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Percentages and ratios (page 9)
Model answers
1 (a) Falls by 30% each year so after one year = 70% = 0·7 = 0·7 × 899 = $629·30
(b) After four years it will be $899 × (0·7) 4 = $215·8499
One quarter of the original is 899 ÷ 4 = $224·75. So it is less than one quarter of the original.
2 A reduction of 15% so sale price = 85% = 0·85 of pre-sale price
The pre-sale price = sale price ÷ 0·85 = $68 ÷ 0·85 = $80.
3 Increase of 8% so multiply by 108% = 1·08 each year.
After six years = 84 000 × (1·08) 6 = $133 297·44 = $133 300 to nearest $100.
4 Price including VAT = 1·175 × basic price
(a) Price including VAT = 1·175 × 650 = $763·75.
(b) If store pays VAT then their price is $650 rather than $763·75. This is a discount of $113·75.
113·75
As a percentage = –––––––– × 100 = 14·8936% = 14·9%
763·75
5 Total parts = 20
8
20
(a) Amount of water = –– × 250 = 100 ml (b) Amount of Eau de Parfum = ––3
20
× 45 = 300 litres
6 Scale 5 cm to 2 km
5
(a) So 7 km is drawn as 7 × –
2 = 17·5 cm (b) 5cm:2km = 5 cm : 200 000 cm = 1 : 40 000
2800
7 (a) Percentage in favour = ––––– × 100 = 70%
4000
7
(b) Total parts = 15 Number of men = ––
15 × 300 = 140 and number of women = 15 × 300 =160
8 ––
Mental methods (page 11)
1 750
2 (a) 2 11 (b) 2·05 × 10 3
3 2·4 × 10 10
1 –2
1 –
2
1 –2
4 (50 + 80 ) × (10 + 25 ) = (7 + 9) × (3 + 5) = 16 × 8 = 128
5 35 × 1·496 × 10 11 = 52·36 × 10 11 = 5·236 × 10 12
Written methods (page 14)
1 450 × 1·06 3 = 535·9572 = $535·96
2 160·48 × 1·025 3 = 172·819... = $172·82
3 T ∝ L
⇒ T = k L
⇒ 1·6 = k 64
⇒ 1·6 = k × 8
⇒ k = 1·6 ÷ 8 = 0·2
⇒ T = 0·2 L
4 (a) S ∝ L 3
⇒ S = kL 3
⇒ 2·4 = k × 4 3
⇒ 2·4 = k × 64
⇒ k = 2·4 ÷ 64 = 0·0375
⇒ S = 0·0375L 3
(b) S = 0·0375 × 6 3 = 8·1 cm
(c) 0·3 = 0·0375 × L 3
⇒ L 3 = 0·3 ÷ 0·0375 = 8
⇒ L = 2 m
5
1
P ∝ –––
Q
⇒
k
P = –––
Q
k
⇒ 12 = ––––
49
⇒ k = 12 × 49 = 12 × 7 = 84
⇒
84
P = –––
Q
1 –
2
2
IGCSE Revision Guide for Mathematics Model Answers © 2004, Hodder & Stoughton Educational