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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.
Questions originales rédigées par les professeurs Studoli dans l’esprit de l’examen GCSE. Ce ne sont pas des sujets officiels.
Mode chronométré
10 questions en 15 minutes, une question à la fois. Vos réponses sont corrigées à la fin ou quand le temps est écoulé.
Notion: Direct proportion
1. y is directly proportional to x². When x = 2, y = 12. Find y when x = 5.
Correction
D. 75
- y = kx², so 12 = k × 4 and k = 3.
- When x = 5: y = 3 × 25 = 75.
Notion: Inverse proportion
2. y is inversely proportional to x. When x = 3, y = 8. Find y when x = 6.
Correction
C. 4
- y = k/x, so 8 = k/3 and k = 24.
- When x = 6: y = 24/6 = 4.
Notion: Reverse percentages
3. After a 20% increase, a price is £84. What was the original price?
Correction
B. £70
- The new price is 120% of the original: multiplier 1.2.
- 84 ÷ 1.2 = £70.
Notion: Combining ratios
4. x : y = 3 : 5 and y : z = 2 : 7. Find x : z.
Correction
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.
Notion: Density
5. A block has a mass of 600 g and a volume of 250 cm³. Find its density.
Correction
D. 2.4 g/cm³
- Density = mass ÷ volume.
- 600 ÷ 250 = 2.4 g/cm³.
Notion: Compound units
6. Convert 72 km/h to metres per second.
Correction
C. 20 m/s
- 72 km/h = 72 000 m in 3600 s.
- 72 000 ÷ 3600 = 20 m/s.
Notion: Growth
7. A population of 500 bacteria doubles every hour. How many are there after 4 hours?
Correction
B. 8000
- After 4 hours: 500 × 2⁴.
- 500 × 16 = 8000.
Notion: Percentage change
8. A price falls from £250 to £190. Find the percentage change.
Correction
A. 24% decrease
- Change = 250 − 190 = 60.
- Percentage change = 60 ÷ 250 × 100 = 24%, and it is a decrease.
Notion: Similar shapes
9. Two similar shapes have lengths in the ratio 1 : 3. What is the ratio of their areas?
Correction
D. 1 : 9
- Area scale factor = (length scale factor)².
- 3² = 9, so 1 : 9.
Notion: Pressure
10. A force of 600 N acts on an area of 0.5 m². Find the pressure.
Correction
C. 1200 Pa
- Pressure = force ÷ area.
- 600 ÷ 0.5 = 1200 Pa (N/m²).