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HKDSE Mathematics Paper 2 Mock Paper (2027): 30 Multiple-Choice Questions with Answers
TUTORZONE ORIGINAL MOCK PAPER · HKDSE MATHEMATICS PAPER 2
Written to the HKEAA 2027 framework: Paper 2 is multiple-choice, 35%, 1 hour 15 minutes, with Section A carrying two-thirds of the paper mark and Section B one-third. This paper has 30 questions (20 in A, 10 in B) with answers and explanations for every item, ready to sit under time.
What is in HKDSE Mathematics Paper 2?
Direct answer: Paper 2 is multiple-choice, 35% of the subject in 1 hour 15 minutes, all questions compulsory, with Section A carrying two-thirds of the paper mark and Section B one-third per the HKEAA framework. There is no SBA; Paper 1 conventional questions are the other 65%.
Assessment at a glance (2027)
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Section A | Questions carrying two-thirds of the paper mark; foundation topics of the Compulsory Part and S1-S3 | 約 2/3 | 45-48 min |
| Section B | Questions carrying one-third of the paper mark; Compulsory Part plus foundation and non-foundation S1-S3 | 約 1/3 | 25-27 min |
Thirty questions in 75 minutes is about 1.5 minutes each, so skipping fast is the core skill: three minutes on one item costs you two others. Mark answers straight onto the answer sheet rather than transcribing twice.
How this paper was built
This is a TutorZone original mock paper: the questions were written to the 2027 framework’s structure (Section A two-thirds, Section B one-third, all multiple-choice) and every answer is our own, not an HKEAA past paper or marking reference.
HKEAA does not publish a fixed question count for Paper 2, so this paper sets its own: 30 questions (20 in Section A, 10 in Section B), proportioned to the paper’s weighting.
Pacing
| Section | Marks | Suggested time | What to do first |
|---|---|---|---|
| Section A | 約 2/3 | 45-48 min (aim 80%+) | 1-1.5 min per item; recall and concept, not long computation |
| Section B | 約 1/3 | 25-27 min plus 5 min checking | Do the ones you know first; flag and skip anything with no route after two minutes |
How should the 75 minutes be split?
Direct answer: 30 questions here: about 45-48 minutes for the 20 in Section A and 25-27 for the 10 in Section B, with 5 minutes to check. The key habit is skipping anything with no route after two minutes – the biggest cause of lost marks is being stuck on one or two items.
Section A: multiple-choice (20 questions, two-thirds of the paper mark)
Aim for 45-48 minutes; about 1 to 1.5 minutes per item.
Question 1
Simplify 2³ × 2⁵ ÷ 2⁴.
A. 64B. 8C. 32D. 16
Question 2
If 3x − 7 = 5x + 3, find x.
A. -2B. 2C. -5D. 5
Question 3
Factorise x² − 9.
A. (x − 9)(x + 1)B. (x − 3)²C. (x + 3)²D. (x − 3)(x + 3)
Question 4
An item costs $80. After a 25% increase, what is the price?
A. $95B. $100C. $105D. $120
Question 5
A car covers 150 km in 2.5 hours. Find its average speed.
A. 60 km/hB. 80 km/hC. 50 km/hD. 75 km/h
Question 6
Simplify (a³b⁻²)².
A. a⁶b⁴B. a⁹b⁻⁴C. a⁵b⁻⁴D. a⁶b⁻⁴
Question 7
A line passes through (2, 1) and (6, 9). Find its gradient.
A. 8B. 1/2C. 2D. 4
Question 8
A circle has radius 5 cm. Find its area in terms of π.
A. 25π cm²B. 20π cm²C. 10π cm²D. 50π cm²
Question 9
A fair die is thrown once. Find the probability of a prime number.
A. 1/2B. 1/3C. 1/6D. 2/3
Question 10
Find the median of 3, 7, 9, 12, 14.
A. 8B. 9C. 12D. 10
Question 11
Find the value of sin 30° + cos 60°.
A. 1B. 3/4C. 1/2D. 2
Question 12
An arithmetic sequence has first term 5 and common difference 3. Find the 10th term.
A. 26B. 35C. 32D. 29
Question 13
Solve 2x + 3 > 11.
