ANSWERS TO fOuNdATiON GCSE MATHEMATiCS fOR CCEA … · F 2013 1 ANSWERS TO fOuNdATiON GCSE MATHEMATiCS fOR CCEA PRACTiCE BOOK Exercise 1 1 7, 33, 89, 661, 921 2 6, 98, 302, 442, 1002

Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 2013 1

ANSWERS TO fOuNdATiON GCSE MATHEMATiCS fOR CCEA PRACTiCE BOOK

Exercise 1 1 7, 33, 89, 661, 921

2 6, 98, 302, 442, 1002

3 a 7652 b 2576 c 7625

4 a 1, 5, 7, 35 b 1, 2, 4, 5, 10, 20 c 1, 13 d 1, 2, 4, 7, 14, 28 e 1, 2, 4, 11, 22, 44 f 1, 2, 3, 4, 5, 6, 10, 12, 15,

20, 30, 60 g 1, 2, 3, 4, 6, 7, 12, 14, 21,

28, 42, 84 h 1, 7, 13, 91

5 a 9, 18, 27, 36, 45 b 7, 14, 21, 28, 35 c 50, 100, 150, 200, 250 d 200, 400, 600, 800, 1000 e 0.2, 0.4, 0.6, 0.8, 1 f 105, 210, 315, 420, 525

g 12

, 1,1 12

, 2,2 12

h 13, 26, 39, 52, 65

6 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

7 31, 37

8 a 1, 3, 5, 15 b 1, 3, 9 c 1, 7 d 1, 2, 4

9 a 35

b 48

c 64

d 117 e 51

f 24 × 53

10 a 256 b 343 c 14641 d 1 048 576 e 9 765 625 f 65 536 g 4096 h 1

11 a 36 b 27 c 12 d 5 e 1 f 15 g 9 h 121

12 9, 643 , 23, 42

13 a 8 b 6 c 16 d 8

14 a 12, 36 b 15,125,1000 c 41, 19 d 36, 121 e 1000, 125

15 a −47, −34, 9, 15, 56 b −15, −14, −1, 8, 10

16 a −4 oC b 7 oC c −13oC d −8 oC e −29 oC f −25 oC g 13 oC h −25 oC

17 −£285 or £285dr

18 15 oC

19 −4 oC

20 No, Factors of 49 are 1, 7, 49 (A prime number has exactly two factors)

21 1 only has one factor

22 64

23 Yes. Because 8 is a factor of 16, the factors of 8 will also divide into 16

Exercise 2 1 a 46 392 b 52 035 c 8 065 017

2 a Twenty seven thousand four hundred and thirty eight

b One hundred and fifteen thousand nine hundred and one

c Thirteen million six hundred and twenty thousand and twenty four

3 a 3 hundredsb 3 tensc 3 thousandsd 3 unitse 3 tens of thousandsf 3 millions

4 sum = 52 difference = 16 product = 612

5 a 193b 2341

6 a 1363b 7749

7 a 163b 1545

Foundation GCSE Mathematics for CCEA Practice Book © Hodder & Stoughton Ltd 20132

8 a 256 b 4038

9 a 230 b 7100 c 1230 d 45 000 e 1300 f 3770 g 36200 h 4800 i 60 j 1500 k 24 000 l 1200

10 a 23 b 71 c 73 d 45 e 13 f 38 g 590 h 860 i 2030 j 654 k 349 l 800 000

11 a 32 b 8600 c 12 000 d 59 e 320 f 6500

12 a 53 and 27 b 25 and 5 c 2 and 14 d 27 and 68 e 5 and 14 f 68 and 37

13 300 pencils

14 200 pupils

15 154 boxes

16 576 light bulbs

17 49

18 21 years

19 947 000

20 1 315 750

21 No. It is only true when you multiply a whole number by 10. It is not true when you multiply a decimal number by 10 e.g. 2.8 × 10 = 28

22 2

Exercise 3 1 a 4 cm b DC c AB or DC d AD and BC e AB and DC f 42 mm

2 a ML or PQ b LQ c ML and PQ d LQ and ML or LQ and PQ e 14.2 cm

3 square or rectangle

4 rhombus or parallelogram

5 right angled triangle

6 b N c SW d SW e NW f SE g S h E i SW

7 a acute b obtuse c right angle d obtuse e reflex f full turn g obtuse h obtuse i straight line j acute k obtuse l obtuse m reflex n reflex o obtuse p acute

