1. Mathematics (9-1) - iGCSE
Year 09
Unit 04 – Answers

2. 4 - Prior knowledge check
Page 639
a b
a. 3 kg b. £7.50 c. 25 litres d. 56m
a b. 3 5
a. £3 b. 45g
a b. 9 4
a b c
a b

3. 4 - Prior knowledge check
Page 639
a b
a. 12 b
a. 2 : 5 b. 9 : 1
8 : 5
1 4
a. 3 eggs b. 75g
a. £15.60 b. 36.4kg c. 153ml d. 40.8m

4. 4 - Prior knowledge check
Page 639
a. 60% b. 81.7% c. 49 out of 60 is better as the score is a higher percentage.
£72
a. 74% b. 150%
a = 65% b = 42.9% c = 138% d = 275%

5. 4 - Prior knowledge check
Page 639
a b c d. 2.1
£31.36
4.6 m
a b. 0.2
3 4 of £120 is £90. This is the largest amount.

6. 4.1 - Fractions
Page 639
a b
a. 10 b. 9 c d
a. 54 b. 40 c. 27
a b (= ) c (= 5 24 ) d. 3 2

7. 4.1 - Fractions
Page 639
a. 2 b c d
a b c d. 6
a b
a b c d
Yes. Students’ own answer, e.g. compare the answers of 3 ÷ and 3 x 2.

8. 4.1 - Fractions
Page 639
= = = = = 8 1 5
a b c d
Yes, the part will fit because it is cm, which is within the acceptable range.
a b c d
10,000m2
a. 4 hours 5 minutes b. 5 hours.

9. 4.2 - Ratios
Page 639
a. 1:2 b. 3:5 c. 4:7 d. 1:5 e. 1:4 f. 15:2
a. 1:5 b. 1:0.5 c. 1:6 d. 1: 7 12
a. 3:1 b :1 c. 15:1 d :1
a. 1:0.2 b. 1: c. 1: d. 1:36.5
11.5:1 b. The first school
Julie (Julie uses 5 parts water to 1 part squash, Hammad uses 5.7 parts water)

10. 4.2 - Ratios £84 a. 5:2 b. 22.5g of resin c. 4.8g if hardener.
Page 639
£84
a. 5:2 b. 22.5g of resin c. 4.8g if hardener.
a. 300:1 b. 81cm
350 students
a b c. Sally gets £21 and David gets £14.
Benji gets 217 bricks and Freddie gets 248.
8.16m

11. 4.2 - Ratios
Page 639
a. £68: £136: £170 b. £5.84: £17.51: £23.35
No, he needs 20 kg of cement.
a. 40:73 b. 142:241 c. 3:7 d. 15:1
Size
Blue
Green
Yellow
1 litre
0.6
0.375
0.025
2.5 litres
1.5
0.9375
0.0625
5.5 litres
3.3
2.0625
0.1375

12. 4.3 – Ratio and Proportion 2:5 and 6:15 a. $360 b. £420
Page 639
2:5 and 6:15
a. $360 b. £420
Cheaper in HK by £2 or HK524.80
a. 1:1.6 b. Adrian by 3.4 km or miles.
Yes; the ratio 4:5 is the same as 16:20
a b. £36.75
He is under 21. We do not know any more than this

13. 4.3 – Ratio and Proportion s = b x 4 3 = 3 4 b b = s x 3 4 = 3 4 s
Page 639
s = b x = 3 4 b b = s x = 3 4 s
a. c = n b. 11 chillies c. c = n 125
a. No b. Yes c. No
Yes
a. Yes, because Q is 1.5 x the value of P b. Q = 1.5 x P c. 2:3

14. 4.3 – Ratio and Proportion
Page 639
P = 48, Q = 56, R = 12.5, S = 45
£5.44
2.4 m
The cheese is cheaper in Switzerland. 160 g would cost ( 3.58 SFr in England.

