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

MathsUKwww.geekhero.co.uk

1.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
2.y is inversely proportional to x², and x is positive. When x = 2, y = 45. Construct the equation connecting x and y, then work out the value of x when y = 5.
(a)6
(b)36
(c)18
(d)30
3.Two quantities are connected by the formula y = 0.8x. Write down the ratio y : x in its simplest form.
y = 0.8x
(a)5 : 4
(b)8 : 1
(c)4 : 5
(d)8 : 10
4.A tangent to the graph of population against time at the point where t = 4 passes through (2, 180) and (6, 260). Work out the instantaneous rate of change of the population at t = 4, in people per year.
(a)20 people/year
(b)84 people/year
(c)80 people/year
(d)−20 people/year
5.A metal cylinder has a mass of 356.5 g and a volume of 47 cm³. Work out the density of the cylinder, in g/cm³, to 1 decimal place.
(a)0.1
(b)403.5
(c)7.6
(d)7.5
6.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.
(a)25:1
(b)1:25
(c)25:8
(d)8:25
7.A box holds 60 crayons. 25 of the crayons are broken and the rest are unbroken. Write the number of unbroken crayons as a fraction of the number of broken crayons. Give your answer in its simplest form.
(a)5/7
(b)2/5
(c)7/12
(d)7/5
8.A scale drawing of a park has a scale of 1 : 2500. On the drawing, the distance between the entrance and the lake is 4.4 cm. A jogger runs from the entrance to the lake and then back to the entrance. Work out the total distance the jogger runs, in kilometres.
(a)110 km
(b)0.22 km
(c)220 km
(d)0.11 km
9.A market stall sells apples at a fixed price per kilogram. Priya buys 3 kg for £5.40. Write the ratio of the mass in kilograms to the cost in pounds, in its simplest form.
(a)1 : 18
(b)9 : 5
(c)5 : 9
(d)3 : 5
10.A charity shop and a school share collection-box money in the ratio 5 : 8. The charity shop receives £47.50. Work out how much the school receives.
(a)£29.69
(b)£76.00
(c)£57.00
(d)£123.50
11.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.
12.In a class, 50% of the students study French, 30% study Spanish and the rest study German. Write down the ratio of French : Spanish : German students, in its simplest form.
(a)5:3:1
(b)3:5:2
(c)50:30:20
(d)5:3:2
13.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.
(a)−1/3
(b)−3
(c)−12
(d)3
14.A road sign 3 m tall casts a shadow 5 m long. At the same time, a nearby lamppost casts a shadow 10 m long. Work out the height of the lamppost.
(a)1.50 m
(b)16.67 m
(c)6.00 m
(d)8.00 m
15.A concrete mix is made from gravel and cement in the ratio 5 : 1 by mass. The mass of cement is c kg and the total mass of the mix is m kg. Write down a formula for m in terms of c.
(a)m = c + 5
(b)m = c/6
(c)m = 6c
(d)m = 5c

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