8 i correct estimates ii a = 52º b = 130º c = 43º d = 293º

9 Angles drawn and labelled

10 a = 124º

11 b = 65º

12 c = 230º

13 d = 43º

14 e = 134º

15 f = 159º

16 g = 39º

17 h = 57º i = 123º j = 123º

18 k = 47º

19 l = 158º

20 m = 69º

21 n = 73º

22 p = 54º q = 126º

23 r = 140º

24 s = 61º t = 119º u = 79º

25 No. 150º + 40º = 190º (a straight line is 180º)

26 a False b False c True d True e False

Exercise 4A 1 1 – B

2 – A

3 – D

4 – C

2 1 – B

2 – C

3 – D

4 – A

5 – F

6 – E


3 A – right angled triangle

B – parallelogram

C – rectangle

D – isosceles triangle

E – rhombus

F – trapezium

G – square

H – trapezium

I – right angled triangle

4 X – hexagon

Y – pentagon

Z – octagon

5 circle, semicircle, crescent

6 A, C, D, F and M

B, E and S

G and Q

I, L, R and T

K, O and V

7 Circle correctly drawn and labelled



Exercise 4B1 Name Number of faces Number of edges Number of vertices

Cube 6 12 8

Cuboid 6 12 8

Triangular prism 5 9 6

Sphere 1 0 0

Cone 2 1 1

Square based pyramid 5 8 5

Hexagonal prism 8 18 12

Hemisphere 2 1 0

Cylinder 3 2 0

Triangular pyramid or tetrahedron 4 6 4

2 a i F ii D

b correct nets drawn

3 correct net drawn

4 a square based pyramidb octagonal prism

5 a Correct net drawnb Correct net drawn

c Correct net drawnd Correct net drawn

Exercise 51 a 3

4

b 38

c 45

d 58

e 510

or 12

f 915

or 35

2 a 5b 12c 20d 18e 72f 24g 45h 88i 90j 84k 2l 7m 9n 7o 32p 135

3 a 12

b 35

c 34

d 23

e 78

f 34

g 45

h 45

i 34

j 47

k 79

l 45

m 23

n 34

o 23

p 1013


4 a 16 ,

14 ,

13 ,

38

b 310

,

720

, 25

,

12

c 512

,

715

,

35

, 1320

d 716

,

920

,

35

,

58

5 a 35

b 2127

c 6070

d 416

6 a 15 kg

b £13

c 12

d £12

e 3.4

f £58

g 28 cm

h 27

i £2800

j 21.6 m

k 210 mm

l £660

7 13

8 a 59

b 3 boys

9 29

10 512

11 36 km

12 49

= 52117

613

= 54117

Finn has read most as 54117

is greater than 52117

13 5

Exercise 6 1 a Tens

b Thousands

c Tenths

d Hundreds

e Thousandths

f Tens

g Hundredths

h Units

i Tens of thousands

j Millions

2 a 7.003, 7.06, 7.1, 7.13, 7.3

b 1.118, 1.25, 1.291, 1.3, 1.8

3 a 63.4

b 97

c 218.3

d 745

e 8053

f 960

g 4

h 50

i 6100

j 30.6

k 81.3

l 94

4 a 8.37

b 3.159

c 0.64

d 0.289

e 0.6473

f 0.8

g 1.3

h 0.04

i 0.00617

j 0.05

k 0.0021

l 0.00249

5 a 100

b 10

c 1000

d 1000

e 10

f 100

g 1000

h 100

6 a 35

b 1750

c 920

d 325

e 18

f 225

g 1720

h 81200

i 13100

j 7125

k 1250

l 310000

7 a 0.1

b 0.25

c 0.2

d 0.7

e 0.75

f 0.6

g 0.15

h 0.48

i 0.11

j 0.375

k 0.175

l 0.007

8 a 15

, 0.23, 14

, 0.3

b 25

, 0.403, 0.45, 12

c 0.3, 0.32, 38

, 39100

9 £4.65

10 48 km

11 5.46 seconds

12 28

13 a 15.04

b 5.67

c 1.4

d 0.78

e 27.19

f 4.96

g 31.2


h 2.43

i 4.8

j 2.292

k 0.134

l 8.0549

m 10.389

n 4.791

o 0.169344

p 34.8

14 Yes 58

= 0.625 which is

greater than 0.6

15 125

16 £441.25

17 £5.75

Exercise 7 1 a 1

2

b 710

c 920

d 225

e 825

f 17100

g 13200

h 13

i 157500

j 3500

k 1 15

l 172000

2 a 0.83

b 0.14

c 0.27

d 0.4

e 0.09

f 0.085

g 0.121

h 3.3

i 0.002

j 1.4

k 0.0005

l 0.0394

3 a 71%

b 20%

c 90%

d 75%

e 3%

f 55%

g 52%

h 94%

i 60%

j 65%

k 8.7%

l 37.5%

4 a 75%

b 64%

c 12%

d 40%

e 8%

f 3.6%

g 21.3%

h 72.25%

i 3.75%

j 120%

k 105%

l 2.01%

5

Fraction Decimal Percentage

a310

0.3 30%

b710

0.7 70%

c35

0.6 60%

d925

0.36 36%

e18

0.125 12.5%

f81

2000.405 40.5%

Fraction Decimal Percentage

g11

4000.0275 2.75%

h25

0.4 40%

i625

0.24 24%

j1725

0.68 68%

k1720

0.85 85%

l1920

0.95 95%

m 125

1.4 140%

n 3 12

3.5 350%

6 a 0.4, 41%, 44100

b 57%, 35

, 0.63

c 0.7, 34

, 77%

d 320

, 0.18, 19.5%

7 60%

8 85%

9 86%

10 60%

11 25%

12 a £5

b 72 g

c 60 m

d £840

e 17.5 km

f 130 litres

g £45

h £112

13 a 183.6 m

b £19.88

c 31.72 cm

d £204.18


e 146.2 g

f 346.48 ml

g 165.36

h £106.25

14 a £2.84

b £0.62

c £0.06

d £62.67

e £5.99

f £0.34

g £0.07

h £2.57

15 a 0.4̇

b 0.3̇4̇

c 0.1̇43̇

d 4.3̇7̇

e 0.71̇2̇

f 5.0̇12̇

g 0.03̇19̇

h 3.1̇749̇

16 a 0.333…

b 0.777…

c 0.3999…

d 0.203203203…

e 0.4212121…

f 3.282828…

g 9.172172172…

h 0.093209320932…

17 a 0.3̇

b 0.4̇

c 0.6̇

d 0.7̇

e 0.83̇

f 0.083̇

g 0.26̇

h 0.5̇71428̇

18 59

and 16

19 0.03̇

20 Joy. 23

is 66.6̇% which is bigger

than 66%

Exercise 8 1 1.87 km, 1.9 km, 2.105 km,

2.12 km, 2.8 km, 3.7 km

2 a six tens

b two hundreds

c eight units

d sixty thousands

e five tenths

f three tens

g eight hundredths

h eight units

i three thousandths

j nine tenths

k six thousands

l three thousandths

3 a 8.1

b 16.4

c 27.5

d 8.61

e 4.4

f 3.5

g 5.28

h 5.55

i 33.99

j 4.56

k 8.58

l 8.75

4 a 30

b 4000

c 5000

d 35

e 75

f 2380

g 9860

h 50

i 23 400

j 401.3

k 120

l 8900

5 a 9

b 4.5

c 80

d 2.8

e 8.8

f 2.35

g 0.088

h 0.055

i 0.37

j 0.0028

k 0.0005

l 0.0038

6 a 1.2

b 3.5

c 4.8

d 1.8

e 16.1

f 34.4

g 38.4

h 25.2

i 21.6

j 9.52

k 26.7

l 165.6

7 a 0.6

b 0.8

c 0.53

d 7.4

e 0.56

f 1.28

g 7.83

h 1.77

i 2.4

j 19.25

k 0.652

l 5.24

8 636

9 354

10 1334

11 862.5

12 32.4 km

13 £17.61


Exercise 9A 1 a = 53º

2 b = 120º

3 c = 60º

4 d = 38º e = 104º

5 f = 69.5º g = 69.5º

6 h = 39º i = 141º

7 x = 123º

8 m = 300º

9 w = 129º

10 74º

11 34º obtuse triangle

12 a i x = 15º ii 30º, 105º, 45º b i y = 33º ii 66º

13 a Correct construction b AB and BC are the same

length (5.4 cm)

14 a Correct construction b DE is 6.2 cm and EF is

8.3 cm c 65 º

Exercise 9B 1 a = 67º

2 b = 55º

3 c = 145º

4 143º

5 100º

6 a i x = 40º ii 120º b i y = 50º ii 95º, 110º, 35º, 120º

7 a PMO = 36º, correct reason

b MOP = 54º, correct reason

8 a ABC = 72º b DAB = 108º

9 QRS = 81º

10 a False b False c True d False

11 a EFG = 127º b GIF = 90º

12 square, rhombus, kite

Exercise 10A 1 a corresponding b vertically opposite c alternate d interior

2 a k b m c p d m e o f l

3 a = 124º (alternate)

4 b = 113º (corresponding)

5 c = 95º (vertically opposite) d = 95º (corresponding)

6 e = 45º (straight line) f = 135º (corresponding) g = 135º (vertically opposite)

7 h = 79º i = 101º j = 101º

8 k = 81º m = 81º n = 99º p = 81º

9 a u = 38º v = 38º t = 142º b w = 108º x = 90º y = 108º c q = 63º d x = 127º

Exercise 10B 1 a hexagon b decagon c quadrilateral

2 a a = 149º b = 67º b c = 43º d = 65º e = 108º

3 a 72º b 108º

4 a AOB = 60º b FED = 120º c 720º d 30º

5 10 sides

6 15 sides

7 72 sides

8 150º

9 18º

10 1260º

11 6120º

12 5 sides

13 43 sides

14 157º

15 Can be divided into 2 triangles; 180º + 180º = 360º

16 No. 180º – 155º = 25º. 360 does not divide evenly by 25

Exercise 11 1 a (10, 2)

b (2, 8)c (6, 4)d (0, 5)e (3, 2)f (9, 6)g (5, 7)h (8, 0)i (12, 10)

2

00

1

2

3

4

5A

IG

D K

B

L

F

C

H J

E6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 x

y


3 O (−4, 0) P (2, −2) Q (−2, 2) R (−2, −3) S (−5, −6) T (3, −4) U (0, 6) V (0, −7) W (−4, 6) X (4, 5) Y (5, 0) Z (5, −7)

4

–1–1

1

2

3

4

5

6

O

X

Q

PS

VU

Y W

R T

Z

0

–2

–3

–4

–5

–6

1 2 3 4 5 6–2–3–4–5–6

y

x

5

–1–1

1

2

3

4

5

6

–2

–3

–4

–5

–6

–2–3

(d)

(b)(f )

(a)

(e)

(c)(g)

–4–5–6 654321

y

x

a squareb parallelogramc trapeziumd kitee right-angled trianglef isosceles triangleg rectangle

6 a MAKE HAY WHILE THE SUN SHINES b EARLY BIRD CATCHES THE WORM

Exercise 121 a x + 10

b 10 – yc 8cd d – 4

e w5

f 4m

g 20e

h w2

i xyj 30 + xk 5x

l n3

m 2 – d

2 a x + 5b x – 4 c 3xd 3x + 2

3 a n – 3 b 4n c 4n – 1 d 4n + 5

4 a 9xb 4yc 6xd 11y e 6xf 9x + 8yg 3x + 10yh 7x + 3yi 9x2 j 5x + 8y k 11x + 5yl 2x + 6ym 4yn 5x – 3yo 9x2 + 3xp –3xq 15x – 2yr −3x – 4y – 2y2

5 a 9b 19c 21d 2e 6f 30g 80h 27i 18j 10k 65l 53m 13


n 43o 2p 6q 18r 15s 10t 25u 10v 3.5w 51x 50y 36

6 a 8pb 4mc 15yd 2cte 7w2

f 24d2

g 63efh 60g2

i 16gj h3

k 3hl 6e2f 2

m 22cd2

n 7jo 24x2y2

7 a 10x + 4b 10

8 5n + 2

9 4x + 13y

10 a 26x + 10b 50x + 12x2

Exercise 13A 1 A 6, 8, 122

B 4C 21, 35D 9, 25, 81, 169

2 A 6, 8B 1, 9, 33C 7, 23, 31D 2

3 A 7, 45B 1, 5C 10, 12, 24D 2, 8

4 A 45, 120B 30, 60C 8, 9D 1, 5, 6, 15

5 a 2005b 1990c 44ºCd 230 mm

6 a Fendt 714 Variob Massey Ferguson 6480c 797 kgd John Deere 6930 – It has

the highest power and is lighter than the New Holland 6080

Exercise 13B1 a Does not include a given

time frame e.g. per weekb Does not allow for zero.

Overlap with the numbersc Suitable question and

response section

2 a Question too long. Leading question.

b No response for ‘don’t know’

c Suitable question and response section

3 a Only asked adults. People at the library are more likely to read more.

b Suitable question and response section

c Example of a more neutral venue. Bigger sample size, at least 30

4 a Leading questionb Doesn’t include response

‘disagree’ c Suitable question and

response section

5 a Question too generalb Doesn’t include ‘other’c Suitable question and

response sectiond A mixture of young and

old people and a mixture of male and female.

6 a Suitable question that is easy to interpret and not leading

b Suitable question that is easy to interpret and not leading

c Suitable question that is easy to interpret and not leading

d Suitable question that is easy to interpret and not leading

Exercise 141 a 2

b 6c 12d 12e 35f 7g 24h 3i 3j 31k 9l 20m 342n 49o 28p 207q 22r 1s −5t −3u 0v −4w −12x −9


2

Nearest 10

Nearest 100

Nearest 1000

a 6870 6900 7000

b 1240 1200 1000

c 9370 9400 9000

d 1930 1900 2000

e 780 800 1000

f 12 370 12 400 12 000

g 28 770 28 800 29 000

h 74 500 74 500 75 000

i 370 400 0

j 1110 1100 1000

k 20 090 20 100 20 000

l 19 320 19 300 19 000

m 789 270 789 300 789 000

n 499 690 499 700 500 000

o 999 670 999 700 1 000 000

3 a 3.2b 8.8c 31.1d 11.3e 9.5f 6.2g 21.9h 133.0i 9.5j 2.1k 8.9l 6.0m 58.0n 4.0o 21.1p 0.5q 3.7r 314.9s 90.0t 129.9u 1999.0v 47.0w 0.0x 200.0

4 a 9.83 b 12.64c 2.04d 98.58e 9.02f 8.95

g 12.90h 1.01i 3.96j 92.78k 9.89l 9.90m 172.34n 18.91o 3.23p 78.86q 20.00r 1.90s 50.00t 0.60u 1.85v 0.00w 2.50x 1.24

5 a 2.884b 83.448c 7.909d 1.827e 9.857f 3.885g 0.815h 1.804i 9.990j 12.004k 1.773l 34.293m 8.772n 1.237o 2.337p 0.896q 9.126r 8.040s 0.690t 29.999u 99.400v 1.004w 2.598x 3.000

6 a 2000b 4000c 50 000d 8e 20f 0.01g 0.008

h 0.02i 0.9j 1k 500000l 8000m 20000n 7o 2p 10q 7r 0.001s 0.06t 8u 10v 30w 1x 1

7 a 2400b 3900c 54 000d 8.5e 16f 0.014g 0.0079h 0.018i 0.94j 0.99k 540 000l 8000m 16000n 7.0o 2.0p 13q 7.0r 0.0014s 0.060t 8.0u 14v 27w 1.0x 1.0

8 a 2370b 3870c 53 700d 8.49e 16.3f 0.0143g 0.00792h 0.0184


i 0.942j 0.995k 539000l 8050m 16000n 7.05o 2.01p 13.0q 7.00r 0.00140s 0.0604t 7.99u 14.0v 27.0w 0.996x 1.00

9 a £2.08b £89.34c £128.48d £3.50e £0.70f £7.00

10 a 7.7b 5.2c 2.80d 4.31e 7.416f 24g 16h 154i 2.65j 1.71

11 1.1

12 36 849

13 4

14 7

15 5

16 12

Exercise 15 1 1, 2, 3, 4, 6, 12

2 12, 24, 36, 48, 60

3 2

4 6

5 24

6 70

7 2, 3, 5, 7, 11, 13, 17, 19

8 a 23 × 3b 2 × 32 × 5c 22 × 3 × 52

d 3 × 72

e 3 × 52 × 11f 22 × 3 × 5 × 7g 2 × 3 × 5 × 7 × 11h 23 × 32 × 52

i 22 × 32 × 17j 24 ×32 × 52

k 2 × 53 × 7l 23 × 3 × 37

9 16

10 120

11 24

12 882

13 a Falseb Truec Trued Falsee Truef Falseg Falseh False

14 a 15 bagsb 11 orangesc 14 lemons

15 6th September

16 a 196b 343c 32d 1e 81f 216g 256h 161 051i 1024j 1k 39.304l –32

17 a 52b 22c 40

d 2e 200f 1.25g 0h 25i 17j 29k 8l 25m 8n 7o 5p 8

18 a 29

b 84

c 107

d 56

e 91

f 38

g 612

h 514

i 84

j 11−2

k 48

l 415

m 96

n 86

o 1111

p 53

q 39

r 66

19 a 3b 4c 9d 5e 5f 6g 7h 11

Exercise 16 1 a 9th April 2011

b 4th May 2011c Sunday

2 a 180 secondsb 120 minutesc 30 minutesd 900 seconds


e 210 minutesf 270 seconds g 48 hoursh 56 daysi 168 hours

3 a 3.00 pmb 11.00 pmc 7.30 amd 4.20 pme 1.10 pmf 8.05 pmg 12.00 pm (12 noon) h 10.45 ami 5.40 amj 10.07 pmk 7.04 pml 8.45 am