A. x > 4B. x > 7C. x < 7D. x < 4
Question 14
Solve x + y = 10 and x − y = 4.
A. x = 3, y = 7B. x = 7, y = 3C. x = 6, y = 4D. x = 8, y = 2
Question 15
Find each interior angle of a regular pentagon.
A. 108°B. 120°C. 100°D. 110°
Question 16
A sector has radius 6 cm and angle 120°. Find its arc length in terms of π.
A. 12π cmB. 4π cmC. 2π cmD. 6π cm
Question 17
Five numbers have a mean of 12. Find their sum.
A. 72B. 60C. 24D. 48
Question 18
Convert 0.0045 km into cm.
A. 4 500 cmB. 450 cmC. 0.45 cmD. 45 cm
Question 19
Solve x² − 5x + 6 = 0.
A. x = 2 或 3B. x = −1 或 −6C. x = −2 或 −3D. x = 1 或 6
Question 20
Find the value of log₁₀ 1000.
A. 100B. 2C. 10D. 3
Section B: multiple-choice (10 questions, one-third of the paper mark)
Aim for 25-27 minutes; flag and skip anything with no route.
Question 1
A circle has centre (2, −1) and radius 5. Find its equation.
A. x² + y² + 4x − 2y − 20 = 0B. x² + y² − 4x + 2y − 25 = 0C. x² + y² − 4x + 2y − 20 = 0D. x² + y² − 2x + y − 25 = 0
Question 2
Two fair dice are thrown. Find the probability that the total is 7.
A. 1/9B. 5/36C. 1/6D. 7/36
Question 3
Find the distance between (1, 2) and (4, 6).
A. 2.6457513110645907B. 6C. 7D. 5
Question 4
y varies directly as x², and y = 8 when x = 2. Find y when x = 3.
A. 24B. 12C. 27D. 18
Question 5
Solve 2^(x + 1) = 32.
A. 6B. 5C. 4D. 3
Question 6
Solve log₂(x + 3) = 4.
A. 13B. 11C. 19D. 16
Question 7
From A the elevation of a tower is 45°; after walking 20 m towards it to B it is 60°. Find the height (3 s.f.).
A. 52.3B. 71.0C. 47.3D. 42.3
Question 8
One angle of a cyclic quadrilateral is 110°. Find the opposite angle.
A. 90°B. 70°C. 110°D. 55°
Question 9
Find the standard deviation of 4, 7, 7, 10 (3 s.f.).
A. 1.5B. 3.0C. 2.0D. 2.12
Question 10
Two similar solids have surface areas in the ratio 4 : 9. Find the ratio of their volumes.
A. 2 : 3B. 4 : 9C. 8 : 27D. 16 : 81
Where are the answers, and is there an explanation?
Direct answer: every question is followed by an answer-and-explanation block giving the correct option, its value, and the one-line reason (for example: same base, so add and subtract the indices). That lets you tag each error as conceptual or arithmetic.
Section A answers and explanations
Question 1
Answer: D (16) Same base: add and subtract the indices, 3 + 5 − 4 = 4.
Question 2
Answer: C (-5) Collect terms: −7 − 3 = 5x − 3x → −10 = 2x.
Question 3
Answer: D ((x − 3)(x + 3)) Difference of two squares: a² − b² = (a − b)(a + b).
Question 4
Answer: B ($100) 80 × 1.25 = 100.
Question 5
Answer: A (60 km/h) 150 ÷ 2.5 = 60 (in km/h).
Question 6
Answer: D (a⁶b⁻⁴) Multiply the indices: a^(3×2) b^(−2×2) = a⁶b⁻⁴.
Question 7
Answer: C (2) (9 − 1) ÷ (6 − 2) = 8 ÷ 4.
Question 8
Answer: A (25π cm²) πr² = π × 5² = 25π.
Question 9
Answer: A (1/2) The primes are 2, 3 and 5 → 3/6 = 1/2.
Question 10
Answer: B (9) Already ordered, 5 values, so the median is the 3rd.
Question 11
Answer: A (1) sin 30° = cos 60° = 1/2, so the sum is 1.
Question 12
Answer: C (32) T₁₀ = 5 + (10 − 1) × 3 = 32.
Question 13
Answer: A (x > 4) 2x > 8 → x > 4 (dividing by a positive keeps the direction).
