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A-Level Maths Mock Test
A timed 25-question mock for the A-Level Mathematics covering algebra, probability & combinatorics, geometry & mensuration. Answer, submit and review every question with its explanation; set negative marking to match your exam’s current scheme.
A-Level Maths mock test
25 questions · 1 mark each · the timer starts with your first answer and the test submits itself when time runs out.
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Q1.AlgebraSolve: x + y = 17 and 3x + 4y = 63
Answer: A — x = 5, y = 12
Elimination/substitution gives x = 5, y = 12. Check: 1(5) + 1(12) = 17 ✓ and 3(5) + 4(12) = 63 ✓.
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Q2.Probability & CombinatoricsIn how many ways can the letters of the word GARDEN be arranged?
Answer: B — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q3.Geometry & MensurationFind the distance between (3, -5) and (6, -1).
Answer: D — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q4.AlgebraSolve: x² + 15x + 56 = 0
Answer: A — -8, -7
Find two roots with sum -15 and product 56: -8 and -7. So x² + 15x + 56 = (x + 8)(x + 7) = 0.
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Q5.Probability & CombinatoricsIn how many ways can a committee of 4 be chosen from 12 people?
Answer: B — 495
Order does not matter → combinations: 12C4 = 12! / (4!·8!) = 495.
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Q6.Geometry & MensurationFind the area of a right triangle with legs 5 cm and 12 cm.
Answer: D — 30 cm²
Area = ½ × base × height = ½ × 5 × 12 = 30 cm².
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Q7.AlgebraSolve: 3x + 2y = 6 and x + 5y = 15
Answer: D — x = 0, y = 3
Elimination/substitution gives x = 0, y = 3. Check: 3(0) + 2(3) = 6 ✓ and 1(0) + 5(3) = 15 ✓.
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Q8.Probability & CombinatoricsIn how many ways can a committee of 3 be chosen from 12 people?
Answer: C — 220
Order does not matter → combinations: 12C3 = 12! / (3!·9!) = 220.
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Q9.Geometry & MensurationA right triangle has legs 8 cm and 15 cm. Find the hypotenuse.
Answer: B — 17 cm
By Pythagoras, hypotenuse = √(8² + 15²) = √289 = 17.
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Q10.AlgebraSolve: x² − 7x − 8 = 0
Answer: C — -1, 8
Find two roots with sum 7 and product -8: 8 and -1. So x² − 7x − 8 = (x − 8)(x + 1) = 0.
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Q11.Probability & CombinatoricsTwo fair dice are thrown. What is the probability that the sum is 6?
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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Q12.Geometry & MensurationFind the distance between (-3, 5) and (0, 9).
Answer: A — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q13.AlgebraFind the sum of the first 26 terms of the AP 20, 27, 34, …
Answer: A — 2795
Sₙ = n/2 × [2a + (n − 1)d] = 26/2 × [40 + 175] = 2,795.
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Q14.Probability & CombinatoricsA card is drawn from a well-shuffled deck of 52. What is the probability that it is an ace or a king?
Answer: B — 2/13
There are 8 such cards in 52, so P = 8/52 = 2/13.
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Q15.Geometry & MensurationFind the distance between (-2, 2) and (4, 10).
Answer: C — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
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Q16.AlgebraSolve: x² − 7x − 18 = 0
Answer: D — -2, 9
Find two roots with sum 7 and product -18: -2 and 9. So x² − 7x − 18 = (x + 2)(x − 9) = 0.
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Q17.Probability & CombinatoricsIn how many ways can the letters of the word PENCIL be arranged?
Answer: C — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q18.Geometry & MensurationFind the volume of a cone with radius 5 cm and height 19 cm.
Answer: A — 497.42 cm³
Using ⅓πr²h with π = 3.1416: 497.42 cm³.
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Q19.AlgebraSolve: 4x + 3y = 72 and 4x + 5y = 96
Answer: D — x = 9, y = 12
Elimination/substitution gives x = 9, y = 12. Check: 4(9) + 3(12) = 72 ✓ and 4(9) + 5(12) = 96 ✓.
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Q20.Probability & CombinatoricsA card is drawn from a well-shuffled deck of 52. What is the probability that it is a red card?
Answer: C — 1/2
There are 26 such cards in 52, so P = 26/52 = 1/2.
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Q21.Geometry & MensurationFind the distance between (3, 3) and (11, 18).
Answer: D — 17
Distance = √((Δx)² + (Δy)²) = √(8² + 15²) = 17.
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Q22.AlgebraSolve: x² + 3x − 40 = 0
Answer: A — -8, 5
Find two roots with sum -3 and product -40: 5 and -8. So x² + 3x − 40 = (x − 5)(x + 8) = 0.
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Q23.Probability & Combinatorics4 fair coins are tossed. What is the probability of at least one head?
Answer: C — 15/16
P(no head) = (1/2)^4 = 1/16; P(at least one head) = 1 − 1/16 = 15/16.
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Q24.Geometry & MensurationFind the area of a right triangle with legs 8 cm and 15 cm.
Answer: D — 60 cm²
Area = ½ × base × height = ½ × 8 × 15 = 60 cm².
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Q25.AlgebraFind the sum of the first 12 terms of the AP 12, 13, 14, …
Answer: A — 210
Sₙ = n/2 × [2a + (n − 1)d] = 12/2 × [24 + 11] = 210.
How the mock test works
- The timer starts with your first answer; the test submits itself when time runs out.
- Choose the negative marking that matches your exam (this test has no negative marking by default — check the official notification).
- After submitting you get your score, accuracy, time taken and a topic-wise breakdown, then every explanation.
- “New mock test” builds another paper — calculation questions get new numbers.
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.
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) |