Checkpoint Maths 1 Answers - Hodder Plus Home

Y - Ans Web - 001-028.qxd

25/3/04

8:19 am

Page 1

Checkpoint Maths 1 Answers SECTION ONE

Exercise 1.5 Pupils’ answers may differ slightly from those listed below.

Chapter 1 – Number

1 (a) 800

Exercise 1.1

(d) 3600

1 (a) 30

(b) 300

(c) 3

(d) 0.03

2 (a) 0.8

(b) 0.08

(c) 0.008

(d) 80 000

3 (a) 500

(b) 500

(c) 0.5

(d) 0.05

4 (a) 10 000

(b) 0.01

(c) 1

(d) 0.001

Number lines leading to the following answers. (i) (i) (i) (i)

38 000 22 000 15 000 58 000

(d) 0.2

(b) (b) (b) (b)

(ii) (ii) (ii) (ii)

38 300 21 800 15 500 58 400

(c) (c) (c) (c)

(iii) (iii) (iii) (iii)

38 270 21 790 15 480 58 440

2 (a) Nearest 100 000 (b) Nearest 10 000 (c) Nearest 1000

3 (a) 5000

(b) 9000

(c) 68 000

(d) 73 000

4 (a) 500

(b) 1700

(c) 100

(d) 12 800

5 (a) 60

(b) 850

(c) 5840

(d) 10

Exercise 1.3

(b) 200

(c) 3

(e) 2

3 (a), (c) and (d)

Exercise 2.1 1 a2

2 b5

3 c7

4 d1

5 e8

6 f3

7 g8

8 h2

9 i2

10 j 5

11 k 5

12 l 1

13 m 2

14 n 2

15 e 11

16 p 9

17 q 2

18 r 17

19 s 3

20 t 19

21 u 4

22 v 4

23 w 7

24 x 12

25 y 10

26 z 7

27 a 2

28 b 3

29 c 6

30 d 12

Exercise 2.2 1 a5

2 b 11

3 c9

4 d 17

5 e4

6 f 18

7 g 10

8 h3

9 i 11

10 j 11

1 (a) 6000 (e) 4

(b) 800 (f) 7

(c) 90 (g) 0.8

(d) 5000 (h) 0.08

2 (a) 6800 (e) 53

(b) 6900 (f) 46

(c) 4.6 (g) 0.87

(d) 7.4 (h) 0.88

3 (a) 87 600

(b) 477 (e) 82.5

(c) 0.876

1 (a) 6.4

(b) 4.1

(c) 0.9

(d) 8.7

(e) 1.1

(f) 0.1

1 a3

2 (a) 4.38

(b) 5.72

(c) 5.80

5 e7

(d) 1.48

(e) 3.90

(f) 6.27

9 i3

3 (a) 0.001

(b) 0.008

(c) 0.005

(d) 3.654

(e) 3.457

(d) 82.4

(c) 8000

(e) 3500

Chapter 2 – Algebra

Exercise 1.2 1 (a) (b) (c) (d)

2 (a) 100

(b) 1800

Exercise 1.4

Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

Exercise 2.3 1 a 12

2 b 10

3 c4

4 d 24

5 e 45

6 f 12

7 g 27

8 h 12

9 i 20

10 j 24

2 b 10

3 c7

4 d 12

6 f 11

7 g6

8 h 15

10 j 3

11 k 7

12 l 15

13 m 12

14 n 4

15 p 5

16 q 20

17 r 3

18 s 11

19 t 3

20 r 4

Exercise 2.4

1 of 28


2

25/3/04

8:19 am

Page 2

Section 1 – Using and applying mathematics/ICT

Exercise 4.2

Chapter 3 – Shape, space and measures

1

Number of litres of milk consumed

Exercise 3.1 1 (a) 10 cm (e) 9.5 cm (i) 6.7 cm

(b) 7 cm (f) 1.5 cm (j) 2.8 cm

(c) 2 cm (g) 4.5 cm

(d) 3.5 cm (h) 0.5 cm

2 Pupils’ drawings of lines.

Number of houses

60

Pupils’ measurements may differ by 2°.

2 (a) (b) (c) (d) (e) (f)

a 90° d 34° h 62° j 33° m 32° q 107°

40 30 20 10 0

Exercise 3.2 1 (a) 45° (d) 138°

50

(b) 22° (e) 115°

2

3 4 Litres of milk

5

6

2 Number of litres of milk consumed

(c) 95° (f) 135°

b 140° e 58° i 298° k 71° n 135° r 328°

1

no reply 13%

c 130° f 122°

g 146°

l 256° o 58° s 326°

p 328° t 39°

easy 24%

hard 21% ok 42%

3

Spain results lose 17%

3 Pupils’ drawings of angles.

Exercise 3.3 Pupils’ constructions of triangles.

Exercise 3.4

draw 22%

Pupils’ constructions of triangles and measurements of angles.

win 61% Turkey results lose 6%

Exercise 3.5 Pupils’ constructions of circles and circle patterns.

Exercise 3.6

draw 36% win 58%

Pupils’ own constructions involving regular hexagons.

Exercise 3.7 Pupils’ constructions of shapes.

Chapter 4 – Handling data Exercise 4.1 1 (a) Embarrassing (b) Biased (c) Unclear (d) Give several answers to choose from (e) Irrelevant (f) Biased (g) Embarrassing 2 Pupils’ own questions for health survey. Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

4 Pupils’ own survey and graphs. 5 Pupils’ own survey and graphs.

Chapter 5 – Using and applying mathematics/ICT Investigation 1 Pupils find that the total of the three angles of each of their triangles is approximately 180°. Results are unlikely to be exactly 180° due to errors in measuring. 2 of 28


25/3/04

8:19 am

Page 3

Section 2 – Number

2 Pupils find that the total of the four angles of each of their quadrilaterals is approximately 360°. Results are unlikely to be exactly 360° due to errors in measuring.

5 Pupils’ angles 6 Pupils’ constructions and measurements. 7

Colour of car sold by a dealer black others 6% 3%

3 Pupils find that the total of the five angles of each of their pentagons is approximately 540°. Results are unlikely to be exactly 540° due to errors in measuring. 4 Each time the total of the angles increases by 180°.

