 (a) Gradient � 4, y intercept � �5

(b) Gradient � 1, y intercept � 0

(c) Gradient � �12�, y intercept � 1

(d) Gradient � �2, y intercept � 1

4 120°

5 a � 75°, b � 135°

6 226.2 cm2

7 8 cm

y

x–2–4

2

4

–2

20 4

y = x + 212

y

x–2

2

4

–2

20 4

y = 2x – 1

0

Distance (km)

Distances travelled bypupils to two schools

0– 1– 2– 3– 4– 5– 6–7

– 8

51015202530354045

Freq

uenc

y

school A

school B

0

Ages of spectators compared

5

10

15

20

25

30Fr

eque

ncy

(100

0s)

Age

0– 10–

20–

30–

40–

50–

60–

70 –

80

football

golf

22 Section 5 – Reviews


D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

8

Review 5B1 y � �2x � 2

2 (a)

(b)

3 (a) Gradient � 3, y intercept � 1

(b) Gradient � 1, y intercept � �4

(c) Gradient � 2, y intercept � �2

(d) Gradient � 2, y intercept � �12�

4 72°

5 a � 100°, b � 80°, c � 220°

6 176 cm2

7 628.3 cm2

8 Pupils’ reports.

y

x–2

2

4

–2

20 4

y = –x + 3

y

x–2–4

2

4

–2

20 4

y = x + 3

Score

Maths test results

90 – 1000– 10– 20– 30– 40– 50– 60– 70– 80–

8

6

4

2

0

Freq

uenc

y

Section 5 – Reviews 23


D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

SECTION SIX –CHECKPOINT QUESTIONSNumber1 5 or 6

2 About 47 000 feet

3 (a) (i) Each small division on the scale shows 10 grams

(ii) Arrow X shows a mass of 280 grams

(b) Pupils’ scales marked to show 70 g.

(c) (i) 39 cents(ii) 11 cents

4 (a) (i) 32 litres(ii) $36

(b) 54 (km)40 (min)60 (km/h)

Algebra1 (a) (7x � 6) cm

(b) 7x � 6 � 20

(c) 8 cm

2 t � �v �

au

�

3 3x(5x � 2)

4 x2 � 5x � 6

5 (2ab � c)(4b � c)

6 3

7 (a) p � 12 (b) q � 7 (c) r � 3

8 (a) �2, �1, 1, 2

(b) Pupils’ graphs with line y � x � 2 drawn.

(c) ��23�

Shape, space and measures1 (a) a 60°, b 60°, c 60°

(b) Equilateral

2 172 cm2

3 6 cm

4 4 cm

5 12 cm2

6 4 minutes

7 (a) 13 km/litre

(b) 117 km

8 (a) (i) 80° (ii) 30°

(b) (i) 35° (ii) 55° (iii) 55°

9 (a) 384 cm2 (b) 512 cm3

10 (a) 444.2 m (b) 14 350 m2

Handling data1 (a) Primary

(b) (i) Pupils’ explanations(ii) Pupils’ own questions

2 (a) Pupils’ scatter diagrams with line of best fitdrawn.

(b) 14

24 Section 6 – Handling data


D - Ans 4 web - 001-024.qxd 17/8/04 11:14 am

checkpoint maths 2 answers pupils’ construction of a regular octagon. 4 (a), (b) pupils’...

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