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.Two mathematically similar cylinders have heights in the ratio 3 : 4. Write the ratio of their volumes in its simplest form.
(a)9 : 16
(b)27 : 4
(c)27 : 64
(d)3 : 4
2.y is directly proportional to x. When x = 8, y = 20. Work out the value of y when x = 12.
(a)14.5
(b)4.8
(c)30
(d)24
3.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.
(a)£598
(b)£494
(c)£478.40
(d)£416
4.Four graphs are described below. Each shows one quantity plotted against another. Write down the description of the graph that shows two quantities in direct proportion.
(a)A curve that falls steeply and then levels off, never touching either axis
(b)A straight line crossing the vertical axis at 5, rising from left to right
(c)A straight line through the origin, rising from left to right
(d)A horizontal straight line at a height of 3 above the horizontal axis
5.Three business partners share a profit of £48,000 in the ratio 3:5:4. Work out how much the partner with 5 parts receives.
(a)£20,000
(b)£12,000
(c)£4,000
(d)£16,000
6.A room plan is drawn to a scale of 1 : 50. A wall in the room is 4 m long in real life. Work out the length of the wall on the plan, in centimetres.
(a)80 cm
(b)20000 cm
(c)0.08 cm
(d)8 cm
7.A plan is drawn to a scale of 1 : 25. A real fence is 10 m long. Work out the length of the fence on the plan, in centimetres.
(a)0.4 cm
(b)4 cm
(c)25000 cm
(d)40 cm
8.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
9.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
10.A printer prints pages at a constant rate. It prints 45 pages in 6 minutes. Work out how many pages it prints in 10 minutes.
(a)70 pages
(b)55 pages
(c)27 pages
(d)75 pages
11.A straight-line graph passes through the origin and the point (4, 10). The line represents y = kx. Write down the ratio x : y in its simplest form.
(a)2 : 10
(b)4 : 5
(c)2 : 5
(d)5 : 2
12.A recipe for 8 people needs 320 g of rice. Sanjay scales the recipe down to serve 5 people, then wants to scale his new amount back up to serve 8 people again. Work out the multiplier he should use to scale his amount for 5 people back up to the amount for 8 people.
(a)8/5
(b)3/5
(c)25/64
(d)5/8
13.The ratio of the number of red beads to blue beads in a bracelet is 3 : 7. There are 21 blue beads. Work out the number of red beads.
(a)14
(b)9
(c)49
(d)24
14.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.
(a)20%
(b)120%
(c)17%
(d)14%
15.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.

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