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.A dog walker's charge, C pounds, for walking a dog for m minutes is shown on a straight-line graph. The line passes through the points (20, 14) and (50, 26). Work out the charge for a 65-minute walk.
(a)£33.80
(b)£40
(c)£32
(d)£26
2.A textbook is reduced from £60 to £45. Work out the percentage reduction.
(a)33%
(b)15%
(c)75%
(d)25%
3.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
4.A water tank is a cuboid measuring 30 cm × 20 cm × 10 cm. The tank is full of water. Work out how many litres of water it holds.
(a)600 litres
(b)6 litres
(c)0.6 litres
(d)60 litres
5.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.
(a)15000 m
(b)1500 m
(c)50000 m
(d)150 m
6.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
7.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
8.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
9.Triangle ABC is mathematically similar to triangle PQR, with AB corresponding to PQ and BC corresponding to QR. AB = 6 cm, BC = 8 cm and PQ = 12 cm. Work out the length of QR.
(a)32 cm
(b)24 cm
(c)16 cm
(d)14 cm
10.The temperature of a chemical reaction, in °C, is modelled by T = 80 − 6t + 0.5t², where t is the time in minutes after the reaction starts. Which of these four statements about the reaction between t = 2 and t = 6 minutes is correct?
(a)Instant rate at t = 6 is −2°C/min
(b)Instant rate at t = 2 is −2°C/min
(c)Average rate, t = 2 to 6, is −2°C/min
(d)Temperature falls 2°C in total
11.The ratio of y to x is always 3 : 4. Write down which equation could represent this relationship.
(a)y = 3x + 4
(b)y = 3/(4x)
(c)y = 4x/3
(d)y = 3x/4
12.Two quantities x and y are in the ratio x : y = 2 : 5, and y = kx for a constant k. Work out the value of k.
(a)5
(b)3
(c)2.5
(d)0.4
13.5 decorators paint 3 rooms in 6 hours. All the decorators work at the same rate. Work out how long it takes 10 decorators to paint 5 rooms.
(a)3 hours
(b)10 hours
(c)5 hours
(d)6 hours
14.A cyclist travels d kilometres in t hours. Write down an expression, in terms of d and t, for the cyclist's average speed in km/h.
(a)d + t
(b)d × t
(c)t ÷ d
(d)d ÷ t
15.Write 75p : £1.50 as a ratio of whole numbers in its simplest form.
(a)2:1
(b)3:4
(c)1:2
(d)50:1

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