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 · Non-calculator · 15 questions

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1.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
2.The table shows values of x and y. x: 3, 5, 8. y: 12, 20, 32. Which statement correctly describes the relationship between x and y?
(a)y is always 4 times x.
(b)y is always double x, plus 6.
(c)y is always x plus 9.
(d)x is always 4 times y.
3.A rectangular garden has its length and width in the ratio 5:3. Given that the perimeter of the garden is 64 m, work out the width of the garden.
(a)8 m
(b)24 m
(c)12 m
(d)20 m
4.A recipe needs 1.2 kg of flour. Dan has 750 g of flour in his cupboard. Write the mass of flour the recipe needs as a fraction of the mass of flour Dan has. Give your answer in its simplest form.
(a)4/25
(b)8/13
(c)5/8
(d)8/5
5.The density of a liquid is 0.92 g/cm³. Work out the density of the liquid in kg/m³.
(a)9.2 kg/m³
(b)92 kg/m³
(c)920 kg/m³
(d)0.00092 kg/m³
6.Simplify the ratio 12 : 18 : 30 to its simplest form.
(a)3:2:5
(b)4:6:10
(c)6:9:15
(d)2:3:5
7.A map has a scale of 1 : 100 000. Two railway stations are 8 km apart in real life. Work out the distance between the stations on the map, in centimetres.
(a)8 cm
(b)800000 cm
(c)0.08 cm
(d)80 cm
8.A shop's daily profit, in pounds, is plotted against the price charged for an item, in pounds. A tangent to the profit graph at a price of £15 passes through the points (12, 540) and (18, 480). Work out the instantaneous rate of change of profit with respect to price at £15, and state whether profit is increasing or decreasing there.
(a)Profit is increasing by £6 per £1 rise in price.
(b)Profit is increasing by £10 per £1 rise in price.
(c)Profit is decreasing by £60 per £1 rise in price.
(d)Profit is decreasing by £10 per £1 rise in price.
9.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.
(a)60
(b)16
(c)11.25
(d)20
10.The width, the length and the height of a box are in the ratio 3:4:5. The length of the box is 16 cm. Work out the height of the box.
(a)20 cm
(b)80 cm
(c)4 cm
(d)12 cm
11.A cyclist rides at an average speed of 24 km/h for 1 hour 15 minutes. Work out the distance travelled, in km.
(a)27.6 km
(b)1800 km
(c)30 km
(d)19.2 km
12.The ratio of cats to dogs in a shelter is 3:4. There are 18 cats. Work out the total number of animals in the shelter.
(a)42
(b)126
(c)25
(d)24
13.A tangent to a curve at the point where x = 3 passes through the points (1, 2) and (5, 14). A candidate says: "The gradient of the tangent at x = 3 is 3, because 14 − 2 = 12 and 12 ÷ 4 = 3." Which statement is correct?
(a)The gradient is 3; the candidate's method is right.
(b)The gradient is −3; the subtraction was done the wrong way round.
(c)The gradient is 16; the two changes were added instead of divided.
(d)The gradient is 1/3; the division was done the wrong way round.
14.A car travels at a constant speed. It travels 150 miles in 3 hours. At the same speed, work out how far it travels in 5 hours.
(a)90 miles
(b)200 miles
(c)250 miles
(d)300 miles
15.Two mathematically similar water bottles have a volume scale factor of 8 from the smaller bottle to the larger bottle. Work out the surface area scale factor from the smaller bottle to the larger bottle.
(a)8
(b)4
(c)2
(d)64

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