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GCSE الرياضيات10 أسئلة

GCSE Maths Higher: Number practice questions

Ten free GCSE Maths Higher tier questions on indices, surds, recurring decimals, standard form, bounds, compound interest and depreciation, 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: Fractional indices

    1. Evaluate 8^(2/3).

    الحل

    A. 4

    • The denominator 3 means cube root: ∛8 = 2.
    • The numerator 2 means square: 2² = 4.

  2. الموضوع: Surds

    2. Simplify √50.

    الحل

    D. 5√2

    • 50 = 25 × 2, and 25 is a square number.
    • √50 = √25 × √2 = 5√2.

  3. الموضوع: Surds

    3. Rationalise the denominator of 6/√3.

    الحل

    C. 2√3

    • Multiply top and bottom by √3: 6√3 / 3.
    • Simplify: 2√3.

  4. الموضوع: Recurring decimals

    4. Write 0.454545... as a fraction in its simplest form.

    الحل

    B. 5/11

    • Let x = 0.4545... Then 100x = 45.4545...
    • Subtract: 99x = 45, so x = 45/99 = 5/11.

  5. الموضوع: Standard form

    5. Work out (3 × 10⁴) × (5 × 10⁻⁷). Give your answer in standard form.

    الحل

    A. 1.5 × 10⁻²

    • Multiply the numbers: 3 × 5 = 15. Add the powers: 10⁴ × 10⁻⁷ = 10⁻³.
    • 15 × 10⁻³ = 1.5 × 10⁻².

  6. الموضوع: Bounds

    6. A length is 7.4 cm, correct to 1 decimal place. What is its upper bound?

    الحل

    D. 7.45 cm

    • To 1 decimal place, the error is half of 0.1, which is 0.05.
    • Upper bound = 7.4 + 0.05 = 7.45 cm.

  7. الموضوع: Negative indices

    7. Evaluate 16^(−1/2).

    الحل

    C. 1/4

    • A negative power means a reciprocal: 16^(−1/2) = 1 ÷ 16^(1/2).
    • √16 = 4, so the answer is 1/4.

  8. الموضوع: Compound interest

    8. £2000 is invested at 3% compound interest per year. How much is it worth after 2 years?

    الحل

    B. £2121.80

    • Multiplier for 3% growth: 1.03.
    • 2000 × 1.03² = 2000 × 1.0609 = £2121.80.

  9. الموضوع: Depreciation

    9. A car worth £12 000 loses 20% of its value each year. What is it worth after 2 years?

    الحل

    A. £7680

    • Multiplier for a 20% decrease: 0.8.
    • 12 000 × 0.8² = 12 000 × 0.64 = £7680.

  10. الموضوع: Surds

    10. Simplify (2√3)².

    الحل

    D. 12

    • (2√3)² = 2² × (√3)².
    • = 4 × 3 = 12.
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