Checkpoint Maths 2 Answers - Hodder Plus Home

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Checkpoint Maths 2 Answers SECTION ONE

5

Chapter 1 – Shape, space and measures 1 Exercise 1.1 1

2

Sunday

0200

1012

1400

2212

Monday

0200

1012

1348

2200

Tuesday

0310

1122

1510

2322

Wednesday

0336

1148

1321

2133

(d) 1845

(e) 2330

(f) 1650

Thursday

0255

1107

1515

2327

(a) 1900

(b) 1200

(c) 0005

Friday

0057

0909

1436

2248

(d) 2210

(e) 0815

(f) 2015

Saturday

0638

1450

1648

0100

(g) 0745

(h) 1945 (a) 1 hour 2 min (b) 1620 (c) 1926

(a) 0840

(d) 2225 7

(c) 0800

Pupils’ own questions and answers.

(a) 1630

Chapter 2 – Number 1

(b) 1606 (c) 1803 (a)

Depart

Exercise 2.1 (b)

Arrive

Depart

Arrive

0523

0631

5.23 am

6.31 am

0715

0823

7.15 am

8.23 am

0904

1012

9.04 am

10.12 am

1028

1136

10.28 am

11.36 am

1 2

3

(a) 14.8

(b) 31.14

(c) 9.66

(d) 100.01

(e) 44.44

(f) 9.1

(a) 11.1

(b) 10.9

(c) 15.04

(d) 0.01

(e) 11.7

(f) 10

(g) 12

(h) 0

(a) 17.02

(b) 159.36

(c) 43.56

(e) 35.1

(f) 5.1

(h) 10

1445

1553

2.45 pm

3.53 pm

(d) 4

1622

1730

4.22 pm

5.30 pm

(g) 18.63

1809

1917

6.09 pm

7.17 pm

2017

2125

8.17 pm

9.25 pm

Exercise 2.2 1

4

Dubai (local time)

(c) 0955

(b) 0820

3

London

(b) 0535

Exercise 1.2

2

Dubai (local time)

(a) 0830

6

1

London

Stansted

0500

0715

0915

1040

1315

Luton

0630

0845

1045

1210

1445

Gatwick

0805

1020

1220

1345

1620

Heathrow

0850

1105

1305

1430

1705

2 3

Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational

(a) 20

(b) 30

(c) 24

(d) 14

(e) 43

(f) 18

(a) 18

(b) 9

(c) 11

(d) 0

(e) 27

(f) 1

(a) 15

(b) 18

(c) 2

(d) 35

(e) 15

(f) 6 1 of 24

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Section 1 – Shape, space and measures 2

(a) (12 8) 2 8

Exercise 3.3

(b) 5 (2 4) 30

1

Pupils’ perpendicular bisector constructions.

2

The orientation of pupils’ diagrams may differ from the ones shown below.

(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

Page 2

(a)

(b)

(d)

(e)

(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 2.3 1 2

(a) 4

(b) 4

(c) 3

(d) 8

(e) 12

(f) 6

(a) 13

(b) 37

(c) 12

(d) 12.8

(e) 0.125

(f) 0.5

(f)

Chapter 3 – Shape, space and measures 2 Exercise 3.1 1

Circumference

2

Radius, radii

3

Chord

4

Diameter

5

Arc

6

Sector

7

Segment

8

Tangent

(g)

Exercise 3.2 1

Pupils’ drawings.

2

Pupils’ drawings.

3

Pupils’ own patterns.


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Section 1 – Using and applying mathematics/ICT

3

Pupils’ construction of a regular octagon.

4

(a), (b) Pupils’ constructions.

Chapter 5 – Using and applying mathematics/ICT 1

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

Investigation

5

Pupils’ constructions.

6

Pupils’ constructions.

Chapter 4 – Handling data 1 Exercise 4.1 1

Primary

2

Secondary

3

Secondary

4

Primary

5

Secondary

Only one possible solution for each number is given below. There are many other correct possibilities. Some solutions have included the use of the factorial (!) which, although not covered in the text, could be introduced for more able students. 1 44 44

4 4 2 4 4

4 3 4 4 4

44 4 4 4

4 5 4 4 4

44 6 4 4

4 7 4 4 4

8 (4 4) 4 4

4 9 4 4 4

44 4 10 4

Pupils’ suggested research.

4 11 4! 4 4

44 4 12 4

Q p.19

4 13 4! 4 4

14 4 4 4 4

Question (c).

15 44 4 4

16 4 4 4 4

Q p.19

4 17 4 4 4

4 18 4 4 4

4 19 4! 4 4

20

4 21 4! 4 4

22 4 4 4 4

23 (4! 4 4) 4

24 4 4 4 4

Q p.19

Pupils’ own questions.

Q p.19 Pupils’ own questions.

Exercise 4.2 Pupils’ rewritten questions.

25

4 4 4

4

4 4 4 4

44 26 4! 4

Exercise 4.3

4 27 4! 4 4

28 4 4 4 4

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

4 29 4 4! 4

30 4 4 4 4


3

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Section 2 – Number 2

SECTION TWO

ICT activity Pupils’ constructions. As the vertex is dragged, the shape of the triangle changes but the circumference of the circle still passes through each of the three vertices.

Chapter 6 – Number 2 Exercise 6.1 1

Review 1A 1

(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

arc sector

chord

2

Pupils’ questionnaires. Pupils’ examples of a biased question which should not be used.

(d) A thousandth

(e) One thousand

(f) A thousandth

(g) A thousandth

(h) One thousand

(i) A millilitre

(j) One million

(a) kg

(b) cm

(c) m or cm

(d) ml

(e) t

(f) m

(g) litre

(h) km

(i) litre

(j) cm

Pupils’ lines and measurements.

4

Pupils’ estimates. Answers may vary considerably.

Exercise 6.2

tangent

8

(b) A hundredth

3

1

7

(a) One hundred (c) One thousand

(a) 1 m is 100 cm so to change from m to cm multiply by 100 to change from cm to m divide by 100. (b) 1 m 1000 mm so to change from m to mm multiply by 1000. so to change from mm to m divide by 1000. (c) 1 cm 10 mm so to change from cm to mm multiply by 10. to change from mm to cm divide by 10.

Review 1B

(a) 40 mm

(b) 62 mm

(c) 280 mm

(d) 1200 mm

2040 on Wednesday

(e) 880 mm

(f) 3650 mm

3

2300

(g) 8 mm

(h) 2.3 mm

4

(a) (7 8) (3 2) 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

1

1625

2

(b) (7 8) 3 2 7

2

3

(c) 7 8 (3 2) 8.6 5

Pupils’ constructions of a perpendicular bisector.

6

Pupils’ examples.

(a) 2 km

(b) 26.5 km

7

Pupils’ questionnaires.

(c) 0.2 km

(d) 0.75 km

8

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

(e) 0.1 km

(f) 5 km

(g) 15 km

(h) 75.6 km


4

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Section 2 – Algebra 1

5 1 kg is 1000 g so to change kg to g multiply by 1000 to 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

Exercise 7.2 1 2 3

(b) 700 ml

(c) 40 ml

(d) 8 ml

8 (a) 1.5 litres

4

(b) 5.28 litres

(c) 0.75 litres

(d) 0.025 litres

5

9 138.3 tonnes 6

10 (a) 720 ml (b) 0.53 litres

7

Chapter 7 – Algebra 1 Exercise 7.1 1 (a) a 2

(b) a 3

(d) a 6

(e) a 5

2 (a) b 7

(b) b 7

(d) b 5

(e) b 8

3 (a) c 4

(b) c 8

(d) c 4

(e) c 8

4 (a) d 2 (d) d 11

(b) d 4 (b) e 4

(d) e 4

(e) e 3

6 (a) f 3

(b) f 3

(d) f 4

(e) f 7

7 (a) g 4

(b) g 12

(d) g 4

(e) g 6

(d) h 5

(b) h 4 (b) k 4

(d) k 4

(e) k 2

10 (a) m 9 (d) m 1

(b) m 17

(b) a 3

(d) a 2

(e) a 2

(a) b 5

(b) b 2

(d) b 2

(e) b 3

(a) c 2

(b) c 5

(d) c 4

(e) c 3

(a) d 2

(b) d 3

(d) d 3

(e) d 3

(a) e 1

(b) e 3

(d) e 3

(e) e 2

(a) f 1.5

(b) f 1

(d) f 3

(e) f 5

(a) g 1

(b) g 5

(d) g 14

(e) g 1

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

Exercise 7.3 (b) a 4 (e) a 1

(c) a 4

2 (a) b 2 (d) b 3

(b) b 3 (e) b 12

(c) b 5

3 (a) c 3 (d) c 8

(b) c 5 (e) c 1

(c) c 9

4 (a) d 9 (d) d 1

(b) d 7 (e) d 5

(c) d 4

5 (a) e 3 (d) e 3

(b) e 2 (e) e 2

(c) e 2

6 (a) f 8 (d) f 4

(b) f 7 (e) f 6

(c) f 3

(c) g 3

7 (a) g 4 (d) g 3

(b) g 14 (e) g 5

(c) g 3

(c) h 5

8 (a) h 2 (d) h 3

(b) h 3 (e) h 3

(c) h 10

(c) k 5

9 (a) j 8 (d) j 14

(b) j 15 (e) j 27

(c) j 32

10 (a) k 6 (d) k 15

(b) k 4 (e) k 16

(c) k 6

(c) b 7 (c) c 3 (c) d 9 (c) e 2 (c) f 6

(e) h 11

9 (a) k 6

(a) a 2

1 (a) a 3 (d) a 5

(e) d 9

5 (a) e 2

8 (a) h 2

(c) a 4

(c) m 13

(e) m 4


5

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Chapter 8 – Shape, space and measures 3

