Answers to activities and exercises

Unit 1

NUMBER 11 ACTIVITY 1

Time (h) Speed (km/h) 1 160 2 80 4 40 6 26.7 7 22.9 8 20

EXERCISE 1

1 a 4 days 2 3 4 5 6 7 8 a a a a a a a 28 days 8 men 12 people 60 years 40 000 men 12 hours 32 km/litre b 2 days b b b b b b b 6 days 16 men 8 people 15 years 20 000 men 72 km/h 20 litres c 2 c c c c c 2 days 3 4.8 days 32 men 6 people 1200 years 400 men

EXERCISE 1*

1 a Number of light bulbs (N) 6 5 2 30 b 3000 = NP 2 a Number of years (N) 1 2 4 10 Number of men (M) 100 000 50 000 25 000 10 000 Power of each bulb (P) 500 600 1500 100

IGCSE Maths Answers – Unit 1

1

b 100 000 = NM 3 a 12 g/cm3 4 a 10 minutes 5 Number of men 100 000 100 000 20 000 400 000 IGCSE Maths Answers – Unit 1 6

b 1.5 cm3 b 12.8 litres/minute Number of tunnels 4 2 8 2 Number of young 18 000 5 9 million 4.5 billion b 1000 b 46 000 tonnes (2 sf) (ii) 30 seconds (iv) 8 seconds Time in years 4 2 40 0.5 Time 1 hour 1 second 1 hour 500 hours c 2.26 108 tonnes c 180 000 tonnes (2 sf)

Number of mosquitoes 1 1 500 500

7 a 5 8 a 16 tonnes (2 sf) 9 a 16 tonnes (2 sf) b (i) 4 minutes (iii) 70 seconds

EXERCISE 2

1 0.375 5 0.28125 9 0.18 13 0.38

3 5 , 20 64 5 21 9 7 25 90 1 29 18

2 0.05 6 0.1375 10 0.36 14 0.94

3 7 9 9 , , , 40 80 25 24 2 22 3 1 26 90 1 30 15

17

18

3 0.08 7 0.2 11 0.26 9 15 16 1 19 3 7 23 9 1 27 30

4 0.1875 8 0.5 12 0.53 5 3 16 , 32 8 4 20 9 24 1 28

1 45

EXERCISE 2*

1 0.46 5 2.30 11 7 3 9 , , 16 40 15 24 13 99

2

2 0.61 6 4.12 7 5 7 10 , , 40 32 8 38 14 99

3 0.046 4 0.161 7 0.301 8 0.280 19 3 5 11 55 9 9 11 12 , , , , , 20 25 64 125 128 512 48 10 31 15 16 33 33

19 990 412 21 999 11 25 90 29 0.037

17 9

29 990 101 22 999 13 26 15 30 0.016

18 8

3 110 128 23 333 28 27 495

19

2 55 158 24 333 31 28 198

20

REVISION EXERCISE 3

2 hours 7.5 km/litre 0.2 0.16 2 5 a 9 1 2 3 4 a a a a 6 mowers 6 litres 0.125 0.4 7 b 90 b b b b c 0.05 c 0.428571 23 c 99 IGCSE Maths Answers – Unit 1 d 3 1 22

REVISION EXERCISE 3*

1 a 16 km/litre 2 a 25 3 0.153846 9 9 11 7 4 , , , 25 256 500 15 7 5 a 9 6 0.12 b 40 litres b 10 g c 6 million km

b

1 90

c

67 99

ALGEBRA 11 ACTIVITY 2

Variables Area of a circle (A) and its radius (r) Circumference of a circle (C) and its diameter (d) Volume of water in a tank (V) and its weight (w) Distance travelled (D) at constant speed and time taken (t) Number of pages in a book (N) and its thickness (t) Mathematical ability (M) and a person’s height (h) Wave height in the sea (W) and wind speed (s) Grill temperature (T) and time to toast bread (t) Related? yes or no yes yes yes yes yes no yes yes

EXERCISE 4

1 a y = 5x 2 a d = 4t 3 a y = 2x b 30 b 60 b 10 cm c 5 c 45 c 7.5 kg

3

M b 5m 20 5 1950 sales 6 Yes, as 210 people would turn up to swim

4 a e=

c 120 kg

EXERCISE 4*

1 a v = 9.8t m 2 a c= 3 3 a d = 150m 4 a m = 6.5n 3y 5 a h= 2 6 a Advertising medium TV Radio Newspapers Internet b £13.4 million b 49 m/s b £2.50 b 1500 km b 975 kg b 0.75 m £x million 1.5 0.5 1.25 0.1 c £3.35 million c 2.5 s c 600 g c 266.7 g c 1540 approx. c 4 months £P million 6 2 5 0.4 d 25%

IGCSE Maths Answers – Unit 1

EXERCISE 5

y = 4x2 p = 2q2 v = 2w2 m = 10 n 5 a y = 5t2 1 2 3 4 a a a a 6 a P= b b b b b 144 18 54 20 45 m c c c c c 4 7 4 25 20 s 4.47s

h 20

3

b £86.40

c 8 cm

EXERCISE 5*

1 g f 2 n m 3 a R= 2 12 1 4 4 48 2 32 6 108 5 500

5 s2 256

b 113 km/h b 2 years old

4 a H = 1.53 3 y 5 x = 10 2 100 6 y= 3 2

4

ACTIVITY 3

t2 3.95 10–20d3 d (million km) 57.9 778 108 228 1430 2870 4500 5950 t (Earth days) (2 sf) 88 4300 220 11 000 31 000 60 000 91 000 IGCSE Maths Answers – Unit 1 5

Planet Mercury Jupiter Venus Mars Saturn Uranus Neptune Pluto

680

Ask pupils to compare these with the actual values.

EXERCISE 6

1 a y= 2 a 3 a 4 a 5 a 6 a

12 x 250 d= t 36 m= 2 n 100 V= 3 w 105 I=4 d2 1 L= 4d 2

b y=6 b d = 125 b m=9 b V = 100 b 0.1 candle power b 25...