Question 14
Answer: B (x = 7, y = 3) Adding the two equations gives 2x = 14.
Question 15
Answer: A (108°) (5 − 2) × 180° ÷ 5 = 108°.
Question 16
Answer: B (4π cm) Arc = 120/360 × 2π × 6 = 4π.
Question 17
Answer: B (60) Sum = mean × count = 12 × 5.
Question 18
Answer: B (450 cm) 0.0045 × 1 000 = 4.5 m; 4.5 × 100 = 450 cm.
Question 19
Answer: A (x = 2 或 3) (x − 2)(x − 3) = 0.
Question 20
Answer: D (3) 10³ = 1000.
Section B answers and explanations
Question 1
Answer: C (x² + y² − 4x + 2y − 20 = 0) (x − 2)² + (y + 1)² = 25 expands to x² + y² − 4x + 2y + 5 − 25 = 0.
Question 2
Answer: C (1/6) Six of the 36 outcomes give 7 → 1/6.
Question 3
Answer: D (5) √(3² + 4²) = √25.
Question 4
Answer: D (18) y = kx², 8 = 4k → k = 2; at x = 3, y = 2 × 9 = 18.
Question 5
Answer: C (4) 32 = 2⁵ → x + 1 = 5.
Question 6
Answer: A (13) x + 3 = 2⁴ = 16 → x = 13.
Question 7
Answer: C (47.3) h cot 45° − h cot 60° = 20 → h = 20 ÷ (1 − 1/√3) ≈ 47.3.
Question 8
Answer: B (70°) Opposite angles of a cyclic quadrilateral are supplementary.
Question 9
Answer: D (2.12) Mean 7; variance = (9 + 0 + 0 + 9) ÷ 4 = 4.5 → s.d. ≈ 2.12.
Question 10
Answer: C (8 : 27) Area ratio = (linear ratio)²; 4 : 9 → 2 : 3, so volumes are 8 : 27.
What level should Paper 2 practice reach?
Direct answer: finish inside 75 minutes with 80%+ correct. Three layers: make formulas and concepts reflexive; train elimination and substitution so many items need no full computation; then train pace down to 1.5 minutes per item.
Where these marks are usually lost
| Mistake | What it looks like | What it costs | Instead |
|---|---|---|---|
| Three minutes on one item | “Let me try once more” | It costs the two items behind it; Paper 2 is a speed paper | No route after two minutes: flag, skip, return |
| Working on the question paper | Computing on the stem | Transcription errors and double the time | One key step on rough paper, answer straight to the sheet |
| Ignoring the options | Full working every time | MC allows substitution, estimation and elimination | Read the options first: many items only need a range or a substitution |
How to use this paper
First sit: no references, full 75 minutes, no formula sheet.
Mark it: separate “did not know” from “did not have time” – the first needs topic work, the second needs skip-and-estimate training.
Second sit: finish the same paper inside 60 minutes with 80%+ correct.
What should I do after this paper?
Direct answer: split the errors into did not know (go back to the topic, then its past-paper questions) and did not have time (train skipping and estimation, and start with your strongest). Roughly 70% of Paper 2 improvement usually comes from the second group.
FAQ
Does Paper 2 really have 30 questions?
No. HKEAA does not publish a fixed count; these 30 are proportioned to the 2:1 section weighting and exist to train pace.
Is a calculator allowed?
Yes – electronic calculators and mathematical drawing instruments are permitted. Many Paper 2 items are still faster by concept or estimation.
How do Papers 1 and 2 split?
Paper 1 conventional questions are 65% and Paper 2 multiple-choice 35%; together 100%, with no SBA.
Official references
| Resource | What to check |
|---|---|
| HKEAA 2027 HKDSE Mathematics Assessment Framework | Confirm Paper 2’s 35%, 1 h 15 min and Section A’s two-thirds share |
| https://www.tutorzone.com.hk/en-dse-maths-paper-2-mc-drill-guide/ | Paper 2 (MC) drilling guide: 75 minutes and the speed methods |
| https://www.tutorzone.com.hk/en-dse-maths-paper-1-mock-2027/ | Paper 1 (long questions) mock paper: full 105 marks |
Related: practice area · Paper 1 mock · IGCSE 0580 mock
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