Chapter 9 – Shape, space and measures 4

Exercise 8.1

Exercise 9.1

(a) 18.85 cm

(b) 78.54 cm

(c) 125.66 mm

(d) 3.14 m

(a) 25.13 cm

(b) 21.99 cm

(c) 75.40 mm

(d) 39.58 m

(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

1 2 3

1

2

3

Exercise 8.2 1

(a) 28.3 cm2

(b) 176.7 cm2

(c) 2.0 mm2 (e) 167.4 cm 2

(d) 918.6 cm2 2

(f) 0.1 cm2

(a) 100.5 cm2

(b) 78.5 cm2

(c) 58.9 cm2

(d) 62.1 cm2

(e) 1.9 cm

2

(f) 43.4 cm2

4

Exercise 8.3 1

(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)

Exercise 9.2 1

(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


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2

7

Exercise 9.3 1

2

3

4

5

6

3

4

Exercise 9.4 The diagrams that follow show only two possible nets for the three-dimensional shapes in the question. Other nets are possible. 1 5

6


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2

4

5

3


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9

Section 2 – Using and applying mathematics/ICT

6

P/D

Perimeter/diagonal for even-sided regular polygons

3.15 3.10 3.05 3.00 2.95 2.90 2.85 2.80

0

2

4

6 8 Number of sides

10

12

14

Perimeter/diagonal for odd-sided regular polygons 3.50 3.45

P/D

3.40 3.30 3.25 3.20

3.15 3.10

0

2

4

6 8 Number of sides

10

12

14

The results for odd and even-sided regular polygons can be combined on a graph as follows:

Chapter 10 – Using and applying mathematics/ICT 2

Perimeter/diagonal for regular polygons 3.6 3.5 3.4

Investigation

3.3

Pupils will produce a variety of nets. The net using the smallest amount of card is shown below:

3.1

P/D

3.2

3.0 2.9 2.8 2.7 2.6 2.5

35 51 cm 8

20

8

20

56 cm

ICT activity 1–7 Pupils generate their own regular polygons and measure the perimeter and diagonal length of each. 8

(a) Pupils’ results should show that, as the number of sides of the regular polygon increases, so the value perimeter diagonal gets closer to .

0

2

4

6 8 Number of sides

10

12

14

Review 2A 1

(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)

(b) The value perimeter diagonal gets closer to , but the results for even and odd-sided regular polygons differ because they approach differently. This is shown in the following graphs. Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational

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Different nets are possible to this one.

10 Different nets are possible to this one.

4 cm

5 cm 5 cm

4 cm

5 cm

4 cm 12 cm

10 cm

5 cm

4 cm

10 Different nets are possible to this one.

SECTION THREE 5 cm 10 cm

4 cm

Chapter 11 – Algebra 2 Exercise 11.1 1

(a) a is less than 6 (b) b is greater than 5

4 cm

(c) c is not equal to 10 2

Review 2B

(a) x is less than or equal to 7 (b) y is greater than or equal to 3

1

(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

6

42.16 cm (2 dp)

7

226.19 cm2

8

(a) 345.6 m

9

Different nets are possible to this one.