4 a 0800b 1120c 0351d 1345e 1830f 2359g 1005h 1647i 0205j 1218k 0001l 2338

5 a 10.21 amb 6.10 amc 11.05 amd 1.15 pme 8.44 pmf 12.25 pmg 3.11 amh 11.57 pmi 12.03 amj 5.38 pmk 9.41 aml 7.15 pm

6 9.50 pm

7 2055

8 1425

9 1 hour 5 minutes

10 a 0745b 50 minutesc 1500 (3.00 pm)

11 a 0915b 42 minutesc 0726 (7.26 am)d 0928 (9.28 am)e No

12 45 minutes

Exercise 17 1 a centimetres

b metresc kilometresd metrese millimetresf centimetres

2 a gramsb tonnesc kilogramsd gramse tonnesf milligrams

3 a millilitresb litresc litresd millilitrese litresf millilitres

4 a 300 cmb 6000 mc 70 mmd 5 kme 9 mf 4 cmg 8200 mh 3.5 cmi 1.2 mj 0.6 kmk 24 mml 740 mmm 6070 mn 0.7 cmo 4080 mmp 23.8 mmq 0.77 m

r 190 000 cms 2.8 kmt 7520 mm

5 a 5000 gb 4000 kgc 7 gd 4 kge 2900 kgf 0.4 kgg 4700 mgh 5.9 kgi 0.608 tonnesj 3.935 gk 0.57 kgl 3040 gm 13 000 kgn 0.605 kgo 300 kgp 0.325 gq 0.06 kgr 300 000 mgs 115 000 gt 0.000065 kg

6 a 6000 mlb 2900 mlc 8 litresd 4300 mle 7.2 litresf 10 000 mlg 1.1 litresh 300 mli 1300 mlj 2430 litresk 0.904 litresl 0.055 litresm 12 800 mln 0.321 mlo 0.015 litresp 0.08 litresq 7.63 litresr 35 000 mls 72.5 mlt 0.002 litres

7 2.39 m (239 cm)

8 15

9 a 3.5 cm, 82 mm, 0.3 m, 45 cm


b 0.75 kg, 840 g, 1050 g, 1.3 kgc 270 ml, 45 cl, 0.48 litres,

705 mld 1.99 km, 2098 m, 2.4 km,

3360 m

10 6.85 m (6850 mm)

11 20

12 6

13 2350 g (2.35 kg)

14 a 600 mm2

b 350 mm2

c 50 000 cm2

d 24 000 cm2

e 8 cm2

f 0.7 cm2

g 6 m2

h 4 750 000 mm2

i 30 mm2

j 90 m2

k 100 cm2

l 2 500 000 m2

15 a 1000 mm3

b 2700 mm3

c 6 000 000 cm3

d 800 000 cm3

e 90 cm3

f 1.385 m3

g 40 mm3

h 17 200 000 cm3

i 7 cm3

j 30 000 cm3

k 0.5 m3

l 3400 litres

16 a 60 ml, 12

litre, 800 cm3, 1 m3

b 11000 mm2, 120 cm2, 0.1 m2, 1 m2

Exercise 18 1 mean = 14

2 mode = 6

3 median = 7

4 median = 11.5

5 mean = 51.25 cm

6 a mean = 74.85%b median = 80%c mode = 72%d range = 84%

7 x = 12

8 range = 13

9 mean height = 162.4 cm

10 a correct values givenb correct values givenc correct values givend correct values given

11 a mode = 2b mean = 3.43c median = 3



14 3, 5, 7

15 5, 5, 6, 9, 10

16 a £39024 b £27750 c Median – no mode and

mean distorted by large salary

17 mode with explanation

18 a i 40<m≤50ii 20<m≤30b i 60<v≤70ii 60<v≤70ci 0 – 1ii 4 – 5

19 9A 9B has a higher mean than

9A, but only by 5%9B has a much bigger range

than 9A, 9A is more consistent

Exercise 191 a 1

25

b 214

c 147

d 612

e 523

f 356

g 5910

h 338

i 813

j 429

k 4411

l 735

m 516

n 934

o 847

2 a 72

b 114

c 256

d 149

e 198

f 145

g 223

h 2910

i 236


j 192

k 237

l 254

m 438

n 416

o 499

3 a 5710

b 235

c 125

d 1212

e 314

f 89

100

g 513100

h 6725

i 334

j 11125

k 621

200

l 91320

4 a 7.5b 3.25c 8.9d 6.4e 2.333…f 4.125g 2.15h 5.07i 4.6363…j 7.65k 23.75l 35.1666…

5 a 57

b 118

c 815

d 1112

e 4170

f 1324

g 710

h 1712

i 1635

j 1815

k 17190

l 4144

6 a 35

b 1324

c 940

d 221

e 815

f 2360

g 712

h 740

i 1033

j 1330

k 940

l 552

7 a 115

b 512

c 335

d 25

e 18

f 14

g 118

h 718

i 12

j 12

k 37

l 1

8 a 25

b 516

c 23

d 115

e 258

f 34

g 114

h 115

i 1

j 121

k 24

l 13

9 a 328

m2

b 15

14 metres


10 3 packets

11 5 pints

12 415

13 720

14 a 2536

cm2

b 313

cm

Exercise 20 1 a 8

b 312

c 535

d 256

e 61115

f 635

g 103

10

h 151130

i 512

j 618

k 41724

l 121120

m 5335

n 15340

o 42355

p 1214

2 a 312

b 335

c 537

d 23

10

e 3720

f 2940

g 4536

h 35

24

i 51970

j 51720

k 11730

l 178

m 13144

n 2330

o 23740

p 31718

3 51920 km

4 241

10 tonnes

5 a 4415 kg

b 11115 kg

Exercise 211 a 45

b 84c £384d £26.03e 300 gf 87g £4.00h 1125

2 a £33b £64c 114d £75.52

e £412.50f 27.6 gg 149.04 kgh 698.64 mI £2.37

3 £42

4 £99.20

5 £1512

6 5 light bulbs

7 £54.60

8 38684

9 a 24%b 55%c 75%d 6%e 12.5%f 20%g 6.4%h 14%i 80%j 5.71%

10 85%

11 60%

12 54.8%

13 44%

14 7.5%

15 13.5%

16 7.0%

17 28.3%

18 £96

19 £150

20 £1456

21 £4611.20

22 £14.40

23 £9033.50

Exercise 221 a 1:600

b 1:150c 1:3000d 1:300 000


e 1:40 000f 1:1 200 000g 1:500h 1:40i 1:2500j 1:25 000k 1:30 000l 1:240 000

2 a 0.4 kmb 1.2 kmc 0.35 kmd 2.3 kme 0.21 kmf 0.05 km

3 a 60 kmb 140 kmc 170 kmd 220 kme 44 kmf 66 km

4 Distance on map

Actual distance

a 5.cm 500 m

b 8.cm 800 m

c 7. cm 14 km

d 2.cm 4 km

e 2.5 cm 25 km

f 2..cm 20 km

g 15.cm 7.5 km

h 4.cm 500 m

i 3.4 cm 510 m

j 14.5 cm 290 m

5 a 35 mb 9 kmc 420 miles

6 a Correct rectangle 12 cm by 3 cmb 62 m

7 a Correct triangle base = 6.5 cm and height = 5 cm

b 82 m

8 a Correct trapezium drawnb AB = 20.3 m AD = 18.3 m

9 a i side ii front iii plan

b i side ii front iii plan

c i side ii front iii plan

d i side ii front iii plan

e i side ii front iii plan

Exercise 23A1 a 13

b 11

c

d 65

2 Correct pictogram with key

3 No key, different sizes of objects, no title

4 a 8b 5c 22

5

6 Bars are different widthsNo numbers on the vertical axisNo labels on the horizontal and vertical axesNo title

50

40

30

20

10

Toast PizzaSnack

Number of snacks eaten at break time

Freq

uenc

y

Fruit Scones0


7 Number of days Tally Frequency

0 / / / / / / / 8

1 / / / / / / / / 10

2 / / / / / 6

3 / / / 3

4 / / 2

5 / 1

30

8 a Number of DVDs Tally Frequency

0−4 / / / / / / / 8

5−9 / / / / / / 7

10−14 / / / / / / 7

15−19 / / 2

24

b

9 a 38 marksb 52 marksc 51.68̇1̇ marksd 7

10 No keyNumbers in the leaf are not in order7 is missing from the stem

11 3 2 2 4 5 74 0 1 1 1 85 1 1 2 66 0 5 5 6 97 2 8 98 3 6

Key8 3 = 8.3

12 a 26.5% b 34%

c 31 pupilsd 41%

13

10X 10Y

4 8

9 9 8 8 5 0 1 1 3 7 8 8 9

9 8 8 7 7 6 0 2 4 4 5 6 8

7 7 6 5 2 2 0 7 1 3 3 3 4 4 9

9 8 8 6 6 8 2

9 8 4 1 9

Key8 2 = 82

Exercise 23B1 Pie chart drawn and labelled Water = 72° Orange juice = 108° Milk = 60° Tea = 90° Coffee = 30°

2 Pie chart drawn and labelled Walk = 32° Bicycle = 60° Car = 84° Bus = 160° Train = 24°

3 Pie chart drawn and labelled Swimming = 48° Running = 88° Walking = 120° Cycling = 64° Other = 40°

4 Pie chart drawn and labelled Cow = 120° Sheep = 70° Horse = 10° Pig = 100° Hen = 60°

5 a 60/360 = 1/6 b 16 pupils c 6 pupils

6 a 36/360 = 1/10 b £30

8

7

6

5

4

3

2

1

00–4 5–9

Number of DVDs

Number of DVDs owned by pupils in class 10A

Freq

uenc

y

10–14 15–19


Exercise 24 1 a 7

b 13c 19

2 a 22b 28c 36

3 a 25b 75c 105

4 a 6.5b 7.25c 8.75

5 a 11.4b 12.6c 13.2

6 a 83b 96c 115

7 a 13.3b 14.7c 15.9

8 a 45b 57.5c 72.5

9 a 675b 850c 1025

10 a 220b 250c 290

11 a 506b 512c 516

12 a 30.2b 30.4c 31.2

13 a 8.43b 8.45c 8.49

14 a 6.84b 6.96c 7.02

15 a 9.15b 9.375c 9.525

16 a 0.253b 0.255c 0.258

17 a 3.465b 3.4875c 3.5025

18 a 8.016b 8.022c 8.028

19 a −7.5b −5.75c −4.25

20 a 9.625b 9.65c 9.6875

Exercise 25 1 a −2

b −4c 0d −6e 6f −8g −9h −23i 5j −18k 11l −1m −9n −12o 1p 26q −8r −8s −12t −5u −45v −27w −4x 6

2 a 3b −6

c −6d −2e −28f 12g 4h −12I −14j 4k −13l 4

3 a −12b −30c −28d −18e 24f −20g −35h −55i 35j 56k −48l 16m 24n −30o −8p −18

4 a −5b −6c 6d 7e −32f −12g −4h −5i 6j −7k −7l –0.3m −9n −32o −4p –2.5

5 a −5b −4c −5d −7e −1


f −40g −21h −100i 8j –3.8k −3l −0.5

6 a 6 and –6b 10 and –10c 13 and –13d 1 and –1

7 A negative number multiplied by 10 will give a smaller number e.g. –5 × 10 = –50

8 No; A negative number divided by 2 will give a larger number e.g. –8 ÷ 2 = –4

Exercise 261 a x = 3

b x = 8c x = 5d x = 13e x = 8f x = 19g x = 4h x = 1i x = 8j x = 12k x = 20l x = 9m x = 8n x = 4o x = 18p x = 50q x = 14r x = 4s x = 4t x = 3.5u x = 0v x = 3 1

3

w x = 2 15

x x = 123

2 a x = 4b x = 3c x = 1d x = 2e x = 6f x = 7g x = 3h x = 4i x = 7j x = 0k x = 7l x = 4m x = 7n x = 4

o x = 7 45

p x = 5.5

q x = 4 23

r x = 14

s x = 2 25

t x = 8.5

u x = 56

v x = 3.5w x = 2.5x x = 0.85

3 a x = −3b x = −1c x = −4d x = −2e x = −3f x = −4g x = −6h x = −1i x = −3j x = −4

k x = −2l x = −9m x = −3.5

n x = −1 13

o x = −5

p x = − 14

q x = −2 15

r x = 15

s x = −1 14

t x = − 13

u x = −2 15

v x = −0.5

w x = − 45

x x = − 45

4 a 3 + 6 = 9 incorrectb 17 – 5 = 12 correctc 2(7) + 3 = 17 incorrectd 4(2.5) – 5 = 5 correcte 7 – 10 = –3 incorrect

Exercise 271 a

A x = −4

B y = −7

C x = −2

D y = 2

E x = 1

F y = 5

G x = 4

H y = −5

b i (1, 5)ii (4, 2)iii (−2, 2)iv (−2, −7)


2

–10–1–2–3–4–5–6 2 3 4 5 6

–2

–3

–4

–5

–6

–7

–8

1

2

3

4

5

7

8

x

y

y = 8x = 4x = 1

x = 0

x = –2x = –5

y = 6

y = 3

y = –5

y = –7

1

6

3 a

x 0 1 2 3 4

y 5 6 7 8 9

b

x 0 1 2 3 4

y 3 7 11 15 19

c

x 0 1 2 3 4

y −4 1 6 11 16

d

x 0 1 2 3 4

y 7 10 13 16 19

e

x 0 1 2 3 4

y −6 −4 −2 0 2

f

x 0 1 2 3 4

y 5 3 1 −1 −3

g

x 0 1 2 3 4

y 12 7 2 −3 −8

h

x 0 1 2 3 4

y 0 −1 −2 −3 −4

4a

x −3 −2 −1 0 1 2 3

y 0 1 2 3 4 5 6

b

x −3 −2 −1 0 1 2 3

y −2 0 2 4 6 8 10

c

x −3 −2 −1 0 1 2 3

y −11 −8 −5 −2 1 4 7

d

x −3 −2 −1 0 1 2 3

y −10 −6 −2 2 6 10 14

e

x −3 −2 −1 0 1 2 3

y 14 11 8 5 2 −1 −4

f

x −3 −2 −1 0 1 2 3

y 9 8 7 6 5 4 3

5 a

–1–1–2–3–4–5–6 10 2 3 4 5 6

–2–3–4–5–6–7–8

1

2

3

4

5

6

7

8

x

y

y = –3x

y = x – 2

y = 4 – x y = 2x + 1

b i (−3, −5) ii (3, 1) iii (1, 3) iv (−2, 6)

6 a 3b 5c 6d 4e 1f −2g −3h −1

7 a y = 8xb y = 3xc y = 4x − 1d y = 2 + 6x


8 a 2b 6c 1d −4e −3f ½

Exercise 28A1 a 16°C

b April and Mayc November

2 a i 1800 ii 0900 and 1000b No we can only tell how many customers

were at the service station at 1000 and 1100. We cannot use the graph for times between 1000 and 1100.

3 a

109876543Age (weeks)

Mas

s (k

g)

2100

10

20

30

40

50

60

70

Mass of a calf

80

90

b 75kg

4

FriThurWedTueDay of the week

Pupils absent from school in one week

Num

ber

of p

upils

abs

ent

Mon

10

20

5 a

50 60 70 80 904030Number of days

Height of sunflower

Hei

ght

(cm

)

20100

20

40

60

80

100

120

140

160

180

200

220

b 126 cm c Between 40 and 50 days. There is the greatest

increase in height between 40 and 50.

6 a i 192 km ii 208 km iii 217 km iv 313 kmb 373 kmc 119 km

7 a i 36.8 miles ii 26.6 miles iii 60.7 miles iv 40.0 milesb 144.4 miles

8 a 3 boysb 12 girlsc 14 boysd 23/30

9 a 12 childrenb Channel 4c ITVd BBC 1 because it has the highest number for

adults and children together.


10 a

iphone Nokia Blackberry Samsung Total

Men 5 11 8 16 40

Women 9 8 12 11 40

Total 14 19 20 27 80

b 12 womenc 11 mend 80 people

11 Other pets may be chosen

Cat Dog Rabbit Horse Other

Boys

Girls

Exercise 28B 1 a positive correlation

b no correlationc negative correlation

2 a positive correlationb negative correlationc positive correlationd no correlatione positive correlationf no correlationg positive correlation

3 a

60 70 80 905040Maths result

Scie

nce

resu

lt

30

30

40

50

60

70

80

90

100

b positive correlationc line of best fit drawnd use pupil’s line

4 a

21Engine size (cc)

Ave

rage

fuel

con

sum

ptio

n (m

pg)

10

20

30

40

50

60

b negative correlationc line of best fit drawnd use pupil’s linee use pupil’s linef suitable explanation

5 a

170 180 190160150Height (cm)

Arm

spa

n (c

m)

140

140

150

160

170

180

190

b positive correlationc line of best fit drawnd use pupil’s linee use pupil’s line


6 a

4 5 6 7 8 932Number of books

Hou

rs w

atch

ing

TV

100

2

4

6

8

10

12

14

16

b negative correlationc line of best fit drawnd use pupil’s linee Adult has a lot of free time, is unemployed, or adult’s employment involves reading books

Exercise 28C1 a

Value of x Value of T

1 8

2 13

3 18

4 23

b 4

2 a

Value of x Value of A

1 5

2 8

3 13

4 20

5 29

6 40

b 6

3 a

Value of x Value of y Value of P

1 1 2

2 2 12

3 3 36

b 36

4 a

Value of x Value of y Value of C Value of D

2 2 4 10

3 3 6 18

4 4 8 28

5 5 10 40

b x = 5 and y = 5

5 a

155 160150145140Height (cm)

Heights of pupils in a year 8 class

Freq

uenc

y

135130

2

1

4

3

6

5

8

7

b 23 pupils


6 a

8 10 12 1464Weight (kg)

Weights of turkeysFr

eque

ncy

200

10

20

30

b 64 turkeys

7 a

70 80 906050Time (minutes)

Time to complete a maths challenge

Freq

uenc

y

40300

10

20

30

b 70 peoplec 30 minutes

8 a

20 25 301510Distance (km)

Distances people travel to work

Freq

uenc

y

500

5

10

15

b 0 km (work at home)

9 a

37 383635Weight (g)

Weight of crisps in a packet

Freq

uenc

y

34330

10

20

30

b 50 packetsc Yes with reason e.g. most packets are more

than 35g so customers will be satisfied; No with reason e.g. too many packets are more than 36g meaning loss of profit

10 a, b

4.2 4.4 4.64.03.8Vital lung capacity (litres)

Vital lung capacities of pupils in year 12

Freq

uenc

y

3.63.40

10

20

30girlsboys

c 124 pupils d Boys have a larger vital lung capacity

Exercise 29 1 a

b 1, 3, 6, 10 and 15 c Triangle numbers

2 a

b 1, 4, 9, 16 and 25 c square numbers

3 a

b

Pattern number 1 2 3 4 5 6

Number of matchsticks 3 5 7 9 11 13


4 a

b



5 a

b



6 a 15, 18, 22b 2, 7, 10c 9, 4, −2d 21, 30, 42

7 a add 11b divide by 3c multiply by 3 and add 1d multiply by 4 and subtract 3

8 a 6, 10, 13b 4, 0, −4c 28, 105, 224d 6, 10, 19

Exercise 301 a b2 = a2 + c2

b r2 = p2 + q2

c x2 = y2 + z2

d e2 = d2 + f2

2 a 13 cmb 5 mc 10 mmd 7.81 cme 20.12 cmf 8.06 mg 14.87 mmh 26.57 cmi 5.64 cmj 5.67 kmk 1.53 ml 1.50 km

3 a 12 cmb 15 mc 13.08 cmd 14.66 me 17.66 mmf 2.83 cmg 2.42 mh 33.09 cmi 8.49 kmj 3.82 mk 1.08 ml 60.10 cm

4 a 13.4 cmb 8.1 mc 21 mmd 4.5 me 56.9 cmf 35.4 cm

5 85.96 m

6 No. 52 + 122 = 169 and 169 = 13

7 6.5 m

8 25 cm

9 155.52 cm2

10 16 m

11 50 cm

Exercise 31 1 a 054º

b 150ºc 200ºd 165º


e 124ºf 320ºg 100ºh 072ºi 346º

2 a 234ºb 330ºc 020ºd 345ºe 304ºf 140ºg 280ºh 252ºi 166º

3 223º

4 341º

5 055º

6 a Correct constructionb Correct constructionc Correct constructiond Correct construction

