Printable · GCSE Higher · ages 14-16

Ratio, proportion and rates of change worksheet — GCSE Higher

Fifteen questions across the ratio, proportion and rates of change statements at Higher 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 Higher

Maths · GCSE Higher · Ratio, proportion and rates of change · 15 questions

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1.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.
(a)121%
(b)11%
(c)21%
(d)20%
2.A fixed job of fitting a solar array is shared between installers, and the time taken is inversely proportional to the number of installers working on it at once. With 4 installers the job takes 18 hours. Construct the equation connecting time T and number of installers n, then work out how long it would take with 6 installers.
(a)27 hours
(b)72 hours
(c)18 hours
(d)12 hours
3.At an animal shelter, the ratio of cats to dogs is 2:5. There are 18 more dogs than cats. Work out the number of cats.
(a)6
(b)12
(c)9
(d)30
4.Write the ratio 2/3 : 1/2 as a ratio of whole numbers, in its simplest form.
(a)4:3
(b)2:3
(c)3:4
(d)1:2
5.Two cars travel at constant speeds. Car A travels 150 km in 3 hours. Car B travels 180 km in 4 hours. Which car is faster, and what is its speed?
(a)Car A, 45 km/h
(b)Car A, 50 km/h
(c)Car B, 45 km/h
(d)Car B, 50 km/h
6.A journey takes 4 hours at an average speed of 60 km/h. The time taken is inversely proportional to the average speed. Work out how long the same journey takes at an average speed of 80 km/h.
(a)4 hours
(b)2 hours 40 minutes
(c)3 hours
(d)5 hours 20 minutes
7.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.
(a)4
(b)0.8
(c)16
(d)3
8.Two mathematically similar jugs have heights 8 cm and 12 cm. The smaller jug holds 200 ml when it is full. Work out how much the larger jug holds when it is full.
(a)675 ml
(b)300 ml
(c)450 ml
(d)900 ml
9.A crate exerts a force of 84 N on the floor through a base with an area of 2.4 m². Work out the pressure on the floor, in N/m².
(a)0.03 N/m²
(b)35 N/m²
(c)201.6 N/m²
(d)81.6 N/m²
10.Write 400 g : 1.5 kg as a ratio in its simplest form.
(a)4 : 15
(b)40 : 150
(c)4 : 1.5
(d)15 : 4
11.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.
(a)7/3
(b)3/5
(c)2/3
(d)3/2
12.y is directly proportional to x², and x is positive. When x = 4, y = 32. Construct the equation connecting x and y, then work out the value of x when y = 200.
(a)10
(b)25
(c)100
(d)20
13.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?
(a)They are not in inverse proportion, because y ÷ x is different for each pair (3.75 and 1.67).
(b)They are in inverse proportion, because x × y = 60 for both pairs.
(c)They are in inverse proportion, because x × y = 40 for both pairs.
(d)They are not in inverse proportion, because x + y is different for each pair (19 and 16).
14.It takes 2 identical pumps 10 hours to empty a flooded basement. Working at the same rate, work out how many hours 5 of these pumps would take to empty the same basement.
(a)4 hours
(b)7 hours
(c)20 hours
(d)25 hours
15.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.
(a)18/25
(b)25/18
(c)3/25
(d)3/5

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