(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

(b) b 1.5

(c) c 5

4

(a) m is less than 8 (b) n is greater than 5 (c) f is not equal to 5

5

(b) 5656 m2

(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

4 cm

Exercise 11.2 12 cm

1

2

3

4

5

6

7

8

9

10

Exercise 11.3 4 cm


1

a 10

2 b 7

3

c 5

4

d6

5

e 10

6 f 76

7

g 12

8

h5

9

j 4

10 k 7 10 of 24

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Exercise 11.4

11

Exercise 11.6

1 2

3

4

5

6

7

2

3

4

5

6

7

2 3

1

3a6

2 4b7

3

6c9

4 0d3

5

2 e 1

6 3 f 3

7

1 g 4

8 3 h 2

5 i 1

2

3

4

5

6

7

9

2

3

4

5

6

7

Exercise 11.7

2

3

4

5

6

7

10 4 j 4

4 5 6 2

3

4

5

6

7

2

3

4

5

6

7

2

3

4

5

6

7

0.5

0.6

0.7

0.8

0.9

1.0

2.2

2.3

2.4

2.5

2.6

2.7

7 8 9

1

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 1n8

9

10 d 12

10 40 n 50

Chapter 12 – Algebra 3 Exercise 12.1

10

1 (a) p m q

(b) q m p

2 (a) p m d

(b) m d p

3 (a) s r 3t

rs (b) t 3 (b) c 2d x

7

xc 4 (a) d 2

12

d 3b 5 (a) a 2

d 2a (b) b 3

6

p 5s 6 (a) r 3

3r p (b) s 5

m 7 (a) r p 2

m (b) p r 2

w 8 (a) r 2p 5

1 w (b) p r 2 5

9 (a) r w dt

wr (b) t d

Exercise 11.5 1 2

3

4

5

6

7

2 2

3

4

5

6

3 7

8

9

10

11

4 1

2

3

4

5

5 2

3

4

5

6

7

6 2

3

4

5

6

7

7 –6

–5

–4

–3

–2

–1

8 –9

–8

–7

–6

–5

–4

–2

–1

0

1

2

3

–1

0

1

2

3

4

9 10 Checkpoint Maths 2 © 2004, Hodder & Stoughton Educational

yc 10 (a) m x

c (b) m yx

Exercise 12.2 1

(a) a c b

(b) b c a

2

(a) a b c

(b) c a b 11 of 24

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s 3 (a) p qr

s (b) r pq

4 (a) q r 3p

rq (b) p 3

5 (a) p t mn

tp (b) n m

r 3q 6 (a) p 2

r 2p (b) q 3

7 (a) m rn

m (b) n r

vw 8 (a) d s

ds (b) v w

tw 9 (a) m n

mn (b) w t

1 10 (a) w t mn

1 (a) q r p

(b) q s 2r

2 (a) r 4p 2q

(b) q 2p 3s

r 3 (a) q p

qs (b) r p

r3 4 (a) p q

q4 (b) r p

5 (a) n r m

e 62°

6 f 55°

7

g 90°

8 h 144°

9

i 154°

10 j 35°

Exercise 13.2

1 1 (b) m t n w

Exercise 12.3

5

1

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 13.3 1

Pupils’ drawings and measured angles.

2


3


4

Pupils’ own observations leading to: vertically opposite angles are equal.

Exercise 13.4 1


(b) n m p

2


3p n 6 (a) m 2

3x q (b) p 2

3


4

uv 7 (a) x y

rs (b) p q

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

2p 5 8 (a) q 6

6q 5 (b) p 2

3x 7y 9 (a) z 4

3x 4z (b) y 7

8q 10 (a) r 2p

(b) q 2pr 8

Chapter 13 – Shape, space and measures 5 Exercise 13.1

Exercise 13.5 1 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°

w 145° x 145° y 35°

1

a 130°

2

b 140°

9 v 35°

3

c 135°

4

d 70°

10 a 36°


t 137°

u 43° z 145° 12 of 24

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13

Section 3 – Using and applying mathematics/ICT 3

Chapter 14 – Handling data 2

3

(a)

Rainfall compared with hours of sunshine

Exercise 14.1 Pupils’ own explanations should accompany each answer.

Rainfall (mm)

1

(a) Likely to be a positive correlation. (b) No correlation. (c) Likely to be a positive correlation. (d) Likely to be a negative correlation, though there will be exceptions for vintage motorcycles.

0

(e) Different correlations possible – check explanation for justification. 4

(a)

(h) Likely to be a positive correlation.

Time (min)

Distance from school plotted against travel time 45 35 25 15 5 0

14

100 80 60 40 20 10

20 30 40 50 60 Adult illiteracy rate (%)

70

(b) Pupils’ explanations.

5

10 15 20 Distance (km)

25

30

Male life expectancy (years)

Distance from school plotted against travel time 45 35 25 15 5 0

5

10 15 20 Distance (km)

(c) Pupils’ explanations. (d)

(c) Pupils’ explanations.

Time (min)

12

120

0

(b) Strong/moderate positive correlation. (d)

4 6 8 10 Hours of sunshine

Correlation between adult illiteracy and infant mortality Infant mortality per 100

(g) Up to adulthood there is a positive correlation. However, once adulthood is reached there is no correlation. (a)

2

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

(f) Likely to be a negative correlation.

2

8 7 6 5 4 3 2 1

25

(e) About 11 km

Correlation between male and female life expectancy in different countries 75 65 55 45 35 30

40 50 60 70 80 90 Female life expectancy (years)

30

Chapter 15 – Using and applying mathematics/ICT 3 Investigation Pupils will each produce a table of results and a graph of their results. Answers to questions will depend on class results.


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