7 a 068º (±2º)b 225º (±2º)c 334º (±2º)

8 a Correct diagramb 4.7 cm

9 a Correct diagramb i 4.8 km ii 321º

Exercise 32A1 a 26 cm

b 36 mc 24 mmd 66 cme 160 mmf 24 mg 17 mh 7.3 cmi 14.4 cmj 44 mm (4.4 cm)k 13.9 ml 38 m

2 5 cm

3 7 cm

4 16 cm

5 12 cm

6 21 cm and 21 cm or 30 cm and 12 cm

7 a 40 cm2

b 54 m2

c 144 cm2

d 77 mm2

e 442 m2

f 7.68 cm2

8 121 cm2

9 24 mm2

10 400 m2

11 25.2 mm2

12 12.6 cm2 (1260 mm2)

13 a 30 cm2

b 42 m2

c 18 m2

d 12 mm2

e 6.4 m2

f 270 cm2

g 58.5 cm2

h 30 mm2

I 165 cm2

14 48 cm2

15 85 m2

16 7.5 cm2

17 380 mm2

18 7.2 cm2

19 5 cm

20 Correct rectangles e. g (18 × 1) or (9 × 2) or (6 × 3) or (4.5 × 4) or (36 × 0.5)

21 8 cm

22 24 m

23 5 cm

24 49 cm2

25 correct rectangles

Exercise 32B 1 a 400 cm3

b 729 m3

c 360 cm3

d 84 mm3

2 a 120 cm3

b 240 mm3

c 45 m3

d 96 cm3 (96 000 mm3) e 0.27 m3 (270 000 cm3)

3 8 cm3

4 1728 mm3

5 32.768 m3

6 10 cm

7 5 cm

8 24 m

9 4 cm

10 Correct cuboids e. g (2×3×10), (1×3×20), (3×4×5), (1×5×12), (2×2×15), (1×1×60)

11 a 360 cm3

b 280 m3

Exercise 331 a 3x + 6

b 5y + 20c 2t + 10d 30 + 6pe 12 + 4xf 27 + 9vg 12x + 20h 10 + 10ni 4e + 8fj 20x + 30wk 15g + 10hl 21a + 35b


2 a 4x – 12b 5d – 10c 3y – 9d 30 – 5te 18 – 9xf 55 – 11pg 6x – 4h 8g – 4i 28v – 63j 18 – 12xk 48x – 42yl 10w – 15e

3 a −2x – 6b –4y – 8c –5m – 5cd −3t – 6ye –16f – 24gf −30x – 36yg –2t + 8h –9a + 27i –3v + 21j –20 + 15wk –77x + 88yl –12m + 54n

4 a x2 + 4xb y2 + 5yc m2 + 3md 3e − e2

e t2 – 4tf a2 – 5ag xy + x2

h 9m − m2

i c2 + cdj 5d − d2

k x3 + 4xl w2 – 2nw

5 a 8x + 10b 9x + 12c 3x + 7d 7y + 6e 7y + 10f 5y + 16g 7c + 4h 7d

i 6m + 6j 8e – 19k 10x + 19l 23a − 39m 3x + 6n –2x – 10o 10x +7yp 11x – 13yq 2x – 8yr 7ts m2 –3m − 4t 2xu 13y – 2y2

v 7x + 7yw 4x – y – cx ab + 4ac + 3b

6 a 12x + 20b 10a2 – 6a

Exercise 341 a i 19, 22

ii Add 3b i 80, 160 ii Multiply by 2c i 6, 0 ii Subtract 6d i 64, 75 ii Add 11e i 5, 0.5 ii Divide by 10f i 22, 17 ii Subtract 5g i 480 000, 9 600 000 ii Multiply by 20h i 1, 1.2 ii Add 0.2

2 a i 29 and 21 ii Subtract 4b i 27 and 43 ii Add 8c i 1 and 27 ii Multiply by 3d i 6, 48 and 192 ii Multiply by 2


e i 45, 30 and 0 ii Subtract 15f i 0.8 and 8 ii Multiply by 10g i 0.8 and 1.04 ii Add 0.08h i 1000 and 62.5 ii Divide by 2

3 a 6, 16, 26, 36, 46 b 40, 34, 28, 22, 16c 11, 22, 44, 88, 176d 1200, 600, 300, 150, 75e 3.6, 3.8, 4, 4.2, 4.4f 3, 7, 15, 31, 63 g 2, 10, 26, 58, 122h 10, 15, 30, 75, 210i 40, 24, 16, 12, 10j 1, 8, 50, 302, 1814

4 a 22b 7c 42

5 a 18b 9c 102

Exercise 35A1 a – f

(a)

(c)

(e) (f )

(d)

(b)

2 a – g(a)

(c)

(e)

(g)

(f )

(d)

(b)

3 a – c (a)

(c)

(b)

4 a rotational symmetry order 4b rotational symmetry order 2c rotational symmetry order 4d rotational symmetry order 2e does not have rotational symmetryf rotational symmetry order 2g does not have rotational symmetryh rotational symmetry order 2i rotational symmetry order 2j rotational symmetry order 3


k rotational symmetry order 2l does not have rotational symmetrym rotational symmetry order 2n rotational symmetry order 4

5 a – b (a) (b)

6 a equilateral triangleb rectangle, rhombusc regular pentagond parallelograme regular octagon

Exercise 35B1

–1–1

1

2

3

4

5

6

–2

–3

–4

–5

–6

–2–3

A

C

B

–4–5–6 654321

y

x

2

–1–1

1

2

3

4

5

6

–2

–3

–4

–5

–6

–2–3

D

E

F

–4–5–6 6

y = 1

x = –1

54321

y

x

3

–1–1–2–3–4–5–6 10 2 3 4 5 6

–2

–3

–4

–6

–7

–8

1

2

3

4

5

6

7

8

x

y

IG

H

y = –2

x = –1

–5

4 a reflection in y = 4b reflection in the x axisc reflection in x = 2d reflection in y = 5e reflection in x = −2f reflection in the x axisg reflection in x = −3h reflection in x = 1i reflection in y = 4½

Exercise 35C1

–1–1

1

2

3

4

5

6

–2

–3

–4

–5

–6

–2–3

A

B

C

–4–5–6 654321

y

x


2

–1–1

1

2

3

4

5

6

–2

–3

–4

–5

–6

–2–3

D

E

F

–4–5–6 654321

y

x

3

–1–1

1

2

3

4

5

6

–2

–3

–4

–5

–6

–2–3

G

H

I

–4–5–6 654321

y

x

4 a rotation 90° clockwise about (0, 0)b rotation 90° anticlockwise about (0, 0)c rotation 90° clockwise about (2, 1)d rotation 180° about (0, 0)e rotation 180° about (1, 0)f rotation 90° anticlockwise about (0, 2)g rotation 90° anticlockwise about (0, −2)h rotation 90° clockwise about (3, 3)

Exercise 35D1 a 2 right and 3 up

b 5 right and 4 downc 6 upd 5 left and 2 upe 5 rightf 3 left and 1 down

2 a 3

5

b −−

4

4

c 1

5−

d 9

0

e 0

6−

f 15

10−

g −

13

11

h 0

7

i −

24

0

3

–1–1–2–3–4–5–6 1 2 3 4 5 6

–2

–3

–4

–5

–6

–7

1

2

3

4

5

6

7

y

7 x–7

D

F

H

B

G

C

T

A

E

4

A to B, 3 right and 1 up, 3

1

A to C, 6 left and 5 down, −−

6

5

A to D, 6 left and 4 up, −

6

4

A to E, 2 right and 5 down, 2

5−

A to F, 3 up, 0

3

A to G, 7 left and 1 down, −−

7

1

A to H, 1 left and 6 down, −−

1

6

A to I, 4 left, −

4

0

A to J, 3 right and 2 down, 3

2−


Exercise 35E1

–1–1

1

2

3

4

5

6

–2

–3

–4

–5

–6

–2–3

A

B

C

–4–5–6 654321

y

x

D

2

–1–1–2–3–4–5–6 1 2 3 4 5 6

–2

–3

–4

–5

–6

–7

1

2

3

4

5

6

7

y

7 x–7

C

B

A

3

–1–1

1

2

3

4

5

6

–2

–3

–4

–5

–6

–2–3

F

G

E

–4–5–6 654321

y

x

4 a enlargement, scale factor 2, centre of enlargement (−6, 2)

b enlargement, scale factor 3, centre of enlargement (−5, 0)

c enlargement, scale factor 4, centre of enlargement (−4, 3)

d enlargement, scale factor 2, centre of enlargement (0, 5)

Exercise 35F1 a translation

12

b rotation 90° clockwise about (0, 0)c reflection in y axisd enlargement, scale factor 2, centre (−4, 5)e reflection in y = 2

f translation −

5

0g rotation 180° about (0, 0)

h translation −

16

i rotation 90° anticlockwise about (2, 2)j enlargement, scale factor 2, centre (−4, 0)

2 a translation 42

b reflection in x axisc rotation 90° clockwise about (−4, 0)d reflection in x = 1e enlargement, scale factor 2, centre (−1, −6)f reflection in y = −3g rotation 180° about (0, −1)

h translation −

62

Exercise 361 a 2(w + 5)

b 3(m + 4)c 5(y – 4)d 2(e – 7)e 3(2m + 1)f 5(3d + 4)g 6(5g – 2)h 4(4i – 5)i 9(2n + 3)j 6(1 – 4c)k 10(2i + 3f)l 7(x + 3y)m 9(m – 4n)n 6(2e +3g)o 4(10j +9k)p 8(p – 2q)q 7(3h – 4e)r 4(t + 8k)


s 12(5i – m)t 15(2w + e)u 15(3x – 2y)

2 a x(5 + y)b e(4 – t)c g(2 – n)d i(10 + m)e h(1 + x)f w(3 – c)g y(y + 1)h e(e + 3)i h(1 – h)j x(1 + 5x)k w(1 + 2n)l c(5 – c)m m(1 + m2)n d(7d – 3)o e(5e – 4h)p f(6g – 5)q x(3y + 5e)r x(8x – 5t)s k(2m – 3k)t b(7c – 4b)u c(ab + de)

