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A-Level Maths Geometry & Mensuration Questions
Practise geometry & mensuration (mathematics) for the A-Level Mathematics: 10 multiple-choice questions, each with the correct answer and a worked explanation. Click an option to check it, or “New questions” for another set.
Geometry & Mensuration practice
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Q1.Find the area of a right triangle with legs 9 cm and 12 cm.
Show answer & explanation
Answer: D — 54 cm²
Area = ½ × base × height = ½ × 9 × 12 = 54 cm².
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Q2.Find the volume of a cylinder with radius 3 cm and height 12 cm.
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Answer: C — 339.29 cm³
Using πr²h with π = 3.1416: 339.29 cm³.
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Q3.Find the distance between (-4, -5) and (1, 7).
Show answer & explanation
Answer: C — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
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Q4.Find the distance between (0, 2) and (8, 17).
Show answer & explanation
Answer: C — 17
Distance = √((Δx)² + (Δy)²) = √(8² + 15²) = 17.
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Q5.Find the distance between (4, 4) and (7, 8).
Show answer & explanation
Answer: C — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q6.Find the distance between (-1, 3) and (2, 7).
Show answer & explanation
Answer: B — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q7.Find the distance between (-3, -4) and (3, 4).
Show answer & explanation
Answer: B — 10
Distance = √((Δx)² + (Δy)²) = √(6² + 8²) = 10.
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Q8.Find the distance between (3, 4) and (6, 8).
Show answer & explanation
Answer: C — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q9.Find the volume of a cone with radius 4 cm and height 6 cm.
Show answer & explanation
Answer: D — 100.53 cm³
Using ⅓πr²h with π = 3.1416: 100.53 cm³.
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Q10.Find the distance between (-2, 4) and (3, 16).
Show answer & explanation
Answer: B — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
How to approach geometry & mensuration questions
Memorise core formulas (circle πr², triangle ½bh, Pythagoras, distance √((x₂−x₁)² + (y₂−y₁)²)). Sketch the figure — most errors come from misreading which length is given.
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) |