Printable · GCSE Foundation · ages 14-16

Ratio, proportion and rates of change worksheet — GCSE Foundation

Fifteen questions across the ratio, proportion and rates of change statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Ratio, proportion and rates of change worksheet — GCSE Foundation

Maths · GCSE Foundation · Ratio, proportion and rates of change · Non-calculator · 15 questions

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1.In a recipe the mass of chocolate to the mass of milk is in the ratio 1:4. Amelia uses 200 g of milk. Work out the mass of chocolate she needs.
(a)800 g
(b)250 g
(c)40 g
(d)50 g
2.Write the ratio 3/4 : 1/2 as a ratio of whole numbers in its simplest form.
(a)3:1
(b)3:2
(c)2:3
(d)2:1
3.A table shows three pairs of values: when x = 2, y = 6; when x = 5, y = 15; when x = 8, y = 24. In every pair the ratio y : x is the same. Write down a formula for y in terms of x.
(a)y = x/3
(b)y = x + 16
(c)y = 3x
(d)y = x + 4
4.A window cleaner charges a call-out fee plus an amount per window. The total charge, C pounds, is shown on a straight-line graph against the number of windows cleaned, w. The line passes through the points (2, 14) and (6, 26). Work out the gradient of the line.
(a)£3.00 per window
(b)£1.50 per window
(c)£2.00 per window
(d)£0.33 per window
5.Which of these ratios is equivalent to 6 : 10 : 14?
(a)8:12:16
(b)3:5:8
(c)9:15:21
(d)12:20:14
6.A class has 28 pupils. 16 of the pupils are girls and the rest are boys. Write the ratio of girls to boys in its simplest form.
(a)4:7
(b)3:4
(c)8:6
(d)4:3
7.Two numbers are in the ratio 3 : 7. Their sum is 60. Work out the positive difference between the two numbers.
(a)80
(b)60
(c)4
(d)24
8.A shop sells fruit juice concentrate that must be diluted with water in the ratio 2 : 5 (concentrate : water) to make squash. Priya has 8 litres of concentrate. Work out how much water she needs to keep the same ratio.
(a)40 litres
(b)3.2 litres
(c)11 litres
(d)20 litres
9.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.
(a)1/9
(b)1/10
(c)9/10
(d)9/1
10.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?
(a)They are not in direct proportion, because y − x is different for each pair (9 and 15).
(b)They are not in direct proportion, because x + y is different for each pair (21 and 35).
(c)They are in direct proportion, because y ÷ x = 2.5 for both pairs.
(d)They are in direct proportion, because x × y = 90 and 250.
11.Two mathematically similar rectangles have lengths in the ratio 3 : 5. The area of the smaller rectangle is 27 cm². Work out the area of the larger rectangle.
(a)675 cm²
(b)75 cm²
(c)125 cm²
(d)45 cm²
12.y is always the same multiple of x. When x = 6, y = 15. Work out the value of y when x = 10.
(a)4
(b)15
(c)25
(d)19
13.A straight-line graph shows the cost, C pounds, of hiring a bike for h hours. The line passes through the points (1, 12) and (4, 27). Which of these statements about the line is true?
(a)The hourly rate is £5 and the fixed fee is £7
(b)The hourly rate is £5 and the fixed fee is £12
(c)The hourly rate is £7 and the fixed fee is £5
(d)The hourly rate is £15 and the fixed fee is £7
14.A bag contains 7 red counters and 15 blue counters. Write down the ratio of red counters to blue counters in its simplest form.
(a)7:5
(b)15:7
(c)1:2
(d)7:15
15.A metal block has a mass of 270 g and a volume of 30 cm³. Work out the density of the block, in g/cm³.
(a)8100 g/cm³
(b)240 g/cm³
(c)9 g/cm³
(d)270 g/cm³

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