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GCSE الرياضيات10 أسئلة

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.

أسئلة أصلية كتبها مدرّسو Studoli بأسلوب امتحان GCSE. ليست أسئلة رسمية.

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.

  1. الموضوع: Direct proportion

    1. y is directly proportional to x². When x = 2, y = 12. Find y when x = 5.

    الحل

    D. 75

    • y = kx², so 12 = k × 4 and k = 3.
    • When x = 5: y = 3 × 25 = 75.

  2. الموضوع: Inverse proportion

    2. y is inversely proportional to x. When x = 3, y = 8. Find y when x = 6.

    الحل

    C. 4

    • y = k/x, so 8 = k/3 and k = 24.
    • When x = 6: y = 24/6 = 4.

  3. الموضوع: Reverse percentages

    3. After a 20% increase, a price is £84. What was the original price?

    الحل

    B. £70

    • The new price is 120% of the original: multiplier 1.2.
    • 84 ÷ 1.2 = £70.

  4. الموضوع: Combining ratios

    4. x : y = 3 : 5 and y : z = 2 : 7. Find x : z.

    الحل

    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.

  5. الموضوع: Density

    5. A block has a mass of 600 g and a volume of 250 cm³. Find its density.

    الحل

    D. 2.4 g/cm³

    • Density = mass ÷ volume.
    • 600 ÷ 250 = 2.4 g/cm³.

  6. الموضوع: Compound units

    6. Convert 72 km/h to metres per second.

    الحل

    C. 20 m/s

    • 72 km/h = 72 000 m in 3600 s.
    • 72 000 ÷ 3600 = 20 m/s.

  7. الموضوع: Growth

    7. A population of 500 bacteria doubles every hour. How many are there after 4 hours?

    الحل

    B. 8000

    • After 4 hours: 500 × 2⁴.
    • 500 × 16 = 8000.

  8. الموضوع: Percentage change

    8. A price falls from £250 to £190. Find the percentage change.

    الحل

    A. 24% decrease

    • Change = 250 − 190 = 60.
    • Percentage change = 60 ÷ 250 × 100 = 24%, and it is a decrease.

  9. الموضوع: Similar shapes

    9. Two similar shapes have lengths in the ratio 1 : 3. What is the ratio of their areas?

    الحل

    D. 1 : 9

    • Area scale factor = (length scale factor)².
    • 3² = 9, so 1 : 9.

  10. الموضوع: Pressure

    10. A force of 600 N acts on an area of 0.5 m². Find the pressure.

    الحل

    C. 1200 Pa

    • Pressure = force ÷ area.
    • 600 ÷ 0.5 = 1200 Pa (N/m²).
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