3

red 33%

silver 19% green 3% blue 11%

ICT activity

white 25%

Pupils carry out their own survey and display results with an appropriate graph using a spreadsheet package. Pupils also make valid conclusions from their results and graphs.

SECTION TWO Review 1A 1 (a) 8.6

(b) 0.8

(c) 4.6

2 (a) 8

(b) 0.8

(c) 5

(b) b 9

(d) d 20

(c) c 4

(e) e 14

(b) 46

(d) 0.65

(e) 10.7

2 (a) 4500

(b) 720

(d) 4.85

5 Pupils’ angles 6 Pupils’ constructions and measurements of angles. 7 Survey on number of bedrooms 5 10%

Exercise 6.1 1 (a) 630

3 Approximately 3000 4 (a) a 4


1 15%

3 (a) 460 000 (b) 6800 (d) 84 4 (a) 68

(b) 7.2

(c) 0.89

(e) 0.0054 (b) 6.55

(d) 0.008

(c) 0.0562

(e) 0.000 34

6 (a) 0.000 64 (b) 0.046 (d) 0.000 008 45

3 30%

Review 1B 1 (a) 0.08

(b) 7.59

(c) 4.96

2 (a) 0.86

(b) 7.5

(c) 29 000

3 Approximately 20 4 (a) a 18 (d) d 9

(b) b 6

(c) c 18

(e) e 2


(c) 380 000

(e) 70 000

(d) 0.064

2 20%

(c) 96

(e) 603.3

5 (a) 35 4 25%

(c) 8.4

7 (a) 57

(b) 49

(d) 84

(e) 11

(c) 9.5 (e) 0.004 (c) 31

8 (a) 56

(b) 54

(c) 8

(d) 9

(e) 8

(f) 6

(g) 9

(h) 8

(i) 7

(j) 36


(b) 0

(c) 3

2 (a) 2

(b) 1

(c) 8

3 (a) 6

(b) 5

(c) 8

4 (a) 1

(b) 2

(c) 6 3 of 28


4

25/3/04

8:19 am

Page 4


Exercise 6.3

Exercise 6.5 (b) 3

(c) 3

(e) 4

(f) 5

2 (a) 5

(b) 7

(c) 4

(d) 4

(e) 7

(f) 4

1 (a) 1

(b) 3

(c) 2

1 (a) 3

(d) 3

(e) 6

(f) 3

(d) 3

2 (a) 1

(b) 1

(c) 3

(d) 5

(e) 1

(f) 1

3 (a) 6

(b) 8

(c) 14

(d) 7

(e) 6

(f) 12

4 (a) 4

(b) 1

(c) 3

(e) 0

(f) 2

5 (a) 1

(b) 3

(c) 4

(d) 1

(e) 4

(f) 2

(d) 1

3

4

(b) 4 °C

(c) 10 °C

(d) 5 °C

(e) 18 °C

(f) 12 °C

(g) 4 °C

(h) 9 °C

(i) 20 °C

6 (a) 10 °C

5

x

5 4 3 2 1 0 1 2 3 4 5

y

3 4 5 6 7 8 9 10 11 12 13

p

5 4 3 2 1 0 1 2 3 4 5

q

8 7 6 5 4 3 2 1

x

4 3 2 1 1 2 3 4

y

6 8 12 24 2412 8 6

0

1

2

(j) 21 °C 7 (a) €260

(b) €290

(c) €1030

Exercise 6.6

(d) €190

1 A grid with the following left uncrossed: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

(e) €470 (b) 9

8 (a) 8 (d) 1

(c) 21

(e) 15

2 Pupils’ solutions from the internet or an encyclopaedia.

9 1450 m 10 64 m

Exercise 6.4

3 (a) 1

2

3

(b) 1

3

9

(c) 1

7

(d) 1

3

5

15

6

1 (a) 48

(b) 30

(c) 28

(e) 1

2

3

4

6

8

12

24

2 (a) 20

(b) 63

(c) 49

(f) 1

2

3

4

6

9

12

18

35

6

7

14

21

42

5

10

20

25

50

3

3

2

1

0

1

2

3

(g) 1

5

7

3

9

6

3

0

3

6

9

(h) 1

5

25

2

6

4

2

0

2

4

6

(i) 1

2

3

1

3

2

1

0

1

2

3

(j) 1

2

4

0

0

0

0

0

0

0

0

1

3

2

1

0

1

2

3

2

6

4

2

0

2

4

6

3

9

6

3

0

3

6

9

4 (a) 8 (d) 10

(b) 2 4 (a) 3 2 (e) 11 22 (f) 7 23 (i) 11 7 3 2

5

(c) 3 2 (g) 24 (j) 7 32 2

2

36

100

(d) 5 23 (h) 13 3

Exercise 6.7

(b) 3

(c) 12

1 (a) 4

(b) 5

(c) 6

(d) 3

(e) 9

(e) 5

(e) 9

2 (a) 42

(b) 60

(c) 70

(d) 90

(e) 231


4 of 28


25/3/04

8:19 am

Page 5

Section 2 – Algebra

5

2 (a)

Exercise 6.8 1 (a) 9 (e) 121

(b) 25

(c) 64

(d) 100

(f) 144

(g) 225

(h) 400

2 Pupils’ diagrams leading to the following answers. (a) 4.41 cm2

(b) 9.61 cm2

(c) 1.44 cm2

(d) 27.04 cm2

(e) 39.69 cm2

(f) 0.49 cm2

(b) 38.44 cm2

(c) 21.16 cm2

(e) 174.24 cm2

(f) 566.44 cm2

3 (a) 5.76 cm2 (d) 56.25 cm2

4 Pupils check answers to 2 and 3 with a calculator.

(b)

Number of white tiles

1

2

3

4

5

Number of grey tiles

5

6

7

8

9

(c) The number of grey tiles is 4 more than the number of white tiles. (d) 104 grey tiles

Exercise 6.9 1 (a) 5 (d) 13

(b) 3

(c) 11

(e) 0.1

(f) 0.3

3 (a)

2 Pupils check answers to 1 with a calculator.

3 (a) (d)

1 3 3 10

(b) (e)

1 7 5 6

(c) (f)

2 7 7 9


(b) 216

(c) 1000

(d) 729

2 (a) 1331

(b) 8000

(c) 15.625

(d) 238.328

(b)


1

2

3

4

5


4

6

8

10

12

(c) The number of grey tiles is double the number of white tiles, plus 2.


