GCSE Maths Higher: Ratio and proportion practice questions
Ten free GCSE Maths Higher tier questions on direct and inverse proportion, reverse percentages, combining ratios, density, growth and similar shapes, each with a worked solution. Suitable for AQA, Edexcel and OCR.
Original questions written by Studoli tutors in the style of the GCSE exam. They are not official past questions.
Timed mode
10 questions in 15 minutes, one question at a time. Your answers are marked when you submit or when the time runs out.
Topic: Direct proportion
1. y is directly proportional to x². When x = 2, y = 12. Find y when x = 5.
Solution
D. 75
- y = kx², so 12 = k × 4 and k = 3.
- When x = 5: y = 3 × 25 = 75.
Topic: Inverse proportion
2. y is inversely proportional to x. When x = 3, y = 8. Find y when x = 6.
Solution
C. 4
- y = k/x, so 8 = k/3 and k = 24.
- When x = 6: y = 24/6 = 4.
Topic: Reverse percentages
3. After a 20% increase, a price is £84. What was the original price?
Solution
B. £70
- The new price is 120% of the original: multiplier 1.2.
- 84 ÷ 1.2 = £70.
Topic: Combining ratios
4. x : y = 3 : 5 and y : z = 2 : 7. Find x : z.
Solution
A. 6 : 35
- Make y the same in both: x : y = 6 : 10 and y : z = 10 : 35.
- So x : y : z = 6 : 10 : 35, and x : z = 6 : 35.
Topic: Density
5. A block has a mass of 600 g and a volume of 250 cm³. Find its density.
Solution
D. 2.4 g/cm³
- Density = mass ÷ volume.
- 600 ÷ 250 = 2.4 g/cm³.
Topic: Compound units
6. Convert 72 km/h to metres per second.
Solution
C. 20 m/s
- 72 km/h = 72 000 m in 3600 s.
- 72 000 ÷ 3600 = 20 m/s.
Topic: Growth
7. A population of 500 bacteria doubles every hour. How many are there after 4 hours?
Solution
B. 8000
- After 4 hours: 500 × 2⁴.
- 500 × 16 = 8000.
Topic: Percentage change
8. A price falls from £250 to £190. Find the percentage change.
Solution
A. 24% decrease
- Change = 250 − 190 = 60.
- Percentage change = 60 ÷ 250 × 100 = 24%, and it is a decrease.
Topic: Similar shapes
9. Two similar shapes have lengths in the ratio 1 : 3. What is the ratio of their areas?
Solution
D. 1 : 9
- Area scale factor = (length scale factor)².
- 3² = 9, so 1 : 9.
Topic: Pressure
10. A force of 600 N acts on an area of 0.5 m². Find the pressure.
Solution
C. 1200 Pa
- Pressure = force ÷ area.
- 600 ÷ 0.5 = 1200 Pa (N/m²).
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