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.An adult cinema ticket costs £15 and a child ticket costs £9. Write the ratio of the adult price to the child price in its simplest form.
(a)5:3
(b)2:3
(c)3:5
(d)5:8
2.A conversion graph between kilometres and miles passes through the origin and the point (50, 31), with the number of kilometres on the horizontal axis and the number of miles on the vertical axis. Work out the number of miles equivalent to 1 kilometre.
(a)0.62 miles
(b)1.24 miles
(c)1.61 miles
(d)31.00 miles
3.3 builders put up a fence in 12 days. All the builders work at the same rate, so the number of days is inversely proportional to the number of builders. Work out how long 9 builders take to put up the same fence.
(a)4 days
(b)9 days
(c)6 days
(d)36 days
4.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.
5.A jumper normally costs £45. In a sale it is reduced by 20%. Work out the sale price, then write the sale price as a fraction of the normal price. Give your answer in its simplest form.
(a)1/5
(b)5/9
(c)4/5
(d)6/5
6.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
7.A metal alloy is made from copper and tin in the ratio 7:3. Work out the mass of tin in 250 g of the alloy.
(a)125 g
(b)75 g
(c)25 g
(d)175 g
8.The volume of water in a paddling pool, in litres, is plotted against the time since the tap was turned on, in minutes. What are the units of the gradient of a tangent to this graph?
(a)minutes
(b)litres per minute
(c)litres
(d)minutes for each litre
9.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
10.A tank is filled at a rate of 3 litres every 2 minutes. Given that 1 litre = 1000 cm³, work out the flow rate in cm³ per minute.
(a)3000
(b)1500
(c)750
(d)2000
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.Two cars leave the same point at the same time and travel in opposite directions. One travels at 80 km/h and the other at 60 km/h. Work out how long it takes until the cars are 350 km apart.
(a)5 hours
(b)2.5 hours
(c)17.5 hours
(d)4.375 hours
14.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
15.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

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