(d) 202 grey tiles

Exercise 7.1 4 (a)

1 (a)

(b)

(b) Number of white tiles

1

2

3

4

5


1

2

3

4

5


2

4

6

8

10


0

2

4

6

8

(c) The number of grey tiles is double the number of white tiles.

(c) The number of grey tiles is double the number of white tiles, minus 2.

(d) 200 grey tiles

(d) 198 grey tiles


5 of 28


6

25/3/04

8:19 am

Page 6


4 (a) 0.2

5 (a)

(b) 0.7

5 (a) Denominator increases by 1 each time (b) 111 6 (a) Numerator and denominator increase by 1 each time (b) 1101 7 (a) Difference increases by 2 each time (b) 100 8 (a) Difference increases by 2 each time (b) 103 9 (a) The difference of the difference increases by 6 each time (b) 1000 (b)


1

2

3

4

5


1

4

9

16

25

(c) The number of grey tiles is the number of white tiles squared. (d) 10 000 grey tiles


(b) 12, 14

2 (a) 2

(b) 11, 13

3 (a) 3

(b) 19, 22

4 (a) 4

(b) 22, 26

5 (a) 7

(b) 36, 43

6 (a) 7

(b) 42, 49

7 (a) 9

(b) 54, 63

8 (a) 0.5

(b) 3, 3.5

9 (a) 0.25

(b) 1.5, 1.75

10 (a) 2

(b) 1, 3

11 (a) 4

(b) 12, 8

12 (a) 12

(b) 96, 84


(b) 1536

2 (a) Difference doubles each time (b) 1023

3 (a) 2

(b)

1 16


10 (a) 5

(b) 9 765 625

Exercise 7.4 1 (a) 13, 15

(b) 2n 1

2 (a) 14, 16

(b) 2n 2

3 (a) 19, 22

(b) 3n 1

4 (a) 20, 23

(b) 3n 2

5 (a) 25, 29

(b) 4n 1

6 (a) 27, 31

(b) 4n 3

7 (a) 31, 36

(b) 5n 1

8 (a) 34, 39

(b) 5n 4

9 (a) 43, 50

(b) 7n 1

10 (a) 59, 69

(b) 10n 1

11 (a) 29, 34

(b) 5n 1

12 (a) 36, 43

(b) 7n 6

13 (a) 20, 24

(b) 4n 4

14 (a) 11.5, 13.5

(b) 2n 0.5

15 (a) 5, 6

(b) n 1

Exercise 7.5 1 (a) 37, 50

(b) n2 1

2 (a) 43, 56

(b) n2 7

3 (a) 35, 48

(b) n2 1

4 (a) 125, 216

(b) n3

5 (a) 126, 217

(b) n3 1

6 (a) 122, 213

(b) n3 3 6 of 28


25/3/04

8:19 am

Page 7

Section 2 – Shape, space and measures

7

3 Isosceles triangle


y 6

Exercise 8.1

5

1

4 y 8

3

7

1

D

2

6

D

5

6 5 4 3 2 1 0 1

C

4

A

2

3

4

5

6x

5

6x

3 4

1 8 7 6 5 4 3 2 1 0 1

1

2

3

4

5

6

2

7 G

3

5

F

8x

5

4 Parallelogram J

H

6

y 6 5

F

7

E

6

4

E

2

2

B

3

1

G

8

4 3 2 1

2 Rectangle

6 5 4 3 2 1 0 1

y 6 5

2

4

3 4

3 D

A

2

5

1

2

3

4

5

2

C

5

3

4 I

H

6x

Exercise 8.2 1 (a) S (6, 2)

3 4

2

6

1 6 5 4 3 2 1 0 1

1

(b) Diagonals cross at (0, 1) B

6

(c) 72 units2 2 (a) Parallelogram (b) 72 units2 (c) It has the same area as the rectangle PQRS, i.e. the slope of the parallelogram does not affect its area.

3 (a) J (0, 10) Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

(b) 0 7 of 28


8

25/3/04

8:19 am

Page 8

Section 2 – Handling data

Exercise 8.3 1 (a) Pupils’ constructions of a regular hexagon. (b) B (7, 4), C (7, 4), D (8, 0), E (7, 4), F (7, 4) 2 (a) Pupils’ drawings of an octagon. (b) Answers will vary depending on length of sides QR, ST, UV and WP. (c) Answers will vary.

Exercise 8.4 1 B 1.5, C 2.4, D 4.8 2 F 0.9,

G 1.5, H 1.75

3 I 4.4,

J 5.2, K 5.9, L 6.3, M 6.8

4 Q 2.4, R 4.6, S 5.8, T 6.4, U 7.8, V 8.8, W 9.8

Exercise 8.5 1 A (1, 1.5),

B (1.2, 1.5),

C (0.9, 1.6),

(D 1.8, 0.7)

2 E (1, 1.8),

F (3, 2.4),

G (3.6, 2.6),

H (1.6, 3.6)

3 J (1, 0.5),

K (0.75, 0.25), L (0.85, 0.25),

4 P (37.5, 25), Q (25, 37.5), 5 Pupils’ graphs

M (0.55, 0.25)

R (37.5, 12.5), S (42.5, 45)

6 Pupils’ plots

Chapter 9 – Handling data Exercise 9.1 1–5 Pupils’ histograms (these will depend on class intervals chosen). Percentage

Frequency

0–9

0

10–19

0

20–29

0

30–39

2

40–49

6

50–59

13

60–69

12

70–79

7

80–89

4

90–99

0

(b)

Percentage scores in test

14 12 Frequency

6 (a)