3 a 3x(e + 2y)b 5w(3c – d)c 4e(2y +3)d 2m(3c +5)e 5y(2e + 5)f 3h(3y – 4)g 10i(2x – 3)h 4x(2y + 1)i 5c(4d – 1)j 7e(1 – 2y)k 3d(d + 3y)l 2y(3x + y)m 6m(2f – m)n 5x(3x +2y)o 8n(2n – e)p 10i(3y – 4i)q 4e(e2 – n)r 3x(2y – x2)s 2w(5c + 4w – 3)t 5x(2x + y – 3x2)u 4b(2a + 3b – c)

Exercise 37A1 a 18.84 cm

b 87.92 cmc 23.55 md 71.592 m

2 a 65. 97 cmb 54.04 mmc 135.09 cmd 270.18 cm

3 a 12 cmb 37.7 cm

4 a 5.5 cmb 34.6 cm

5 12.73 cm

6 10.35 cm

7 a 61.68 cmb 57.12 cmc 55.12 cmd 107.38 cm

8 1.885 km

9 63 complete revolutions

Exercise 37B1 a 113.04 cm2

b 19.625 m2

c 153.86 cm2

d 102.0186 m2

2 a 254.47 cm2

b 10.18 mm2

c 176.71 cm2

d 10.64 m2

3 200.96 cm2

4 132.67 m2

5 4.3 cm

6 8.56 cm

7 6.6 cm

8 a 508.68 cm2

b 153.86 cm2

c 131.5034 m2

d 169.25 cm2

e 146.98 cm2

9 a 69.5 cm2

b 45.87 cm2

c 100.48 cm2

d 292.805 cm2

e 113.04 cm2

Exercise 37C 1 a 16 cm b 50.3 cm c 201.1 cm2

2 a 12.5 cm b 78.5 cm c 490.9 cm2

3 20.4 cm2

4 34 cm

5 24.3 cm

6 44.1 m

7 336.2 cm2

8 a 226.08 cm3

b 235.5 cm3

c 2797.74 cm3

d 28.26 m3

9 404.1 cm3

10 a 6.908 litres b 12.717 litres c 74.2924 litres

11 7.96 cm

12 9.92 cm

13 3.24 cm

14 29.84 cm

15 9.26 cm

16 5.6 times bigger (1 d.p.)

17 80 full tanker loads

Exercise 38 1 a 5:3 b 3:5 c 4:5 d 5:3:4 e 4:3:5


2 a 1:2 b 3:2 c 3:4 d 3:2 e 5:6 f 7:10 g 4:5 h 4:5 i 6:1 j 40:43 k 4:7 l 3:6:5

3 a 1:15 b 1:9 c 5:1 d 3:20 e 25:4 f 2:3 g 3:7 h 24:5 i 30:1 j 4:3 k 5:3 l 50:1

4 a 8:20 b 30:48 c 42:49 d 54:60 e 16:24:56 f 15:35:40 g 2:7:9 and 18:63:81 h 1:5:12 and 6:30:72

5 16 males

6 160 g

7 2304 cm2

8 a 40 ml b 180 ml

9 £136

10 390 ml

11 24 sweets

12 a 59

b 49

13 a 18

b

78

14 a 512

b 13

15 1:3

16 3:2

17 3:4

Exercise 39A 1 a x = 3

b y = 12c d = 4d x = 16e c = 6f m = 5g g = 3h h = 4i x = 8j c = 3k y = −5l d = −3m x = −7n e = −10o x = 3

12

p h = 59

q w = −3

r t = 323

s m = −123

t x = − 45

u y = −312

v x = 37

w x = 0

x p = 25

2 a x = 8b m = 35c c = 32d w = 24e d = 100

f y = 16g x = 30h e = 24i h = 12j x = 6k t = 28l c = −30m n = −12n r = −8o t = −24p x = −15q y = −32r d = −14s t = 21t b = −45u c = 12v x = 120w x = 0x p = −45

3 a x = 3b x = −2c x = −3d x = 3e x = 1f x = 2g x = 7h x = 3i x = 4j x = 15k x = −10l x = 4m x = −40n x = 40o x = −2p x = 3q x = 24r x = 3s x = 35t x = 6u x = 30v x = 5w x = 12x x = −1

4 a x = 3b y = 7c w = 10d m = 1e e = 2


f g = 3g x = 7.5

h d = 323

i n = 115

j t = 1

38

k c = 14

l y = 13

m x = −1n m = −3o w = −4p p = 0

q y = − 12

r x = −2s t = 10t x = 3u x = 2v x = 6w x = 1x x = 3

5 a x = 6b y = 8c m = 5d e = 4e t = 10f d = 3g f = 2h w = 2i t = 4j y = 3k c = 4l x = 3m h = −7n y = −6o a = −2p x = 2q y = 1r c = 4s d = 2t x = 10u t = −1v y = 2w b = −2x g = 4

13

6 a x = 5b x = 2c y = 10d d = 2e h = 10f w = 3g x = 2h t = 3i d = 1

j c = 112

k m = 30l y = −22m m = −30n y =

1

14

o t = 4p p = 4q g = 1r x = 3

s x = 13

t x = −223

u x = −125

v x = 1w x = 1

x x = 112

7 a always trueb sometimes truec never trued sometimes truee never truef sometimes trueg always trueh sometimes true

Exercise 39B1 a 2x + 40 = 180 x = 70º

b 4x + 140 = 360 x = 55ºc 5x + 15 = 180 x = 33ºd 3x – 12 = x + 6 x = 9ºe 4x + 100 = 360 x = 65ºf 2x + 38 = 180 x = 71º

2 4x + 8 = 56 x = 12

3 3x + 3.20 = 15.20 x = 4

4 2x – 10 = 130 x = 70 pence

5 5x – 3 = 27 Biggest field is 12 acres

6 3x + 6 = 201 Kyle’s mass is 73 kg

Exercise 39C1 a x = 3.2

b x = 5.4c x = 4.3d x = 1.8e x = 2.7

2 a x = 5.18b x = 4.41c x = 9.63d x = 4.72e x = 5.71

Exercise 401 a Yes. Valid reason

b No. Valid reasonc Yes. Valid reasond Yes. Valid reasone Yes. Valid reasonf No. Valid reasong Yes. Valid reasonh No. Valid reasoni No. Valid reasonj Yes. Valid reason

2 x = 8 cm

3 y = 15 cm

4 d = 4 cm and e = 15 cm

5 x = 12.5 cm

6 m = 12 cm

7 a Trueb Falsec Trued Falsee Truef False

8 a No. Corresponding sides are not in the same ratio.

b No. Corresponding angles are not equal.

c Yes. Corresponding sides are in the same ratio 1:2 and corresponding angles are equal.


Exercise 41A 1 a i £2.40 ii £6 iii £12 iv £8.40

b 11 ice-creams

2 a i £105 ii £255 iii £90

b 6 hours

3 a £70b £40c £60d £65

4 a £204.20b £254.60c £179

5 a i 2 hours 45 minutes ii 6 hours 30 minutes iii 4 hours 15 minutes iv 3 hours 52 minutes

30 secondsb 4 pounds

6 C = 75x

7 C = 3.5y

8 C = 25x + 30y

9 W = 4m + 6n

10 a P = 6.8H + 0.4Mb i £63.20

ii £40.80c 35 hours

Exercise 41B 1 T = 12

2 W = 13

3 D = 34

4 H = 24

5 L = 22

6 A = 27

7 C = 28

8 Y = 3

9 E = 10

10 y = 4

11 A = 9

12 T = 12

13 C = −20

14 W = 1

15 B = 13

16 F = −8

17 M = 40

18 A = −6

19 N = −4

20 C = 4

21 a equationb expressionc formulad expressione equationf formulag equationh formulai expressionj formulak expressionl equation

22 a always evenb could be odd or evenc always oddd always evene could be odd or evenf always eveng always oddh could be odd or even

Exercise 41C 1 a x = y – 4

b x = w – tc x = 12y + 4d x = m + 2pe x = 2y – 3f x = 2t – 9c

g x = q3

h x = 47m

i x = 34y

j x = yw

k x = zy

l x = 3wt

m x = 4wn x = pqo x = 3mwp x = 6wtq x = 2d – 7c

r x = 118

g

s x = 7k – 8h

t x = e fab

2 a x = ghb x = 3 + hc x = c – h

d x = wh

e x = w – 5f x = gh + d

g x = p3

h x = 7cdi x = ef + cj x = jk – t

k x = fgk

l x = 8mym x = kp – t – d

n x = w ka+

2

o x = a – 2b – 3w

p x = dm

y3

3 a x = w y−2

b x = m −12

c x = t + 23

d x = e −54

e x = n + 410

f x = c y−2

g x = m d+4

h x = w k−6


i x = 25

t g+

j x = 43e

k x = 132m

l x = n7

m x = 54y

n x = g tn−

o x = m ye+ 2

p x = 4e – dq x = 5d + c

r x = 32

h y+

s x = 4I nk−

t x = 2(m – 3)u x = 3(e + n)v x = 5(c – t)w x = w(d + 5)x x = gh(D−y)

4 a x = 3 – yb x = c – yc x = 8 – 3pd x = t − ghe x = 5 – tf x = n – 4g x = 5y – wh x = 9wi x = 3 – dj x = m2 – y

k x = m t−2

l x = e d−4

m x = L k−3

n x = −35y

o x = 4(m – 3)p c = 5(d−C)q x = h – 4gr x = n – cI

s x = 3 52

− ed

t x = h tyg−

5 a x = e n−3

3

b x = c + 10

5

c x = d −124

d x = m j−217

e x = i hh

−2

f x = t mm

+ 3

g x = 33

n y−

h x = 105− g

i x = 44

t w−

j x = 3i fi−

k x = km Lk−

l x = m t+ 36

m x = wy dw−3

n x = 3 53

f t−

o x = 3 23

p −

p x = 2 32

y d−

Exercise 421 a (2, 4)

b (5, 6)c (2, 8)d (2, 7)

e (7, 7 12

)

f (1, 2)g (−2, 3)h (−1, −1)i (−6, 0)

j ( 5 12

, 3 12

)

k (2, −2 12

)

l ( 2 12 , −2 1

2)

2 a (2, 2)b (1, 0)c (3, −1)d (3, −1)e (1, 4)f (0, 6)g (1, −4)h (−1, −6)

3 a 10b 5c 13d 9.22e 8.06f 9.49g 7.81h 12.81i 18.38j 7.21k 14.87l 7.81

4 a ( 12

, 5 12

)

b 7.616

5 a (7, − 12

)b 6.4

6 LN = 8.94

Exercise 431 metres, centimetres

2 yards, inches

3 grams, tonnes

4 stones, pounds

5 litres, millilitres

6 pints gallons

7 a metres b kilograms c millilitres d grams


e millimetres f litres

8 a milesb poundsc gallonsd yards or feete gallonsf stones or pounds

9 a 13.2 lbsb 5.5 lbsc 10 kgd 3.64 kge 32 kmf 19.2 kmg 40 milesh 62.5 milesi 28 pintsj 5.25 pintsk 8 litresl 17.14 litresm 30 kgn 112 kmo 10.5 pintsp 41.8 lbsq 4800 metresr 800 metres

