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HKDSE Maths Past Paper Drilling Guide: By Year or By Topic, and the Drill Order from S4 to S6
TUTORZONE EXAM DRILL GUIDE · HKDSE MATHEMATICS (COMPULSORY PART)
HKDSE Mathematics is not won by doing the most papers; it is won by knowing exactly what each paper has to show. Everything below is taken from the HKEAA 2027 assessment framework: Paper 1 is 65%, Paper 2 is 35%, and there is no school-based assessment.
How many papers does HKDSE Mathematics (Compulsory Part) have, and what are they worth?
Direct answer: the Compulsory Part is assessed by two compulsory papers worth 100% in total. Paper 1 (conventional questions) is 65% and lasts 2 hours 15 minutes (2¼ hours); Paper 2 (multiple-choice questions) is 35% and lasts 1 hour 15 minutes (1¼ hours). There is no school-based assessment in Mathematics, and candidates may use an electronic calculator and mathematical drawing instruments. The Extended Part modules M1 (Calculus and Statistics) and M2 (Algebra and Calculus) are separate subjects, each assessed by a single paper worth 100% and lasting 2 hours 30 minutes.
Assessment framework at a glance: 2027 HKDSE Mathematics
| Component | Content | Weighting | Duration |
|---|---|---|---|
| Public exam · Paper 1 | Conventional questions; all questions must be attempted | 65% | 2 h 15 min |
| Public exam · Paper 2 | Multiple-choice questions; all questions must be attempted | 35% | 1 h 15 min |
| School-based assessment | Not applicable to Mathematics | — | — |
| Extended module M1 | Calculus and Statistics: one paper (Section A 50 marks short, B 50 marks long) | 100% | 2 h 30 min |
| Extended module M2 | Algebra and Calculus: one paper (Section A 50 marks short, B 50 marks long) | 100% | 2 h 30 min |
The Compulsory Part and an Extended module are separate subjects. A strong M2 performance does nothing for the Compulsory Part grade, so the two must be drilled separately.
Put differently: Paper 1 alone carries two-thirds of the grade, yet it is only one hour longer than Paper 2 (135 minutes against 75). That is why running out of time in Paper 2 is the single most common way candidates lose marks, while writing slowly in Paper 1 usually costs only the tail-end marks.
Paper 1 (conventional questions): three 35-mark arenas
Under the framework, Paper 1 is divided into two sections and three parts, all compulsory, with a total of 105 marks:
| Part | Content assessed | Marks | Questions | Role |
|---|---|---|---|---|
| Section A(1) | Foundation Topics of the Compulsory Part and of the S1-S3 curriculum | 35 | 8–11 | Easiest marks — must not be lost |
| Section A(2) | Compulsory Part with foundation and non-foundation S1-S3 topics | 35 | 4–7 | Designed to reward fluency |
| Section B | Compulsory Part with foundation and non-foundation S1-S3 topics | 35 | 4–7 | The grade separator |
All three parts are worth the same, but they test different things. A(1) tests whether you can compute correctly, A(2) whether you are fluent, and Section B whether you can decompose a problem. So mark your practice scripts in three separate 35-mark blocks. Candidates who only ever know ‘I got 60’ have no idea whether the missing 45 marks went on careless slips in A(1) or on questions in Section B they never started.
Paper 2 (multiple-choice): two-thirds foundation, one-third non-foundation
| Part | Content assessed | Share of the paper |
|---|---|---|
| Section A | Foundation Topics of the Compulsory Part and of the S1-S3 curriculum | two-thirds |
| Section B | Compulsory Part with foundation and non-foundation S1-S3 topics | one-third |
How many questions are there in HKDSE Maths Paper 2?
Direct answer: the HKEAA 2027 HKDSE Mathematics Assessment Framework states only that Paper 2 has a Section A carrying two-thirds of the paper mark (foundation topics) and a Section B carrying one-third (with non-foundation topics), that all questions are multiple-choice, and that all questions must be attempted. It does not publish a question count, so a fixed figure such as ’45 questions’ is not part of the framework. Pace your practice by minutes per section, not by a memorised question total.
Common mistake: treating Paper 2 as overtime after Paper 1. It is only 35% of the grade, but it must clear the same foundation content in 75 minutes — roughly three times the time pressure per question. If you never time yourself on Paper 2 in practice, you will not finish it in the hall.