15. 4.4 – Percentages
Page 639
a b. 1.3 c. 1.05
a b c. 0.94
£379.26
£550
£770
a. £7680 b. £6144
a. i. £30 ii. £6144 b. £17,436.25

16. 4.4 – Percentages a. £3300 b. £3752 c. £8427 d. £19167 a. £128 b. 4%
Page 640
a. £3300 b. £3752 c. £8427 d. £19167
a. £128 b. 4%
8.5%
23%
250% Jo
£43.80
1.0506, £1.0506x

17. 4.4 – Percentages
Page 640
a. 7.1% b. £160,000
a. Students' own answers, e.g. Let original value = n; 20% increase → 1.2n; 20% of 1.2n = 0.24n; 1.2n n = 0.96n, which is a decrease of 4%
The final amount will be the same.

18. 4.5 – Fractions, Decimals and Percentages
Page 640
a. m = b. n = -4 c. p = 32
Fraction
Decimal
Percentage
1 8
0.125
12.5%
9 20
0.45
45%
2 3
0.6
66.6%
4 5
0.8
80%
3 2
1.5
150%

19. 4.5 – Fractions, Decimals and Percentages
Page 640
a b. 10 c d. 168 e f. £47.50
a. £ b % 24
30%
4 7
Students’ own answer.
£13.60

20. 4.5 – Fractions, Decimals and Percentages
Page 640
0.6 = 2 3 , students‘ own answer.
a. Yes, because s = a constant x t. b. t = s 4 c. 1:4
a b c d e f
b and d are recurring

21. 4 – Problem Solving
Page 640
a. £430 b. £375
Caroline pays £615 and Naomi pays £410. 6
No, because their weights are 75 kg and 90 kg.
£2000
Accountant 2 days, book-keeper 3 days, clerk 5 days. 27

22. 4 – Check Up
Page 640
a b
a b. 4
a. 7:40 b. 1: 18 5
a. 1:7 b. £385
a. €57.15 b. £385
a. 200:75 = 8:3 b. f = 8𝑏 3 c. 80 Biscuits

23. 2 and students’ own answers.
4 – Check Up
Page 640
£66, £44, £22.
a. £ b kg
20%
£720
a. 9.3% b. £
2 and students’ own answers.

24. 4 – Strengthen Fractions a. 4 5 b. 4 9 c. 8 3 d. 15 8 e. 9 4 f. 7 11
Page 640
Fractions
a b c d e f
a b c d
a b c d
a. 5 b c d e
a b c. 4 d

25. 4 – Strengthen Ratio and Proportion a. D only b. A and C
Page 640
Ratio and Proportion
a. D only b. A and C
a. i. 1:5 ii. 0.2:1 b. i. 1:0.125 ii. 4:1 c. i. 1:8 ii :1 d. i. 1:0.57 ii. 1.75:1
a. 13:8 b. 10:17 c. 7:10 d. 7:11
a. i. $8 ii. $10 iii. Double the number of £ b. i. £3 ii. £5 iii. Halve the number of $
X = 18 Y = 20
5.4 = 27 5
Kiran = £14.20, Stephen = £28.40, Jane = £49.70

26. 4 – Strengthen Fractions, Decimals and Percentages
Page 640
Fractions, Decimals and Percentages
a b c
a % b c. £46.58
a. 95.8% b c. £34.49
a. 4.5% b. Student's own answers.
a. 2.25, 8, % b. 25, 145, 17.2%
a g b. £3.75 c. £12

27. 4 – Strengthen
Page 640
a b x → → 13.44
£10.50
a. £780 b. £185,000
a x = £5125 b. £
x 1.28

28. 4 – Extend
Page 640
£48
a b c d. 3 8
50%
17 42
£1.92
43.5%
a. 2:1 b. 25%

29. Actual = 9227 bottles. Estimate = 9600 = 16 x 150 x 4 £164.00 £960.68
4 – Extend
Page 640
43%
a. 1 b. 1 c
Actual = 9227 bottles. Estimate = 9600 = 16 x 150 x 4
£164.00
£960.68
50% 51

30. 4 – Unit Test Sample student answer
Page 641
Sample student answer
The question has asked them to ‘Compare’ the costs of the handbags. They must state, using the costs found, which handbag is cheaper/more expensive. For example, 'The handbag is cheaper in Manchester as it costs £52.50, whereas in Paris it costs £54.'