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Gaokao-style Maths Algebra Questions
Practise algebra (mathematics) for the Gaokao-style Mathematics practice: 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.
Algebra practice
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Q1.Solve: x² + 4x − 21 = 0
Show answer & explanation
Answer: A — -7, 3
Find two roots with sum -4 and product -21: 3 and -7. So x² + 4x − 21 = (x − 3)(x + 7) = 0.
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Q2.Solve: x² + 8x + 12 = 0
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Answer: C — -6, -2
Find two roots with sum -8 and product 12: -6 and -2. So x² + 8x + 12 = (x + 6)(x + 2) = 0.
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Q3.Find log₃ 81.
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Answer: C — 4
log_3(81) asks “3 to what power gives 81?” → 3^4 = 81, so the answer is 4.
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Q4.Solve: x² + 8x + 7 = 0
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Answer: A — -7, -1
Find two roots with sum -8 and product 7: -1 and -7. So x² + 8x + 7 = (x + 1)(x + 7) = 0.
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Q5.Find the sum of the first 14 terms of the AP 5, 7, 9, …
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Answer: D — 252
Sₙ = n/2 × [2a + (n − 1)d] = 14/2 × [10 + 26] = 252.
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Q6.Find log₃ 243.
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Answer: B — 5
log_3(243) asks “3 to what power gives 243?” → 3^5 = 243, so the answer is 5.
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Q7.Solve: x² + 6x − 16 = 0
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Answer: C — -8, 2
Find two roots with sum -6 and product -16: 2 and -8. So x² + 6x − 16 = (x − 2)(x + 8) = 0.
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Q8.Find log₅ 25.
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Answer: B — 2
log_5(25) asks “5 to what power gives 25?” → 5^2 = 25, so the answer is 2.
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Q9.Solve: x² − 7x − 8 = 0
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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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Q10.Find log₂ 16.
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Answer: A — 4
log_2(16) asks “2 to what power gives 16?” → 2^4 = 16, so the answer is 4.
How to approach algebra questions
Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution. For simultaneous equations, elimination is usually faster than substitution under time pressure.
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) |