10 27 litres

11 10 cm

12 2.4 oz

13 160 km

14 17.5 pints

15 64 km/hr

16 152 km

17 300 g

Exercise 44 1 a 23, 28 (add 5)

b 64, 128 (multiply by 2)c 28, 25 (subtract 3)d 34, 40 (add 6)e 7000, 70000

(multiply by 10)f 2, −3 (subtract 5)

g 7.6, 8 (add 0.4)h 6, 3 (divide by 2)

2 a 3,6,9,12,15b 3,5,7,9,11c 2,6,10,14,18d 4, 9, 14, 19, 24e –2,−4,−6,−8,−10f −2, −5, −8, −11, −14g 5, 4, 3, 2, 1h 17, 14, 11, 8, 5i 1, 4, 9, 16, 25j 4, 7, 12, 19, 28k 1, 8, 27, 64, 125l 60, 30, 20, 15, 12

m 12

, 1, 1 12

, 2, 2 12

n 12

, 23

, 34

, 45

, 56

o 1, 12

, 13

, 14

, 15

3 a i 10th term = 20 ii 50th term = 100b i 10th term = 20 ii 50th term = 140c i 10th term = 41 ii 50th term = 201d i 10th term = 10 ii 50th term = −30e i 10th term = −30 ii 50th term = −150f i 10th term = −5 ii 50th term = −85g i 10th term = 100 ii 50th term = 2500h i 10th term = 1

10

ii 50th term = 12

i i 10th term = 10 ii 50th term = 2

4 a 5nb 2n + 3c 4n +1d 3n – 1e 5n – 2f 10n + 3g n + 5


h 6n + 2i 4n – 3j 2n + 5k –3nl –10nm 10 – 2nn 9 – 3no 2 – 5np –1 – 2nq 6 – nr n – 8

5 a

Pattern 4 Pattern 5b

Pattern number

1 2 3 4 5

Number of matchsticks

4 7 10 13 16

c 31d 16e No. 3n + 1 = 80 3n = 79 n = 79

3 79 does not divide exactly by 3 and n must be

a whole number

6 a

b

Pattern number 1 2 3 4

Number of black tiles 1 1 1 1

Number of white tiles 4 8 12 16

Total number of tiles 5 9 13 17

c i 4n ii 4n + 1d 11e 13f 24

7 a

b

Pattern number 1 2 3 4

Number of tables 1 2 3 4

Numbers of chairs 6 10 14 18

c 4t + 2d 7e 12

Exercise 45A1 a 90

b 400c 2100d 2e 37f 27g 19.2h 0.14i 16j 40k 360 000l 766m 0.7n 1060.8o 8000p 400q 0.64r 590s 720t 160u 1600v 2020.4w 40x 270

2 a 70b 30c 10d 50e 700f 30g 400


h 200i 240j 500k 6l 80

3 £50 000

4 2400 litres

5 80 000 light bulbs

6 £1400

7 5 boxes

8 60 miles per gallon

9 £1400

10 a £56b £240c £3200

11 4400

12 a 40 000 m2

b 800 m

13 Accept appropriate estimates.a 5.1b 6.9c 5.5d 10.2e 4.2f 12.4g 7.3h 11.2i 8.8j 14.1

Exercise 45B 1 a 149 – 56 = 93

b 97 + 186 = 283c 1495 ÷ 23 = 65d 25 × 64 = 1600e 62.23 ÷ 6.35 = 9.8f 812 25. = 28.5g 84 × 28.5 = 2394

2 a 10 320b 120c 10.32d 860

3 a 399 b 142.5 c 28 d 3.99

4 a 3.375 b 202500 c 2.025 d 600

5 a 0.32 b 0.18 c 0.3 d 0.06 e 0.04 f 2.4 g 6.3 h 6.6 i 11.5 j 9.1 k 55.8 l 48 m 28.8 n 34.8 o 44.1 p 86.4

6 a 60 b 50 c 170 d 90 e 400 f 500 g 6 h 250 i 540 j 145 k 3640 l 482 m 187.6 n 10.5 o 10.85 p 35.8

7 No. e.g. 0.1 × 5 = 0.5 (0.5 is smaller than 5)

8 a 95 b 104

c 475d 624

9 a 750b 849

10 Minimum height = 95.5 cm Maximum height = 96.5 cm

11 Minimum dimensions 7.5 m by 4.5 m. Maximum dimensions 8.5 m by 5.5 m

12 a 32

b 5

c 18

d 110

e 54

f 34

g 49

h 314

i 52

j 57

k 423

l 100301

13 0

14 a 16

b 83

c 56

d 1041

e 2067

f −5

Exercise 46A 1 a 13

b 14 c 11 d 3


e 15f 6g 15h 10i 23j 20k 12l 10m 11n 52o 48p 13q 10r 8s 0t 46u 8v 40w 30x 14

2 a 18b 9c 6d 5e 30f 35g 7h 20i 7j 7k 4l 18m 14n 6o −12p −5q −21r 2s 17t 32u 11v 5w 14x 112

3 a 25b 64c 46d 44

e 54f 32g 33h 23i 100j 64k 162l 32m 100n 48o 25p 5q 36r 31s 5t 75u 324v 12w −7x 16

4 a 27b 16c 20d 8e 7f 12g 23h 12i 3j 9k 27l 225m 21n 32o 137p 28q 37r −3s −15t 33u 23v 13w −77x 0

5 a 8 × (7 – 4) = 24b 20 ÷ (2 + 3) = 4c (3 + 4) × 2 = 14d (10 – 4) × 3 = 18

e 10 – (3 + 7) = 0f 6 × (1 + 4) = 30g (2 + 3) × (6 – 1) = 25h 3 × (2 + 1) × 2 = 18i 6 + 8 × (7 – 4) = 30j (12 + 6) ÷ (5 – 2) = 6k (11 – 4) × (3 + 2) = 35l (6 – 2)2 × 3 = 48

6 a 2b 3c 6d 21e 4f 4g 24h 1i 7j 4k 3l 3

Exercise 46B1 a x6

b x14

c x6

d w13

e k16

f h23

2 a y6

b y9

c y5

d g7

e x9

f x −3

3 a y12 b y14 c y25 d x18 e m55 f t0

4 a x16

b y −3

c y7

d n56

e x9

f y7

g m6


h m8

i m −2

j m8

k m9

l m7

m y4

n y15

o m3

Exercise 47 1 a £7.60

b £45.60

2 £37.80

3 a £482 b £102

4 £1432

5 £136

6 6 hours

7 £1140

8 a £6000 b £24 000

9 £21 600

10 a €14.16 b €354 c €80.83 d £200 e £35 f £52.54 g £83.05

11 a $1825.68b $684.63c $179.53d £5000e £45 000f £354.94g £36.99

12 a €27.36b £263.16c $317.50d €982.68e $608.08f £884.10g £1381.41 Yes they can

afford the painting

13 a 1345 unitsb £175.93c £8.80d £184.73

14 a £18.81b £29.19drc £487.54drd £970.80e £2470.80

Exercise 48A 1 a

C

A B5 cm

40°

6 cm

b 3.9 cm

2 a

7 cm

5 cm

60°P Q

R

b 6.2 cm

3 a N

L M6 cm

70° 60°

b 6.8 cm

4 a F

D E65° 50°

b 4 cm c 3.4 cm

5 a I

G H6 cm

7 cm 7 cm

b 65º

6 a

X Y5 cm

8 cm

Z

6 cm

b 39º

7 a A B

C6 cm

4 cm

D

b 56º


8 a P Q

S R8 cm

5 cm

40°

b 7.8 cm

9 a

5 cm

5 cm

b 9.2 cm

10 a

6 cm

6 cm

b 6.6 cm

Exercise 48B

1 a A B

b 3.5 cm

2

3

DC T

4

R

P

Q

5 P

X Y

6

7

8

9

A3 cm

10 A B

4 cm 2 cm

11 3.5 cm

12

2 cm

3 cm

A D

B C

6 cm

13

5 cm

6 cm

3 cm

B

A C

14

4 cm

W X

Z Y5 cm

15

7 cm4 cm

8 cm

3 cmA

D

B

C

Shed

Exercise 49 1 a £4, £16

b £15, £3c £8, £20d £27, £63e £70, £50f £800, £2200g £6, £12, £24 h £40, £60, £140

2 £24

3 108º

4 12 sweets

5 45º, 90º, 90º, 135º

6 54 p

7 £5.85


8 48 minutes

9 21 minutes

10 375 g plain flour, 5 eggs, 50 g sugar, 600 ml buttermilk

11 1000 g mince steak, 750 g tinned tomatoes, 2 1

2onions,

1500 ml cheese sauce

12 a 8 oranges (38 p per orange)

b 3 litres of milk (57 p per litre)

c 60 minutes (2.6 p per minute)

d 500 g of butter (0.44 p per gram)

Exercise 50A 1 a x < 4

b y > 2c m 8d t > −5e w < −6f c 10

2 a x = 1, 2, 3, 4b x = 0, 1, 2, 3c x = 3, 4d x = 2, 3e x = 3, 4, 5, 6f x = −2, −1, 0, 1g x = −5, −4, −3, −2, −1

h x = −7, −6i x = −3, −2j x = −5k x = 4, 5l x = 5

3 a x = 1, 2b x = 2, 3, 4, 5c x = −3, −2, −1d x = −6, −5, −4, −3e x = 4, 5f x = 2, 3, 4, 5, 6g x = −2, −1, 0, 1h x = −2i x = −4, −3, −2, −1, 0, 1, 2

4 a x > 0b x 10c x < 0d x > 10e x −4f x −5g x > 5h x < 4i x 4j x > 18k x 16l x −40m x > 4n x 5o x 5p x < 2 2