10 8 6 4 2 0

0–9


10–19 20–29 30–39 40–49 50–59 60–69 70–79 80–89 90–99 % score

8 of 28


25/3/04

8:19 am

Page 9


7 (a)

9

(b) Oranges on tree

Number of oranges

Frequency

0–19

6

20–39

8

7

40–59

8

6

60–79

2

80–99

5

100–119

4

2

120–139

7

1

9

Frequency

8

5 4 3

0 0–19

20–39 40–59 60–79 80–99 100–119 120–139

Number of oranges

8 (a)

(b) Number of

Number of computers repaired

Frequency

9

computers repaired

0–9

2

10–19

8

20–29

3

30–39

6

40–49

7

50–59

3

60–69

2

8 7 Frequency

6 5 4 3 2 1 0 0–9

10–19 20–29 30–39 40–49 50–59 60–69

Number of computers

Chapter 10 – Using and applying mathematics/ICT Investigation

Size of square

Number

11

4

22

1

Total

5

Size of square

Number

11

9

22

4

33

1

Total

14

1 In a 2 2 board there are a total of 5 squares. These can be broken down like this.

2 In a 3 3 board there are a total of 14 squares. These can be broken down like this.


9 of 28


10

25/3/04

8:19 am

Page 10

Section 2 – Reviews

3 In 4 4 and 5 5 boards the results are as follows. Results for 4 4

Results for 5 5

Review 2A

Size of square

Number

11

16

22

9

33

4

44

1

Total

30

Size of square

Number

11

25

8 3n 1

22

16

9 A (3, 4), B (2, 4), C (4, 1), D (4, 2)

33

9

44

1 Pupils’ definitions of the square root of a number. 2 (a) 68.9

(b) 15.8

3 11, 13, 17, 19 4 5 32 2 5 36 6 12 7 (a) 23, 27

10 (a)

(b) 27, 18

Number of people

Frequency

4

0–19

0

55

1

20–39

11

Total

55

40–59

16

60–79

7

80–99

2

For an 8 8 board the total number of squares is given by: 82 72 62 52 42 32 22 12 204 4 Total number of squares for an n n board is given by:

(b)

Attendance at youth club 20 Frequency

n2 (n 1)2 (n 2)2 … 12 5 Total number of squares in an n m rectangle, where m n is given by: mn (m 1)(n 1) (m 2)(n 2) …mn1

15 10 5 0

ICT activity The spreadsheet below summarises the results for 2 2 2, 3 3 3, 4 4 4, 5 5 5, 10 10 10 and N N N sized cubes.

0–19 20–39 40–59 60–79 80–99 Number of people

Review 2B 1 64 2 (a) 0.9

(b) 0.3

3 97 4 2357 5 13 6 264 7 (a) 36, 49

(b) 88, 77

8 5n 2 9 P (0.4, 1), Q (0.5, 1), R (0.3, 1), S (0.8, 1.5) Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

10 of 28


25/3/04

8:19 am

Page 11

11


10 (a)

Number of people

Frequency

151–200

1

201–250

2

251–300

11

301–350

2

351–400

9

401–450

5

Exercise 11.2 1 (a) (d) 2 (a) (d)

(b) (e)

5 15 and 7 21 3 9 15 , and 10 30 50

(b) (e)

1 9 2 5

(c)

5 20 and 8 32 6 3 15 , and 32 1 6 80

(c) all

(f)

3 16 5 8

(f) none

3 Pupils’ diagrams.

Exercise 11.3

(b)

1 (a) True

(b) True

(c) True

(d) True

(e) True

(f) False

Attendance at production

2 (a) 36, 59, 23

12

(c)

10 Frequency

1 5 6 7

8

3 Player B

6

4

4

9 25

(b)

1 10 6 , , 3 2 6 13

(d)

10 , 84 27 , 30

2 3 , 6 7 37 14 , 40 15

is a higher proportion

5 Grape, pineapple, orange, mango, passion fruit

2 0 151–200 201–250 251–300 301–350 351–400 401–450

Number of people

Exercise 11.4 1 (a)

5 9

(b)

5 11

(c)

5 7

(d)

10 13

(e)

22 23

2 (a)

5 9

(b)

3 7

(c)

3 11

(d)

7 23

(e)

2 5

3 (a)

5 7

(b)

2 3

(c)

2 3

(d)

1 2

SECTION THREE

4 (a)

(b)

5 14

(e)

47 60 11 48

(c)

(d)

17 30 3 26


5 (a)

18 35

6 (a)

9 56

7 (a)

1 16

(b)

5 18

(c)

(d)

1 60

(d)

3 8


(b) 30

(c) 45

2 (a) 9

(b) 27

(c) 63

3 (a) 12

(b) 60

(c) 108

4 (a) 13

(b) 91

(c) 143

5 (a) €1.55

(b) €3.21

(c) €56.84 6 (a) 609 7 (a)

8 20

(d) €1236.15 (b)

5 12

(or equivalent)

8 (a) 123

(b) 512

(f) 0

3 14

(c) 11728

Exercise 11.5 1 (a)

6 24

(b)

1 4

2 7 hours and 12 minutes

3 20 minutes 4

10 27

(b) 0.75 litres

5 3 hours, 11 minutes and 15 seconds

(c) 2.25 litres

6 (a) 8 (d) 48

8 (a) €48 (b)

35 24 0

(or

7 ) 48

(c) €7 Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

7 (a) (d)

9 20 7 12

(b) 25

(c) 18

(e) 44

(f) 8

(b) (e)

7 30 7 8

(c) (f)