The myth: drilling more papers is not the same as being prepared
| Myth | What it looks like | What actually happens | Instead |
|---|---|---|---|
| Drilling without marking | Finish a paper, check answers, nod at the solutions | The same conceptual error survives for three months | For every wrong item write down why: concept, arithmetic, or misread condition |
| Full papers too early | An S4 student sits a full 2 h 15 min paper in week one | A(1) gets done, Section B is blank, morale drops, little is learnt | Drill by topic until fluent, then graduate to full papers |
| Never timing yourself | Think slowly, write only when sure | In the hall you cannot produce answers you can do at leisure | Run a timer on every drill, Paper 2 included |
The value of a practice paper is not that it is finished; it is that each one buys you a clear diagnosis: which question type is weak, which error keeps repeating, and what to improve deliberately next time. If you cannot name those three things afterwards, the paper was wasted.
Drill order: by topic first, then by year
| Approach | Best period | Advantage | Limitation |
|---|---|---|---|
| By topic | S4 to mid-S5, and whenever a topic is first taught | Quickly exposes whether a topic is genuinely understood; errors cluster and diagnose well | Does not train pacing or the stamina of a full paper |
| By year | Late S5 through S6 | Trains pacing, endurance and question selection under exam conditions | Errors scatter, so a single topic’s weakness is harder to see |
The recommended order in one line: drill by topic to build the base, then by year to train pace, then return to by topic in the final 3–4 weeks to plug the holes. Doing it the other way round — years first — is the most common and most wasteful sequence.
How should you split your time between drilling by topic and drilling by year?
Direct answer: divide the drilling period into three blocks. Block one (roughly 6–8 weeks) is 100% by topic, working 10–15 years of the same question type back to back. Block two (roughly 3–4 weeks) switches to by year, one timed Paper 1 and one timed Paper 2 each week. The final 3–4 weeks return to by topic, targeting only the two or three topics flagged repeatedly in your error log. Timed full papers should be no more than one third of total drilling time.
A 12-week drilling timetable for S4, S5 and S6
A 12-week plan for the S6 year, assuming 6–8 hours of drilling per week:
| Week | Phase | Paper 1 (65%) | Paper 2 (35%) | Weekly check |
|---|---|---|---|---|
| 1–2 | By topic: foundation topics | Topic-by-topic A(1)-level questions, two topics a week | The same topics in MC, 1.5 minutes per question | Do the same error types recur? |
| 3–5 | By topic: algebra and functions | Quadratics, indices and logs, sequences, inequalities | As above, start logging Section A completion time | Can you recall the formulas unaided? |
| 6–7 | By topic: geometry and trigonometry | Circle properties, lines and circles, trigonometry, 3-D figures | As above, but without drawing a diagram | Is the habit of sketching reliable? |
| 8 | By topic: statistics and probability | Probability, statistical charts, dispersion | Section B-level MC | Are counting cases classified clearly? |
| 9–10 | By year: timed full papers | One Paper 1 a week, 135 minutes, no formula sheets | One Paper 2 a week, 75 minutes | Trend of A(1), A(2) and B marks |
| 11 | By year: recent papers | Only the latest 3–4 years, full exam conditions | As above; review Section A timing | Still losing marks in the same topic? |
| 12 | Back to by topic: plug holes | Only the topics flagged red in the error log | Only the topics flagged red in the error log | Redo the errors — all correct now? |
Use it properly: the twelve weeks are not a check-list to finish. Keep one hour a week for redoing past errors only, or from week 9 you will find yourself repeating the same batch.
Paper 1: pacing 135 minutes and writing for method marks
Paper 1 gives 135 minutes for 105 marks — about 1.29 minutes per mark, but the three parts cost very different amounts of time. A pacing plan for candidates targeting Level 5 or above:
| Part | Marks | Suggested time | Strategy |
|---|---|---|---|
| Section A(1) | 35 | 35–40 min | Target full marks. 3–4 minutes each: do what you can immediately, skip and return; never get stuck at the start |
| Section A(2) | 35 | 45–50 min | Aim for 28+. Watch for marks lost to skipped working even when the answer is right |
| Section B | 35 | 35–40 min | Start with your two strongest questions; leave a hard one once the key steps are written and go back to check |
| Review | — | 8–10 min | Check units, significant figures, and any sub-part left unanswered |
How do you write for method marks? Markers separate method marks from answer marks. To secure method marks, every decisive step must be visible and followable: define the unknown, set up the equation, state the formula used, show the discriminant or the condition, and only then give the answer. An answer with no working can lose method marks even when the number is right, while complete working with an arithmetic slip usually still collects most of them.
Paper 2: three ways to genuinely save time in 75 minutes
| Method | How | Why it saves time |
|---|---|---|
| Scan before you solve | Spend two minutes reading the whole paper, then start with what you own | Stops hard questions from eating the time of easy ones |
| Back-substitute and estimate | Put answer options back into the question; judge the order of magnitude | Eliminates two or three options without a full computation |
| MC-only techniques | Special values, sketch-and-read, symmetry, unit checking | Legitimately bypasses long algebra in MC (not in Paper 1, where working is required) |
What if you run out of time in HKDSE Maths Paper 2?