3

q x > 2 23

r x 1 15

s x > 8 12

t x 4u x < 7v x 4w x > 3x x < 1y x > 9z x − 3

4

5 a 2 < x < 6b 2 x 8c 1 < x 3d 3 < x < 5 1

2e − 1

4 < x 2

f 23

< x < 3 13

g 1 25

x < 4

h 56

x 2

i − 34

x 0

Exercise 50B 1 a x > 3

b x < 1c x > −2d x −2e 1 x 4f 2 < x < 5g −1 x < 3h −2 < x 2


2 a −3−4 −2 −1 0 1 2 3 4

b −3−4 −2 −1 0 1 2 3 4

c −3−4 −2 −1 0 1 2 3 4

d −3−4 −2 −1 0 1 2 3 4

e −3−4 −2 −1 0 1 2 3 4

f −3−4 −2 −1 0 1 2 3 4

3 a x 4 −3−4 −2 −1 0 1 2 3 4 5 6

b x < 1 −3−4 −2 −1 0 1 2 3 4 5 6

c −2 x < 4 −3−4 −2 −1 0 1 2 3 4 5 6

d −3 < x 2 −3−4 −2 −1 0 1 2 3 4 5 6

e x 4 −3−4 −2 −1 0 1 2 3 4

f x > −2 −3−4 −2 −1 0 1 2 3 4 5 6

4 a x = 0, 1, 2, 3, 4 −1 0 1 2 3 4 5

b x = −2, −1 −3 −2 −1 0 1 2 3

c x = 1, 2, 3 −2 −1 0 1 2 3 4

d x = 0, 1, 2 −2 −1 0 1 2 3 4

e x = 2, 3, 4, 5 −1 0 1 2 3 4 5 6

f x = 3, 4 −1 0 1 2 3 4 5


Exercise 511 a

Number of duck eggs 1 2 3 4 5

Cost (pence) 30 60 90 120 150

b

0

30

60

90

Pric

e (p

ence

)

Number of duck eggs

Cost of duck eggs

120

1 2 3 4 5

150

180

c 540 pence or £5.40

2 a Number of days 1 2 3 4 5

Cost (£) 75 100 125 150 175

b

0

25

50

75

Cos

t in

(£)

Number of days

Cost of hiring a car

100

1 2 3 4 5

125

150

175

6 7

3 a

Pounds (£) 1 2 3 4 5

Thai Baht 40 80 120 160 200

b

0

40

80

120

Tha

i Bah

t (T

HB

)

Pounds (£)

Conversion graph for£ and THB

160

1 2 3 4 5

200

240

6 7

c i £2.50 ii 440 THB iii 2800 THB

4 a

100 125 150 1757550Speed (mph)

Spee

d (k

m/h

r)

250

40

80

120

160

200

240

280

b 96 km/hrc 87/88 mphd 750 mphe 400 km/hr

5 a

Metres 3 6 9 12 15

Feet 10 20 30 40 50


b

6 9 12 153metres

Conversion graph for metres and feet

Feet

0

10

20

30

40

50

60

70

c approx. 17 feetd 12.6 me approx. 667 feet

6 a 840 gramsb £25,000c £500,000

7 a 26 kmb 17 minutesc 72 km/hr

8 a 8 milesb 5 minutesc 2 milesd 36 mph

9 a 0840b i 20 minutes

ii 40 minutes iii 10 km

c 1010 and 1040d 15 km/hr

10 a i 10 km ii 20 minutes iii 30 minutes iv 60 km/hr

b

0900 0910 0920 09300850Time

Distance time graph for Neil’s mother

Dist

ance

from

hom

e (k

m)

08400

2

4

6

8

10

12

Exercise 52A1

impossible unlikely evens likely certain

2 a impossibleb certainc evensd likelye unlikely

3 a 29

b 39

or 13

c 0

d 69

or 23

4 a 16

b 36

or 12

c 16

d 26

or 13

5 1022

or 511


6 a 213

b 313

c 0

d 513

7 a 35

b 25

c 0

8 a 720

b 520

or

14

c 1520

or

34

d 0

9 a 16

b 36

or

12

c 26

or 13

d 26

or 13

e 46

or 23

10 a 126

b 1326

or 12

c 1226

or

613

d 1626

or 813

11 a 12

b 30200

or

320

c 79200

d 1

12 No. Each outcome is not equally likely (e.g. Melissa may be a better tennis player)

13 Winning, losing and drawing a match are not 3 equally likely outcomes.

Exercise 52B 1 a 30%

b 88%

c 29

d 415

e 0.35f 0.2g 0.96

h 1930

i 63%

2 0.7

3 0.58

4 36%

5 0.15

6 a 0.15b 0.7

7 a H1 H2 H3 H4 H5 H6

T1 T2 T3 T4 T5 T6

b i 312

or 14

ii 112

8 a 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 9 9b i 5

30or 1

6

ii 1530

or 12

iii 0

9 a

Y Y Y B B

R RY RY RY RB RB

R RY RY RY RB RB

B BY BY BY BB BB

B BY BY BY BB BB

Y YY YY YY YB YB

Y YY YY YY YB YB

b i 430

or 215

ii 2230

or 1115

iii 1030

or 13

iv 1230

or 25


10 a A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 C1 C2 C3 C4 C5 C6

b i 118

ii 318

or 16

iii 818

or 49

iv 318

or 16

Exercise 52C1 a 9

20b 42

2 a 0.13b 160

3 a 36%b 60 sheep

4 a 0.38b 18

5 a 495b 360c 162

6 a 320b 140c 52

7 a i 730

ii 1230

or 25

iii 2430

or 45

b i Yes. Suitable reason ii Increase the number of trials

8 a 510

, 3050

, 62100

, 125200

b No. 125200

is a more accurate relative frequency

Exercise 531 a 28 cm

b 40 cm2

2 99 cm2

3 250 cm

4 160 cm2

5 12 cm

6 108 cm2

7 45 cm2

8 a 90 cm2

b 54 cm3

9 640 cm3

10 2400 cm2

11 a 15 kgb 2000 cm2

Exercise 541 y = x2 + 5, y = 3x – x2, y = x2 + 6x + 3

2 a

x −3 −2 −1 0 1 2 3

y 9 4 1 0 1 4 9

b

x −3 −2 −1 0 1 2 3

y 13 8 5 4 5 8 13

c

x −3 −2 −1 0 1 2 3

y 6 2 0 0 2 6 12

d

x −3 −2 −1 0 1 2 3

y 0 −2 −2 0 4 10 18

e

x −3 −2 −1 0 1 2 3

y 4 1 0 1 4 9 16

f

x −3 −2 −1 0 1 2 3

y 15 8 3 0 −1 0 3

g

x −3 −2 −1 0 1 2 3

y 1 −3 −5 −5 −3 1 7

h

x −3 −2 −1 0 1 2 3

y 1 6 9 10 9 6 1

i

x −3 −2 −1 0 1 2 3

y −15 −8 −3 0 1 0 −3

3 a

x −3 −2 −1 0 1 2 3

y 12 7 4 3 4 7 12


b

–3 –2 –1 0 1

1

2

3

4

5

6

7

8

9

10

11

12

2 3 x

y

c accept y = 9.2 or 9.3d x = 2.2 and x = −2.2

4 a

x −4 −3 −2 −1 0 1 2 3

y 3 −2 −5 −6 −5 −2 3 10

b

–3 –2 –1 0 1

1

2

3

4

5

6

7

8

9

10

11

12

2 3 x

y

–4 –1

–2

–3

–4

–5

–6

c x = 1.4 and x = −3.4 d y = −3.75 (accept −3.7 or −3.8) e x = 1.2 and x = −3.2

5 a

x −2 −1 0 1 2 3 4 5

y 6 0 −4 −6 −6 −4 0 6

b

–1 0 1

1

2

3

4

5

6

7

2 3 x

y

–2 –1 4 5

–2

–3

–4

–5

–6

–7

c x = 4 and x = −1d accept x = −6.2 or x = −6.3e x = 4.5 and x = −1.5

Exercise 55A1 a 84 cm2

b 18 cm2

2 a 38 cm2

b 70 cm2

c 74 cm2

d 82 cm2

e 108 cm2

f 66.5 cm2

3 a 52 cm2

b 43 cm2

4 a 35 cmb 29.9 m

5 a Area = 63 cm2 Perimeter = 40 cmb Area = 81 cm2 Perimeter = 52 cmc Area = 119 cm2 Perimeter = 64 cmd Area = 94 cm2 Perimeter = 54 cm

Exercise 55B1 a 18 cm2

b 210 cm2

c 60 cm2

d 54 m2

e 98 cm2

f 115 cm2


g 90 cm2

h 63 cm2

i 0.6 m2 (6000 cm2)j 105 mm2 (1.05 cm2)

2 a 120 cm2

b 60 mm2 (0.6 cm2)c 128 cm2

d 60 cm2

3 a i Perimeter = 82 cm ii Area = 360 cm2

b i Perimeter = 56 cm ii Area = 84 cm2

c i Perimeter = 46 cm ii Area = 112 cm2

d i Perimeter = 30 cm ii Area = 60 cm2

4 a h = 7 cmb h = 3 cmc h = 4 md h = 3.6 m

5 Area = 330 cm2

Exercise 55C 1 a 24 cm2

b 104 cm2

c 122 cm2

d 224 cm2

2 a 96 cm2

b 124 cm2

c 68 cm2

d 39600 cm2 (3.96 m2)

3 a 180 cm2

b 320 cm2

4 a 432 cm3

b 13818 mm3

5 1125 cm3

6 4760 mm3 (4.76 cm3)

7 a 420 cm3

b 216 cm3

c 61.2 cm3

d 1296 mm3

8 a 2520 cm3

b 1500 cm3

9 a 360 cm3

b 512 cm3

10 12.5 cm

11 24 mm2

Exercise 56A 1 a 120 minutes

b 210 minutesc 15 minutesd 36 minutese 72 minutesf 96 minutesg 168 minutesh 18 minutes

2 a 14

hour

b 16

hour

c 25

hour

d 1112

hour

e 120

hour

f 160

hour

g 310

hour

h 1120

hour

3 a 40 mphb 30 mphc 46 mphd 56 mphe 60 mphf 64 mphg 51 mphh 72 mph

4 a 50 km/hb 38 km/hc 66 km/hd 65 km/he 37.5 km/h

f 96 km/hg 60 km/hh 84 km/h

5 45 mph

6 112 mph

7 1 hour and 40 minutes

8 105 km

9 50 km/h

10 a 27.5 milesb 62.5 milesc 2

12

hours

d 114

hours

e 80 km/hf 54 mphg 3 kmh 15 minutes ( 1

4hour)

Exercise 56B 1 5 g/cm3

2 a 0.03 kg/cm3

b 30 g/cm3

3 1200 g

4 a 2080 gb 2.08 kg

5 80 cm3

6 400 cm3

7 a 5 g/cm3

b 4.6875 g/cm3

c 3.5 g/cm3 d 2.5 g/cm3

8 0.78125 g/cm3

9 0.6 g/cm3

10 a 336 gb 4896 g

11 6 cm

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ANSWERS TO fOuNdATiON GCSE MATHEMATiCS fOR CCEA … · F 2013 1 ANSWERS TO fOuNdATiON GCSE MATHEMATiCS fOR CCEA PRACTiCE BOOK Exercise 1 1 7, 33, 89, 661, 921 2 6, 98, 302, 442, 1002