4 5 19 20

11 of 28


12

25/3/04

8:19 am

Page 12


Exercise 11.6 1

Numerator 2

3

4

5

6

7

8

9

10

11

12

1

1

2

3

4

5

6

7

8

9

10

11

12

2

0.5

1

1.5

2

2.5

3

3.5

4

4.5

3

0.3333 0.6667 1

1.3333 1.6667 2

4

0.25

0.5

0.75

1

1.25

5

0.2

0.4

0.6

0.8

1

6

0.1667 0.3333 0.5

7

0.1429 0.2857 0.4286 0.5714 0.7143 0.8571 1

1.1429 1.2857 1.4286

1.5714 1.7143

8

0.125

1

1.25

1.375

9

0.1111 0.2222 0.3333 0.4444 0.5556 0.6667 0.7778 0.8889 1

1.1111

1.2222 1.3333

10

0.1

1

1.1

1.2

11

0.0909 0.1818 0.2727 0.3636 0.4545 0.5455 0.6364 0.7273 0.8182 0.9091

1

1.0909

12

0.0833 0.1667 0.25

0.9167 1

Size of cube

1

0.25

0.2

5

5.5

2.3333 2.6667 3

3.3333

3.6667 4

1.5

1.75

2

2.25

2.5

2.75

3

1.2

1.4

1.6

1.8

2

2.2

2.4

1.6667

1.8333 2

0.6667 0.8333 1

0.375

0.3

0.5

0.625

0.4

0.5

1.1667 1.3333 1.5

0.75

0.875

0.6

0.7

0.3333 0.4167 0.5

4 Pupils’ own answers, for example,

1 5

0.8

0.9

0.5833 0.6667 0.75

0.8333

1.5

3 Numerator denominator.

2 Numerator is bigger than denominator. 1 2

1.125

6

2 5.

5 Yes, followed by pupils’ explanation.

6 Pupils’ descriptions.

Exercise 11.7 1 (a) 0.05

(b) 0.2

(c) 0.25

. . . (d) 0.214 285 7 (e) 0.0416

2 (a)

3 10

(b)

3 25

(c)

5 8

(d)

37 10 0

(e)

17 80

3 (a)

2 3

(b)

37 99

(c)

75 99

(d)

1 90

(e)

353 999

4 (a) 0.55, 0.7 (d) 0.3003, 0.303, 0.33

.. (f) 0.17

(b) 0.100, 0.27

(c) 0.625, 0.73, 0.8

(e) 0.01, 0.10, 0.101

(f) 0.32, 0.403, 0.43

2 (a) €71.80

3 (a) 0.69 m

Exercise 11.8 1 (a) €5.35

(b) €4.65

4 (a) €110.81

(b) €68.81 overdrawn

(b) €14.80 5 €818 422.22

(b) 69 cm 6 €35.70

Exercise 11.9 1 white 47% blue 23% red 30% 4 (a)

73 10 0

(b)

28 1 00

(c)

10 1 00

2 70% (d)

3 (a) 60%

(b) 40%

25 10 0

5 (a) 27%

(b) 30%

(c) 14%

(d) 25%

6 (a) 0.39

(b) 0.47

(c) 0.83

(d) 0.07

(e) 0.02

(f) 0.2

7 (a) 31%

(b) 67%

(c) 9%

(d) 5%

(e) 20%

(f) 75%


12 of 28


25/3/04

8:19 am

Page 13


3


y 6

Exercise 12.1

4

1 (a) y 6

2

(b) y 2 (c) x 6

8 6 4 2 0 2

(d) x 1 (e) y x

4

(f) y 3x

6

(g) y x

2

4

6

8

10

x

2

4

6

8

10

x

2

4

6

8

10

x

2

4

6

8

10

x

8

(h) y x 3

4

y

2 Horizontal

6

3 Vertical

4

4 Sloping

2

5 Sloping

8 6 4 2 0 2

6 Vertical 7 Horizontal

4

8 Sloping

6 8

Exercise 12.2 1

13

5 y

y 6

6

4

4

2

2 8 6 4 2 0 2

2

4

6

8

10

8 6 4 2 0 2

x

4

4

6

6

8

8

2

6

y

y 14

6

12

4

10

2

8

8 6 4 2 0 2

2

4

6

8

10

x

4 6 8 Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

6 4 2 8 6 4 2 0

13 of 28


14

25/3/04

8:19 am

Page 14



5

Exercise 13.1 1

6

2

7

3

4


8

14 of 28


25/3/04

8:19 am

Page 15


Exercise 13.2

15

5

1

6 2

3

Exercise 13.3 1 Order 4

2 Order 6

3 Order 13

4 Order 3

5 Order 2

6 Infinite order

Exercise 13.4 1

4

Order of rotational symmetry

Angle between images

2

180°

3

120°

4

90°

5

72°

6

60°

8

45°

9

40°

10

36°

12

30°

20

18°

2 Pupils’ own designs.

3 Pupils’ pictures depicting rotational symmetry. Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

15 of 28


16

25/3/04

8:19 am

Page 16


Exercise 13.5

6 (a) (d)

1

7 (a)

2 26 3 26

or 113

(c)

21 26

(e) Pupils’ answers

1 5 10 20 5 19

8 (a) (i)

(a)

5 26

(b)

(b) (i)

or equivalent (ii)

3 20

(ii)

2 19

9 (a) TCA TAC CAT CTA ATC ACT

(b)

(c) (d)

(b)

1 6 3 6

2 6 1 6

(c)

(d) or equivalent

(e)

or equivalent

2 (a) 4 units to the right and 1 unit upward. (b) 9 units to the right. (c) 2 units to the left and 2 units upward. (d) 3 units downward. (e) 7 units to the left and 3 units downward.

Exercise 14.2 1 (a) Dice 1

3 (a) Corresponding vertices on object and image

1

2

3

4

1

1, 1

2, 1

3, 1

4, 1

2

1, 2

2, 2

3, 2

4, 2

3

1, 3

2, 3

3, 3

4, 3

4

1, 4

2, 4

3, 4

4, 4

are not joined. Dice 2

(b) One possible arrow is shown here.

(b) (c) (d)

4 16 6 16 8 16

or equivalent or equivalent or equivalent

2 (a) Dice 1

Chapter 14 – Handling data Exercise 14.1 1 6

(ii)

1 6

1 3

(iii)

(b) (i) 10 (ii) No, as it is down to chance. 2 (a) (d)

1 6 5 6

3 (a) (i) (c)

1 6

(c)

(e) 0

(f)

(b) 1 7

(ii)

1 2 6 6

Dice 2

1 (a) (i)

or 1

6 7

1 7

67 1 It is certain that a baby is born either on a Tuesday, or not on a Tuesday.

