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.A car is bought for £17,500. Its value decreases by 12% in the first year, and by a further 10% of its reduced value in the second year. Work out the value of the car at the end of the second year, giving your answer to the nearest pound.
(a)£15,400
(b)£13,860
(c)£13,650
(d)£15,750
2.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?
(a)They are not in direct proportion, because y − x is different for each pair (9 and 15).
(b)They are not in direct proportion, because x + y is different for each pair (21 and 35).
(c)They are in direct proportion, because y ÷ x = 2.5 for both pairs.
(d)They are in direct proportion, because x × y = 90 and 250.
3.Work out the value of x when 4/x = 2/5.
(a)10
(b)2.5
(c)20
(d)8
4.40% of a number is 12 more than 25% of the same number. Work out the number.
(a)48
(b)80
(c)15
(d)30
5.Priya invests £750 in a savings account that pays simple interest. After 3 years, the account contains £840. Work out the annual rate of simple interest.
(a)12%
(b)4%
(c)112%
(d)0.04%
6.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
7.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
8.A train travels at a constant speed of 90 km/h. Work out the speed in m/s.
(a)1.5 m/s
(b)25 m/s
(c)324 m/s
(d)90000 m/s
9.A force of 126 N acts on an area of 3.5 m². Work out the pressure on the area, in N/m².
(a)36
(b)0.03
(c)129.5
(d)441
10.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.
(a)6
(b)12
(c)30
(d)37.5
11.The number of tickets a group can afford is inversely proportional to the price per ticket. At £4 per ticket, the group can afford 12 tickets. Work out how many tickets the group can afford at £6 per ticket.
(a)6
(b)18
(c)12
(d)8
12.Order these three values from smallest to largest: 3/8, 0.43, 41%.
(a)3/8, 41%, 0.43
(b)0.43, 41%, 3/8
(c)3/8, 0.43, 41%
(d)41%, 0.43, 3/8
13.6 identical printers can print a batch of exam papers in 40 minutes, all working at the same rate. Working at the same rate, work out how many minutes 4 of these printers would take to print the same batch.
(a)60 minutes
(b)40 minutes
(c)26.7 minutes
(d)24 minutes
14.The time taken for a train journey is inversely proportional to the average speed of the train. At an average speed of 60 km/h the journey takes 2 hours. Work out the time taken at an average speed of 40 km/h.
(a)2 hours
(b)1.5 hours
(c)3 hours
(d)1 hour 20 minutes
15.Two mathematically similar cubes have edge lengths 2 cm and 6 cm. Write the ratio of the volume of the smaller cube to the volume of the larger cube in its simplest form.
(a)27 : 1
(b)1 : 9
(c)1 : 27
(d)1 : 3
16.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
17.Grace's mean mark in her maths tests rises from 70 to 84. Work out the percentage increase in her mean mark.
(a)20%
(b)120%
(c)17%
(d)14%
18.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.
(a)£15
(b)£57.60
(c)£22.50
(d)£54
19.Write the ratio 0.75 : 2 as a ratio of whole numbers in its simplest form.
(a)0.75 : 2
(b)75 : 200
(c)3 : 2
(d)3 : 8
20.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
21.Write 350 ml : 1.4 l as a ratio in its simplest form.
(a)2:8
(b)25:1
(c)4:1
(d)1:4
22.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.
(a)4
(b)0.8
(c)16
(d)3
23.An amount of money is shared in the ratio 1:2:3. The largest share is £90 more than the smallest share. Work out the total amount that was shared.
(a)£180
(b)£540
(c)£135
(d)£270
24.The price of a cycling helmet rises from £80 to £116. Work out the percentage increase.
(a)45%
(b)145%
(c)36%
(d)31%

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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