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Gaokao-style Maths Mock Test
A timed 25-question mock for the Gaokao-style Mathematics practice 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.
Gaokao-style 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: x² + 2x − 48 = 0
Answer: D — -8, 6
Find two roots with sum -2 and product -48: -8 and 6. So x² + 2x − 48 = (x + 8)(x − 6) = 0.
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Q2.Probability & Combinatorics4 fair coins are tossed. What is the probability of at least one head?
Answer: A — 15/16
P(no head) = (1/2)^4 = 1/16; P(at least one head) = 1 − 1/16 = 15/16.
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Q3.Geometry & MensurationFind the area of a circle of radius 3 cm.
Answer: C — 28.27 cm²
Using πr² with π = 3.1416: 28.27 cm².
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Q4.AlgebraFind the sum of the first 13 terms of the AP 17, 22, 27, …
Answer: B — 611
Sₙ = n/2 × [2a + (n − 1)d] = 13/2 × [34 + 60] = 611.
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Q5.Probability & CombinatoricsA card is drawn from a well-shuffled deck of 52. What is the probability that it is a heart?
Answer: C — 1/4
There are 13 such cards in 52, so P = 13/52 = 1/4.
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Q6.Geometry & MensurationFind the area of a right triangle with legs 8 cm and 15 cm.
Answer: C — 60 cm²
Area = ½ × base × height = ½ × 8 × 15 = 60 cm².
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Q7.AlgebraSolve: x² + 6x + 9 = 0
Answer: A — -3, -3
Find two roots with sum -6 and product 9: -3 and -3. So x² + 6x + 9 = (x + 3)(x + 3) = 0.
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Q8.Probability & CombinatoricsIn how many ways can a committee of 2 be chosen from 9 people?
Answer: A — 36
Order does not matter → combinations: 9C2 = 9! / (2!·7!) = 36.
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Q9.Geometry & MensurationFind the area of a right triangle with legs 6 cm and 8 cm.
Answer: D — 24 cm²
Area = ½ × base × height = ½ × 6 × 8 = 24 cm².
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Q10.AlgebraFind the sum of the first 10 terms of the AP 11, 15, 19, …
Answer: A — 290
Sₙ = n/2 × [2a + (n − 1)d] = 10/2 × [22 + 36] = 290.
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Q11.Probability & CombinatoricsTwo fair dice are thrown. What is the probability that the sum is 7?
Answer: C — 1/6
6 of the 36 equally likely outcomes give a sum of 7, so P = 6/36 = 1/6.
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Q12.Geometry & MensurationFind the volume of a cylinder with radius 8 cm and height 10 cm.
Answer: C — 2,010.62 cm³
Using πr²h with π = 3.1416: 2,010.62 cm³.
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Q13.AlgebraFind the sum of the first 9 terms of the AP 6, 15, 24, …
Answer: C — 378
Sₙ = n/2 × [2a + (n − 1)d] = 9/2 × [12 + 72] = 378.
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Q14.Probability & CombinatoricsIn how many ways can a committee of 3 be chosen from 7 people?
Answer: A — 35
Order does not matter → combinations: 7C3 = 7! / (3!·4!) = 35.
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Q15.Geometry & MensurationFind the volume of a sphere of radius 8 cm.
Answer: D — 2,144.66 cm³
Using (4/3)πr³ with π = 3.1416: 2,144.66 cm³.
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Q16.AlgebraFind log₃ 81.
Answer: B — 4
log_3(81) asks “3 to what power gives 81?” → 3^4 = 81, so the answer is 4.
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Q17.Probability & CombinatoricsIn how many ways can the letters of the word PLANET be arranged?
Answer: B — 720
All 6 letters are different, so arrangements = 6! = 720.
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Q18.Geometry & MensurationFind the area of a right triangle with legs 7 cm and 24 cm.
Answer: D — 84 cm²
Area = ½ × base × height = ½ × 7 × 24 = 84 cm².
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Q19.AlgebraSolve: x² + 16x + 63 = 0
Answer: B — -9, -7
Find two roots with sum -16 and product 63: -9 and -7. So x² + 16x + 63 = (x + 9)(x + 7) = 0.
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Q20.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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Q21.Geometry & MensurationA right triangle has legs 7 cm and 24 cm. Find the hypotenuse.
Answer: C — 25 cm
By Pythagoras, hypotenuse = √(7² + 24²) = √625 = 25.
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Q22.AlgebraSolve: x² + 4x − 12 = 0
Answer: B — -6, 2
Find two roots with sum -4 and product -12: -6 and 2. So x² + 4x − 12 = (x + 6)(x − 2) = 0.
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Q23.Probability & CombinatoricsTwo fair dice are thrown. What is the probability that the sum is 9?
Answer: C — 1/9
4 of the 36 equally likely outcomes give a sum of 9, so P = 4/36 = 1/9.
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Q24.Geometry & MensurationFind the volume of a cylinder with radius 5 cm and height 20 cm.
Answer: A — 1,570.8 cm³
Using πr²h with π = 3.1416: 1,570.8 cm³.
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Q25.AlgebraFind the sum of the first 22 terms of the AP 13, 14, 15, …
Answer: C — 517
Sₙ = n/2 × [2a + (n − 1)d] = 22/2 × [26 + 21] = 517.
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 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.
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) |