24 questions across ratio, direct and inverse proportion, compound measures and area and volume scale factors.

⚗️ Ratio and proportion mastery — Higher

Maths · GCSE Higher · 24 questions · ~45 min

MathsUKwww.geekhero.co.uk

Ratio, proportion and rates of change is 20% of a Higher paper and it is the area that rewards method over recall. This sheet works through it in one sitting: simplifying and sharing in a ratio, including the questions that give you one share or the difference rather than the total; expressing one quantity as a fraction or percentage of another; direct and inverse proportion, both numerically and as an equation with a constant k; compound measures — speed, density and pressure — with unit conversions built in rather than avoided; and the similar-shapes work where lengths, areas and volumes scale by the factor, its square and its cube. That last group is where Higher candidates lose the most marks in this area, so it is deliberately over-represented here.

1.The price of a share falls by 10% on Monday and then rises by 10% on Tuesday. Work out the overall percentage change from Monday's starting price.
(a)0%
(b)−1%
(c)−2%
(d)+1%
2.The price of a jacket increases by 50% and then decreases by 50%. Describe the overall change from the original price.
(a)no change
(b)an increase of 25%
(c)a decrease of 25%
(d)a decrease of 50%
3.Maya is paid £105.30 for working 9 hours. Work out her rate of pay, in £ per hour.
(a)£11.70
(b)£117.00
(c)£947.70
(d)£96.30
4.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
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.Two mathematically similar rectangles have lengths in the ratio 3 : 5. The area of the smaller rectangle is 27 cm². Work out the area of the larger rectangle.
(a)675 cm²
(b)75 cm²
(c)125 cm²
(d)45 cm²
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.A shop sells rope by the metre. 3 m costs £7.50 and 5 m costs £11.00. Does this data show that the cost is directly proportional to the length of rope bought? Choose the correct verdict and reason.
(a)No — the cost per metre differs: £2.50/m vs £2.20/m
(b)Yes — because both amounts increase as length increases
(c)No — because 5 m costs more than 3 m in total
(d)Yes — the cost per metre is £2.50 in both cases
9.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
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.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.
(a)5:3
(b)2:5
(c)2:3
(d)3:2
12.Two quantities x and y are in direct proportion. When x = 8, the value of y is 20. Work out the value of y when x = 14.
(a)26
(b)5.6
(c)28
(d)35
13.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
(a)£40
(b)£60
(c)£57.60
(d)£38.40
14.A recipe uses flour, sugar and butter in the ratio 8 : 3 : 5. Write the ratio of flour to the rest of the mixture (sugar and butter combined) in its simplest form.
(a)3 : 5
(b)8 : 3
(c)1 : 2
(d)1 : 1
15.The cost of manufacturing a spherical container is proportional to the cube of its radius. A container of radius 3 cm costs £54 to manufacture. Construct the equation connecting cost C and radius r, then work out the cost of a container of radius 5 cm.
(a)£150
(b)£250
(c)£10
(d)£90
16.A shop sells ribbon by the metre. 2 m costs £3.00, 4 m costs £6.00, and 7 m costs £10.50. Does this data show that the cost is directly proportional to the length of ribbon bought? Choose the correct verdict and reason.
(a)Yes — the cost per metre is £1.50 each time
(b)Yes — the cost increases as the length increases
(c)No — 10.50 ÷ 7 gives 1.05, unlike the other rates
(d)No — the cost must double whenever length doubles
17.A printer prints at a constant rate. The time taken to print a batch of forms is inversely proportional to the printer's speed, in pages per minute. Printing at 20 pages per minute takes 15 minutes. Work out how long the same batch takes to print at 25 pages per minute. Give your answer in minutes.
(a)12
(b)10
(c)18.75
(d)20
18.Two mathematically similar triangular flags have areas in the ratio 4 : 25. The height of the smaller flag is 6 cm. Work out the height of the larger flag.
(a)15 cm
(b)27 cm
(c)37.5 cm
(d)2.4 cm
19.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
20.Priya is paid £58.50 for working 7.5 hours on a Saturday. Work out her rate of pay, in £ per hour.
(a)£7.80
(b)£438.75
(c)£51.00
(d)£0.13
21.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
22.A jug of squash is made by mixing water and syrup in the ratio 6:1. Nia wants to make 8.4 litres of squash. Work out how much syrup she needs, in litres.
(a)0.84
(b)1.4
(c)1.2
(d)7.2
23.Two mathematically similar tins have heights 8 cm and 12 cm. Jayden says that the volume of the larger tin is 1.5 times the volume of the smaller tin. Give a reason why Jayden is incorrect, and work out the correct volume scale factor.
(a)3.375
(b)2.25
(c)4.5
(d)1.5
24.Write the ratio 5 : 8 in the form 1 : n.
(a)1:0.6
(b)1:1.6
(c)1:1.5
(d)0.6:1

What is on this worksheet?

The sheet holds 24 questions drawn from the MathsUK bank — the content area covered: Ratio, proportion and rates of change (statements R4, R5, R9, R10, R11, R12, R13). It is pitched at GCSE Higher and takes about 45 minutes to work through in full. It is built for independent practice, with full answers at the end for self-marking.

How to use the sheet well

Print it or open it on screen — both work. Printing is A4; the screen view fits phones and tablets.
Do all 24 questions before checking — about 45 minutes is the guide, but there is no time pressure.
Check the answers — press “Show answers” or print the answer page separately.
Redo the questions you got wrong — twice as effective as doing 24 fresh ones.
“New questions” — builds a fresh sheet on the same statements, so you can practise again without repeats.

Why this sheet helps

MathsUK worksheets use questions graded by difficulty and a fair spread of correct-answer positions (the answer is not always (a)) — so the student really has to think about each question rather than guess a pattern. Every question is tagged to a DfE content statement and checked before it enters the bank. The answers come with a step-by-step explanation, not just a value — so a wrong answer becomes a lesson.

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