Direct answer: split the 75 minutes into three blocks: the first 45–50 minutes for Section A (two-thirds of the paper, foundation topics, and the block you cannot afford to lose); the next 20–25 minutes for Section B; and the final 5 minutes for checking — that the answer sheet has no blanks and every skipped question has been returned to. If a question resists you for more than two minutes, flag it and move on rather than letting it take the time of the foundation questions behind it.
The error log: a three-round drilling method
| Round | What you do | Purpose |
|---|---|---|
| 1. Consolidate | After a topic drill, log every error the same day in three lines: what was wrong, why, and the first step of the correct method | Turns a mistake into something re-readable |
| 2. Timed | Redo the same batch 3–7 days later, against the clock | Tests understanding rather than just-read-the-solution recall |
| 3. Final stretch | In the last 3–4 weeks read only the error log, ordered by frequency; fix anything appearing 3+ times first | Puts limited time where the marks actually leak |
An error log does not need to be beautiful, it needs to be re-readable. One book per subject; on each page put the question or an extract on the left, and three lines on the right: (1) what I got wrong, (2) the first step of the correct method, (3) which topic this belongs to. Reading only the right-hand column is far more efficient than re-doing whole papers.
How many years of past papers should you drill?
| Stage | Suggested allocation | Format |
|---|---|---|
| S4 | Topic by topic, drawing on 2012–2018 papers (stable syllabus, clear question styles) | By topic; untimed first, timed second |
| S5 | Full papers from 2018–2022 plus earlier questions on the same topics | Mostly by topic, with one timed full paper every 3–4 weeks |
| S6 first term | 2019–2024: one Paper 1 and one Paper 2 each week | By year, fully timed |
| S6 final 4–6 weeks | The latest three papers, plus old items from the error log | Exam conditions: no formula sheet, no interruptions |
How many years of HKDSE Maths past papers should you drill?
Direct answer: there is no official number, but measured by topic coverage, working through every HKDSE Mathematics paper from 2012 onwards covers almost all of the topics in the current Compulsory Part. If time is short, the most recent five years must be done properly (recent papers match the current paper structure and emphasis most closely), while earlier years can be raided only for the questions that target your weak topics. The aim is to have seen the same topic set in different ways, not to have completed every paper end to end.
Frequently asked questions
Is there school-based assessment in Mathematics?
No. The Compulsory Part is assessed entirely by public examination: Paper 1 at 65% plus Paper 2 at 35%.
May I use a formula sheet while drilling?
Not for Paper 1 practice. The examination provides some formulas (M2 candidates receive trigonometric formulas), but in the Compulsory Part you must have the common formulas and identities at your fingertips or you will run out of time.
Arithmetic slips are my biggest problem. What helps?
Treat them as a separate topic. Record whether each slip was a sign, a bracket, a unit or a rounding issue, then redo the same question type under time pressure. Sloppy arithmetic usually comes from rushing, not from not knowing.
M1 or M2?
M2 leans on algebra and calculus and is often chosen by strong mathematics students heading for engineering or science; M1 leans on statistics and calculus and sits closer to business and social science requirements. Both are separate subjects, one paper of 2 hours 30 minutes worth 100%.
Is S4 too early to start past papers?
No, but at S4 the point is to consolidate topics by drilling by topic. Save full timed papers for late S5, when they pay off much more.
Official references
| Resource | What to use it for |
|---|---|
| HKEAA 2027 HKDSE Mathematics Assessment Framework | Check the 65% / 35% split, the durations, and the marks and question ranges of each part |
| HKEAA HKDSE subject information | Assessment frameworks, sample papers and examination reports |
| EDB Mathematics Education Key Learning Area | The S4-S6 Curriculum and Assessment Guide and its learning objectives |
| Primary 6 Mathematics mock paper | Rebuild the S1-S3 foundation topics that Paper 1 A(1) and Paper 2 Section A both test |
Related practice and guides: IGCSE Maths 0580 mock paper · DSE exam practice area · HKDSE Mathematics subject guide
Next step: find a tutor / register as a tutor
Students and parents: the hardest step after drilling is telling a conceptual error from a careless one. Tell us the year group, the school and your available times, and TutorZone will match you with a tutor who knows the HKDSE Mathematics papers and marking conventions — try a lesson first, decide afterwards.
Tutors: if you can explain how method marks are earned and turn an error log into a topic diagnosis, parents are looking for you. Register free; you pay only when a match succeeds.
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