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A-Level Maths Practice Questions
Original practice questions for the A-Level Mathematics (AQA, Pearson Edexcel, OCR and other boards), mixed across 3 topics with instant answers and explanations. Practise by topic below or take the timed mock test.
A-Level Maths mixed practice
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Q1.AlgebraSolve: 5x + y = -27 and 3x + y = -17
Show answer & explanation
Answer: D — x = -5, y = -2
Elimination/substitution gives x = -5, y = -2. Check: 5(-5) + 1(-2) = -27 ✓ and 3(-5) + 1(-2) = -17 ✓.
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Q2.Probability & CombinatoricsIn how many ways can a committee of 2 be chosen from 6 people?
Show answer & explanation
Answer: C — 15
Order does not matter → combinations: 6C2 = 6! / (2!·4!) = 15.
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Q3.Geometry & MensurationFind the area of a right triangle with legs 6 cm and 8 cm.
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Answer: B — 24 cm²
Area = ½ × base × height = ½ × 6 × 8 = 24 cm².
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Q4.AlgebraSolve: x² + 4x − 5 = 0
Show answer & explanation
Answer: B — -5, 1
Find two roots with sum -4 and product -5: -5 and 1. So x² + 4x − 5 = (x + 5)(x − 1) = 0.
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Q5.Probability & CombinatoricsTwo fair dice are thrown. What is the probability that the sum is 6?
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Answer: C — 5/36
5 of the 36 equally likely outcomes give a sum of 6, so P = 5/36 = 5/36.
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Q6.Geometry & MensurationFind the volume of a sphere of radius 8 cm.
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Answer: A — 2,144.66 cm³
Using (4/3)πr³ with π = 3.1416: 2,144.66 cm³.
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Q7.AlgebraFind the sum of the first 14 terms of the AP 2, 4, 6, …
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Answer: B — 210
Sₙ = n/2 × [2a + (n − 1)d] = 14/2 × [4 + 26] = 210.
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Q8.Probability & CombinatoricsIn how many ways can a committee of 3 be chosen from 8 people?
Show answer & explanation
Answer: B — 56
Order does not matter → combinations: 8C3 = 8! / (3!·5!) = 56.
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Q9.AlgebraFind the sum of the first 13 terms of the AP 16, 25, 34, …
Show answer & explanation
Answer: A — 910
Sₙ = n/2 × [2a + (n − 1)d] = 13/2 × [32 + 108] = 910.
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Q10.Probability & CombinatoricsIn how many ways can the letters of the word GARDEN be arranged?
Show answer & explanation
Answer: C — 720
All 6 letters are different, so arrangements = 6! = 720.
About A-Level Maths
A-Level Mathematics — conducted by AQA, Pearson Edexcel, OCR and other boards. Pure maths, statistics and mechanics for university entrance in the UK.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
Practise by topic
- Algebra questions — Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution.
- Probability & Combinatorics questions — Probability = favourable ÷ total outcomes.
- Geometry & Mensuration questions — Memorise core formulas (circle πr², triangle ½bh, Pythagoras, distance √((x₂−x₁)² + (y₂−y₁)²)).
- A-Level Maths mock test — 25 timed questions.
A-Level Maths practice topics
| Topic | Section | Question source |
|---|---|---|
| Algebra | Mathematics | Calculated (new numbers every set) |
| Probability & Combinatorics | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |