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Gaokao-style Maths Practice Questions
Original practice questions for the Gaokao-style Mathematics practice (Practice in the style of China’s National College Entrance Examination; not affiliated), mixed across 3 topics with instant answers and explanations. Practise by topic below or take the timed mock test.
Gaokao-style Maths mixed practice
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Q1.AlgebraSolve: x + 2y = 2 and 4x + 5y = 17
Show answer & explanation
Answer: B — x = 8, y = -3
Elimination/substitution gives x = 8, y = -3. Check: 1(8) + 2(-3) = 2 ✓ and 4(8) + 5(-3) = 17 ✓.
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Q2.Probability & CombinatoricsIn how many ways can the letters of the word MOTHER be arranged?
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Answer: C — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q3.Geometry & MensurationFind the volume of a cylinder with radius 3 cm and height 15 cm.
Show answer & explanation
Answer: B — 424.12 cm³
Using πr²h with π = 3.1416: 424.12 cm³.
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Q4.AlgebraSolve: x² + 4x − 45 = 0
Show answer & explanation
Answer: A — -9, 5
Find two roots with sum -4 and product -45: 5 and -9. So x² + 4x − 45 = (x − 5)(x + 9) = 0.
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Q5.Probability & CombinatoricsIn how many ways can the letters of the word ORANGE be arranged?
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Answer: B — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q6.Geometry & MensurationFind the distance between (1, -1) and (6, 11).
Show answer & explanation
Answer: B — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
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Q7.AlgebraFind the sum of the first 11 terms of the AP 6, 11, 16, …
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Answer: D — 341
Sₙ = n/2 × [2a + (n − 1)d] = 11/2 × [12 + 50] = 341.
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Q8.Probability & CombinatoricsIn how many ways can a committee of 2 be chosen from 12 people?
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Answer: A — 66
Order does not matter → combinations: 12C2 = 12! / (2!·10!) = 66.
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Q9.Geometry & MensurationFind the distance between (0, -5) and (3, -1).
Show answer & explanation
Answer: C — 5
Distance = √((Δx)² + (Δy)²) = √(3² + 4²) = 5.
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Q10.AlgebraFind the sum of the first 20 terms of the AP 10, 14, 18, …
Show answer & explanation
Answer: D — 960
Sₙ = n/2 × [2a + (n − 1)d] = 20/2 × [20 + 76] = 960.
About Gaokao-style Maths
Gaokao-style Mathematics practice — conducted by Practice in the style of China’s National College Entrance Examination; not affiliated. Practice in the style of the maths paper of China’s university entrance exam: functions, sequences, probability and geometry.
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)).
- Gaokao-style Maths mock test — 25 timed questions.
Gaokao-style 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) |