4 (a)

1 500

5 (a)

20 32

(b)

1 10

(b)

12 32

(c) 1

(d) 0


(b) (i) (iii) (v) (vii)

1 24 4 24 6 24 6 24

1

2

3

4

1

1, 1

2, 1

3, 1

4, 1

2

1, 2

2, 2

3, 2

4, 2

3

1, 3

2, 3

3, 3

4, 3

4

1, 4

2, 4

3, 4

4, 4

5

1, 5

2, 5

3, 5

4, 5

6

1, 6

2, 6

3, 6

4, 6

(ii)

4 24

or equivalent

(iv)

0

or equivalent

(vi)

or equivalent

(viii)

18 24 6 24

or equivalent or equivalent or equivalent 16 of 28


25/3/04

8:19 am

Page 17


17

Chapter 15 – Using and applying mathematics/ICT Investigation 1 2

1 1 1 2

1 3

1 4 1 12

1 6 1 12

1 3

1 20 1 30

1 20

1 4

1 5 1 30 1 60 1 60

1 30

1 5

1 6

1 7 1 42

2 Pupils describe some of the patterns they see in the fraction triangle.

1 105 1 140

1 105 1 42

1 6 1 7

ICT activity An example of a possible spreadsheet is shown below. Pupils should be encouraged to use formulae wherever possible. The spreadsheet showing which ‘Microsoft Excel’ formulae were used is also shown.

If the cost of labour increases to €10.00/hr, the retailer will have to pay €22.96 for each coat. Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

17 of 28


18

25/3/04

8:19 am

Page 18


Review 3A

7

1 (a) 180 (b) 63 2 (a)

31 35

(b)

29 72

3 (a) 0.75, 75% (b) 0.875, 87.5% . . (c) 0.5, 55.5% 4 (a) 720 (b) 150 5 (a) y 10 8 6 4 2 8 6 4 2 0 2

2

4

6

8

10

x

4 6

8 45° 9 (a)

11 24

(b)

6 24

or equivalent

10 250

8

(b)

Review 3B y

1 (a) 60

10

(b) 36

8 6

2 (a) 11210

4

(b)

2

3 (a)

4 5

(b)

3 4

(c)

5 8

8 6 4 2 0 2

2

4

6

8

10

4

6 y 2x, x y 9 Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

x

23 72

4 (a) 140 (b) 210 18 of 28


25/3/04

8:19 am

Page 19


19

8 (a) 7 units to the right and 2 units downward.

5 (a)

(b) 6 units downward.

y

(c) 5 units to the left.

10 8

9 12

6

10 400

4

SECTION FOUR

2 10 8 6 4 2 0 2

2

4

6

8

10

x

Chapter 16 – Number Exercise 16.1

4

1 (a) 25%

(b) 75%

(c) 20%

(d) 60% (e) 30%

6

(f) 70%

(g) 15%

(h) 65%

(i) 8% (j) 17.5%

8

2 (a) 0.75

(b) 0.4

(c) 0.75

(d) 0.4

10

(f) 0.9

(g) 0.06

(h) 0.175 (i) 1.25 (j) 3.75

(e) 0.12

Exercise 16.2

(b) y 10

1 (a) 6

(b) 40

(c) 90

2 (a) 10

(b) 30

(c) 70

8

3 (a) 23

(b) 23

(c) 11.5

6

4 (a) 87.5

(b) 8.75

(c) 26.25

4

5 (a) 21.6

(b) 64.8

(c) 108

2

6 (a) 81

(b) 8.1

(c) 0.81

8 6 4 2 0 2

2

4

6

8

x

7 612

8 84

9 3150

10 63

4 6

Exercise 16.3

8

1 (a) 50%

(b) 20%

(c) 25%

2 (a) 10%

(b) 60%

(c) 90%

6 x 6, y 12 x 3

3 (a) 10%

(b) 30%

(c) 70%

7

4 (a) 5%

(b) 15%

(c) 20%

5 (a) 25%

(b) 2.5%

(c) 17.5%

6 Win 68%

Draw 8%

Lose 24%

(b) 30%

(c) 25%

1 (a) 120%

(b) 150%

(c) 103%

2 (a) 88%

(b) 70%

(c) 93%

7 87.5% 8 (a) 45%

Exercise 16.4


19 of 28


20

25/3/04

8:19 am

Page 20


Exercise 16.5 1 (a) 200

(b) 280

(c) 195

2 (a) 180

(b) 240

(c) 175

3 9200 tonnes

4 €212.50

5 €2300

6 €4320

7 €7475

8 €6877

Chapter 18 – Shape, space and measures Exercise 18.1 1 (a) Yes (b) Scale factor 2 2 (a) No


3 (a) Yes (b) Scale factor 4

Exercise 17.1 1 2x 8

2 2x 2y

4 3y

5 4p 4q

4 (a) Yes

3 6m 8

(b) Scale factor 2 5 (a) No 6 (a) Yes

Exercise 17.2 1 4a 12

2 3b 6

3 5c 35

4 4d 12

5 6e 6

6 4f 36

7 11j

8 7h

(b) Scale factor 112

Exercise 18.2 Exercise 17.3

1

1 (a) (y 2)(y 3)

(b) y2 5y 6

2 (a) (m 8)(m 2)

(b) m2 10m 16

3 (a)

1 2

x(x 2)

(b)

1 2

x2 x

4 (a) x(y 2)

(b) xy 2x

5 (a) 3(x 5) x(x 2)

(b) x2 5x 15

6 (a)

1 2

(x 1)(x 4)

(b)

1 2

x2 52 x 2

7 (a) (x y)(x 2)

(b) x2 2x xy 2y

8 (a) x(y 1) 15

(b) xy x 15

9 (a)

1 2

(m 2)(m 2)

(b)

1 2

m2 2

10 (a)

1 2

(x 1)(x 1)

(b)

1 2

x2 12

2

Exercise 17.4 1 (a) x2 x 6

(b) x2 5x 24

2 (a) x2 2x 3

(b) x2 2x 63

3 (a) x 6x 9

(b) x 12x 35

4 (a) a b

(b) p2 q2

5 (a) 6y2 23y 20

(b) 18y2 15y 3

6 (a) 18p2 2

(b) 28p2 44p 24

7 (a) 4x2 24x 36

(b) 4x2 9

8 (a) 8y2 18

(b) 25y2 70y 49

2

2

2

3

2


20 of 28


25/3/04

8:19 am

Page 21


4

21

Exercise 18.3 1

2

O

O

3 O

4 5

O

5

O

6

6 O


21 of 28


22

25/3/04

8:19 am

Page 22


Exercise 18.4 1 (a) Scale factor 3 (b)

2 (a) Scale factor 2 (b)






22 of 28


25/3/04

8:19 am

Page 23


Chapter 19 – Handling data Q p. 124 (a) The coach is more likely to choose the second runner for an individual event as he/she is capable of doing very well. (b) For a team event the coach is more likely to choose the first runner as he/she is more consistent and therefore less likely to let the team down.

23

Chapter 20 – Using and applying mathematics/ICT Investigation Pupils carry out their own research into sales promotions and identify which are better value.

ICT activity Below is an example of a possible spreadsheet to answer questions 1–3.

Q p. 124 If inconsistent sportswomen and sportsmen are chosen this is usually because these athletes perform better on ‘big’ occasions.

Exercise 19.1 1 Mean 3.3 Mode 4

Median 4 Range 4

2 Mean 6.4 Mode 5.6

Median 5.6 Range 5.9

3 Mean 2.9 Mode 4

Median 3 Range 6

4 Mean 36.5 Mode 23

Median 23 Range 95

5 Mean 1.8 Mode 1, 2

Median 2 Range 5

6 A: Mean 34 Mode 32, 35 B: Mean 34.5 Mode 38

Median 34.5 Range 4 Median 34 Range 8

Pupils’ explanation 7 88.4 kg 8 94 points 9 Pupils’ answer 10 Pupils’ answer

Exercise 19.2 1 Pupils’ analysis 2 (a) No, as the mean is €30 000 (b) Yes, as both the mode and median are €20 000

3 Pupils’ report Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

Total attendance 366 420

Mean attendance 11 820

4 The mean attendances were highest on Saturdays and Sundays as these are at the weekends. 5 Pupils’ reasons. 23 of 28


24

25/3/04

8:19 am

Page 24


Review 4A 1 (a) 25%

Review 4B 1 (a) 33.3%

(b) 70%

(b) 45%

(c) 60%

(c) 40%

2 (a) 210 (b) 280

3 (a) 195

2 (a) 122.5

(b) 30

3 (a) 350

(b) 172.5

4 €6000

(b) 4200

5 (a) Expression

4 3600 tonnes

(b) Equation

5 (a) Expression

(c) Equation (d) Expression

(b) Expression (c) Equation

6 (a) 6a2 5a 6

(d) Equation

(b) 2b2 9b 5

6 (a) a2 2a 8

7

(b) b2 10b 21 7

8 Scale factor of enlargement 2

8 Scale factor of enlargement 3

9 Mean = 6.5 Median 6 Mode 6 and 7

9 Mean = 4123 Median 41 Mode 39

10 Mode pupils’ explanation Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

10 78.3 kg 24 of 28


25/3/04

8:19 am

Page 25


SECTION FIVE

Exercise 21.5 1 9 units


2 24 000

Exercise 21.1 1

1 4

2

2 5

3

3 8

2 8

4 10

6 16

4 16

8 20

9 24

3 6000

16 64

20 50

15 40

3 12

4 81 tonnes

16 40

5 (a) 20 hours 50 minutes

27 72

1 15

1 4:5

2 60 kg

8 : 10 40 : 50 12 : 15 35 : 10 49 : 14

3 8 : 5 80 : 50 32 : 20

(b) 384 m

Exercise 21.6

Exercise 21.2 2 7 : 2 14 : 4

25

4 : 2.5

Exercise 21.3

3 22 litres 4 36

Exercise 21.7

1 1 : 24

1 150,

2 1 : 14

2 48,

3 1 : 1.75

3 4 kg,

4 1 : 4.8

4 25 minutes,

35 minutes

5 1 : 2.5

5 1 m,

5m

6 516

6 10 km,

7 120 g

7 40 minutes,

8 48

8 600 g,

9 540

9 300 ml,

10 352

10 0.4 cm,

Exercise 21.4 1 4m

100 96 6 kg

2 m,

15 km,

20 km

1 hour,

900 g,

2 hours 20 minutes

500 g

1200 ml,

1500 ml

0.6 cm or 4 mm,

6 mm


2 80 m

Exercise 22.1

3 67.5 m

1 (a) 12

(b) 1

(c) 6

(d) 5

4 4.25 m

2 (a) 15

(b) 10

(c) 78

(d) 24

5 2.08 m

3 (a) 13

(b) 34

(c) 19

(d) 57

6 20 km

4 (a) 16

(b) 0

(c) 14

(d) 28

(e) 7

(f) 2

(b) 4

(c) 20

(e) 16

(f) 6

(b) 23

(c) 6

(e) 61

(f) 49

7 13.75 km 8 8 km 9 12 cm 10 16 cm Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

5 (a) 5 (d) 16 6 (a) 80 (d) 1

25 of 28


26

25/3/04

8:19 am

Page 26


Exercise 22.2 1 (a) P 22 cm,

Exercise 23.2 A 28 cm

2

1 (a) 90 cm2

(b) 104 cm2

(b) P 40 cm,

A 96 cm2

2 (a) 66 cm2

(b) 48 cm2

(c) P 13 cm,

A 9 cm

(d) P 20.5 cm,

A 18 cm2

(e) P 81.6 cm,

A 32 cm2

(f) P 3.4 cm,

A 0.6 cm2

(g) P 2.9 m,

A 0.45 m2

(h) P 12.6 m,

A 2.9 m2

2 (a) 32.5 m2

2

Exercise 23.3 1 (a) 28 cm2 (c) 75 cm (d) 1 cm

(b) 30 cm2

4 (a) 420 volts

(b) 3200 volts

(c) 600 volts2

3 (a) 22 cm (c) 18 cm2

(d) 400 volts2

(b) 40 °C

(d) 100 °C

(c) 15 °C

(e) 0 °C

2 527 777 760 °C

(d) 1.275 m2 (b) 900 cm2

(c) 5 cm

cm

(b) 625 cm2 or 0.0625 m2 (d) 30 cm or 0.3 m

(e) 30 cm or 0.3 m

Exercise 23.4

Exercise 22.3 1 (a) 15 °C

(c)

