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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.
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: Fractional indices
1. Evaluate 8^(2/3).
Correction
A. 4
- The denominator 3 means cube root: ∛8 = 2.
- The numerator 2 means square: 2² = 4.
Notion: Surds
2. Simplify √50.
Correction
D. 5√2
- 50 = 25 × 2, and 25 is a square number.
- √50 = √25 × √2 = 5√2.
Notion: Surds
3. Rationalise the denominator of 6/√3.
Correction
C. 2√3
- Multiply top and bottom by √3: 6√3 / 3.
- Simplify: 2√3.
Notion: Recurring decimals
4. Write 0.454545... as a fraction in its simplest form.
Correction
B. 5/11
- Let x = 0.4545... Then 100x = 45.4545...
- Subtract: 99x = 45, so x = 45/99 = 5/11.
Notion: Standard form
5. Work out (3 × 10⁴) × (5 × 10⁻⁷). Give your answer in standard form.
Correction
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.
Notion: Bounds
6. A length is 7.4 cm, correct to 1 decimal place. What is its upper bound?
Correction
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.
Notion: Negative indices
7. Evaluate 16^(−1/2).
Correction
C. 1/4
- A negative power means a reciprocal: 16^(−1/2) = 1 ÷ 16^(1/2).
- √16 = 4, so the answer is 1/4.
Notion: Compound interest
8. £2000 is invested at 3% compound interest per year. How much is it worth after 2 years?
Correction
B. £2121.80
- Multiplier for 3% growth: 1.03.
- 2000 × 1.03² = 2000 × 1.0609 = £2121.80.
Notion: Depreciation
9. A car worth £12 000 loses 20% of its value each year. What is it worth after 2 years?
Correction
A. £7680
- Multiplier for a 20% decrease: 0.8.
- 12 000 × 0.8² = 12 000 × 0.64 = £7680.
Notion: Surds
10. Simplify (2√3)².
Correction
D. 12
- (2√3)² = 2² × (√3)².
- = 4 × 3 = 12.