3313

(b) 120 cm2

(e) 40 cm 2

(d) 3600 cm2

3 (a) 9 cm2

2

2 (a) 32 cm2

(b) 4675 m2

(c) 18 225 mm2

(c) 300 cm2

1 (a) 100 cm2

(b) 108 cm2

2 a 4 cm,

b 10 cm,

c 1313 cm

3 (a) 200 m2

(b) 120 m2 (e) 5 m2

(c) 60 m2 (f) 15 m2

(d) 12 m

3 273.15 °C

Chapter 24 – Handling data Chapter 23 – Shape, space and measures Exercise 23.1 1 (a) 10 cm2

The more times an experiment or event is repeated, the closer the overall result will be to the theoretical probability.

(b) 18 cm2 2

(c) 3600 cm or 0.36 m2

Q p. 152

(d) 7.04 cm2 or 704 mm2 2 (a) 48 cm2

There is an equal chance of it landing heads or tails. Just because a coin has already landed tails 5 times does not mean a head is more likely next time.

(b) 38 m2

(c) 1504 cm2 or 0.1504 m2 (d) 1.02 m2 or 10 200 cm2 (e) 2475 cm2 or 0.2475 m2 or 247 500 mm2

3 (a) 61.2 cm2

(b) 10 cm

(c) 16 cm

(d) 25 cm

2

(b) 20 cm

4 (a) 6 cm

(c) 55 cm2

(d) The area is the same in all three parts. Any variations result from inaccuracies of drawing and measuring. 6 (a) 17.28 cm2

Q p. 152 0.426

5 (a), (b), (c) Pupils’ triangles and calculations

(c) 2 cm

Q p. 152

Q p. 152 The result of the 1000 spins is the most accurate as it is least likely to be affected by rogue results.

Exercise 24.1

(b) 10 cm

1 Pupils’ results

(d) 10 cm

2 Pupils’ results


26 of 28


25/3/04

8:19 am

Page 27

27


Exercise 24.2 1 Pupils’ results 2 (a)

1 36

(b)

6 36

or equivalent

3 (a) Pupils’ results (b) Pupils’ results are likely to show that the greater the number of results, the closer the experimental results resemble the theoretical probability. 4 The larger the sample size, the closer the results are to the theoretical probability.

Chapter 25 – Using and applying mathematics/ICT

The graph is likely to show that, as the number of times the experiment is carried out increases, the experimental results get closer to the theoretical probability, i.e. 12.

Review 5A

Investigation

1 20 cm 1 98 cm2

2 6 : 12 : 24

2 92 cm2

3 36°,

3 18 cm2 4

54°,

90°

4 (a) 26

Base length and

Total area of

Area of piece left

height of triangle

pieces removed

(cm2)

0 cm

0

100

1 cm

2

98

2 cm

8

92

3 cm

18

82

4 cm

32

68

5 cm

50

50

6 cm

68

32

7 cm

82

18

(b) 29

5 (a) Perimeter 2 (length + width) or equivalent (b) 26.4 cm 6 48 cm2

7 60 cm2

8 (a) 7

(b) 16 or equivalent

Review 5B 1 12 m 2 750 kg,

3 60°,

1000 kg, 90°,

1250 kg

120°,

90°

4 (a) 21 5 (a)

(b) 29

Area 12 base

(b) 18.48 cm

8 cm

92

8

9 cm

98

2

6 8 cm

10 cm

100

0

8 (a)

length height

2

7 6.2 cm

Dice 1

2

3

4

5

6

H

H1

H2

H3

H4

H5

H6

T

T1

T2

T3

T4

T5

T6

Pupils record their results in a spreadsheet. A spreadsheet is given here showing the types of formulae that could be used to carry out some of the calculations. Checkpoint Maths 1 © 2004, Hodder & Stoughton Educational

Coin

ICT activity

(b)

1 12

27 of 28


28

25/3/04

8:19 am

Page 28

Section 6 – Checkpoint questions

SECTION SIX – CHECKPOINT QUESTIONS

20.1 12 g 20.2 24 g marked on scale

Number

Algebra

1.1 1.2 1.3 1.4

1004 1545 1055 2044

2

0.01, 0.10, 1.01, 1.10, 1.11

3

350, 300

4 5

1

4(x 1) cm

2

3y 15

3

x6

4

a9 b6

126 miles

5

x4

9

6

a 1 b1 c3 d7

6.1 Day 2, Day 3, Day 5, Day 1, Day 4 6.2 9 °C 6.3 1 °C 7.1 152 7.2 3 7.3 13 8.1 14 8.2 10% 8.3 40% 9.1 3 4 5 2 9.2 21 15 4

7.1 13 7.2 7 8

54.2

Shape, space and measures 1

41 m2, 30 m

2.1 isosceles

10

33

11

$12.75

2.3 obtuse

12

12.8 km

2.4 reflex

13

10.69 minutes

2.5 80 degrees

14.1 14.2 14.3 14.4 14.5 14.6 14.7

11 12 4 8 9 7 10

3

15

£7.20

16

$1105

17

$72

1

2 5

18

$20.70

2

1, 2

19

2.6 km 2600 metres 0.34 m 340 millimetres 1874 ml 1.874 litres 350 g 0.35 kilograms

3.1 16 to 20 hours 3.2 11 to 15 hours


2.2 acute

A (3, 3) B (1, 3)

4.1 2 4.2 3 5

192 cm2

Handling data or 0.4 or 40%

(i) 11 (ii) 3.3 60 degrees

13 24

28 of 28