Mathematics Compulsory Part is one of the four HKDSE core subjects every Hong Kong secondary school student must sit, alongside Chinese Language, English Language and Citizenship & Social Development. For most JUPAS programmes, the Mathematics grade is just as load-bearing as English: a Level 2 is the bare minimum to keep your “3322” alive, and competitive degrees in business, engineering, science and medicine routinely demand Level 4 or Level 5. This guide walks 2026 candidates through what Paper 1 and Paper 2 actually look like, how marks are distributed, which topics carry the most weight, and how to plan a focused revision cycle without wasting time on low-yield drills.

Why the Compulsory Part decides so much of your JUPAS scorecard

Before diving into format, it helps to understand the leverage Mathematics carries in admission. Almost every Hong Kong undergraduate programme uses Mathematics as one of the “best 5” or “best 4+2” subjects in its scoring formula. Engineering, computing, actuarial science, finance, architecture, medicine, dentistry and the natural sciences typically weight Mathematics by 1.0 or higher; some quantitative programmes (e.g. HKUST Quantitative Finance, CUHK Risk Management Science) apply a x1.5 or x2.0 multiplier. That means each level you climb in Mathematics can be worth 5 to 14 admission points depending on the formula, often making the difference between Band A interview and rejection.

The Compulsory Part itself is what HKEAA calls a “Category A” subject. The grade you receive is on the standard 1-to-5** scale. The Extended Part Module 1 (Calculus and Statistics) and Module 2 (Algebra and Calculus) are separate Category A subjects with their own grades and are not the focus of this guide.

Paper 1: Long-question paper

Paper 1 carries 65% of the total subject mark and is sat over 2 hours 15 minutes. It is divided into three sections, all of which are compulsory.

Section A(1) — roughly 24 marks, made up of about eight to nine short questions. These target the Foundation Topics from the Junior Secondary curriculum (S1-S3) plus easy Compulsory Part items: directed numbers, percentages, simple algebraic manipulation, basic geometry and the simpler trigonometric ratios. Most students who attended class regularly should be able to clear A(1) cleanly; losing marks here is what separates a Level 3 from a Level 4.

Section A(2) — roughly 35 marks, about four to five medium-length questions covering core Compulsory Part topics: functions, polynomials, equations and inequalities, coordinate geometry, mensuration and basic statistics. A(2) is where the Level 4 boundary lives. The questions usually have three to four sub-parts, each scaffolding into the next.

Section B — roughly 35 marks, three to four extended questions designed to discriminate the top end (Level 5, 5*, 5**). Expect locus problems, 3-D geometry with multiple cross-sections, harder probability, complex sequences and series, and proof-style coordinate-geometry items. Section B questions are often worth 12 to 14 marks each and require a clear written argument, not just a numerical answer.

Marks are awarded on a method-then-answer basis. HKEAA’s marking scheme typically allots M-marks for correct method, A-marks for correct intermediate or final answers, and follow-through (ft) marks if a downstream answer is correct based on a wrong earlier value. This is why showing every step matters: a candidate who writes only “x = 3.7” with no working can lose two-thirds of the mark even if the answer is right.

Time budget for Paper 1

A workable allocation for the 135 minutes:

• Section A(1): 25 minutes
• Section A(2): 50 minutes
• Section B: 55 minutes
• Checking / re-attempting: 5 minutes

Many candidates fail to finish Section B because they over-spend on a single A(2) question they cannot crack. Discipline yourself to skip and return — Section B’s first sub-parts are usually easier than late A(2) sub-parts.

Paper 2: Multiple-choice paper

Paper 2 carries 35% of the subject mark and is sat over 1 hour 15 minutes. There are 45 questions, all multiple choice with four options (A/B/C/D), and all carry equal marks (1 each, 45 total before scaling).

The paper splits into two sections:

• Section A — 30 questions on Foundation Topics and the easier Compulsory Part topics.
• Section B — 15 questions targeting the harder, more synthetic Compulsory Part material, including bearings, more demanding statistics, harder sequences, and “trick” probability or counting items.

There is no negative marking. You must answer every question — leaving blanks is throwing away free expected value.

Paper 2 strategy that actually scales

Multiple choice rewards three skills that are different from Paper 1:

1. Backward substitution. Instead of solving an equation, plug each option into the equation and see which works. For “find the roots of 2x² - 5x - 3 = 0”, testing the four candidate values takes 15 seconds versus 60 seconds of factoring.
2. Numerical sanity checks. Before committing to an answer involving probability or percentage change, ask whether the result is even physically possible (probabilities cannot exceed 1, a percentage decrease cannot give a value larger than the original).
3. Special-value testing. For algebraic identity questions, plug in x = 0, 1, or -1 to eliminate options quickly.

Aim for an average of 100 seconds per question. Front-load Section A — most candidates can clear all 30 questions in 35 minutes, leaving 40 minutes for the 15 harder Section B items.

Topic-by-topic syllabus map

The Compulsory Part curriculum groups all topics under three Strands: Number and Algebra, Measures/Shape and Space, and Data Handling. Below is a working frequency map based on the 2014-2025 past papers.

Number and Algebra (≈ 40-45% of total marks)

• Quadratic equations and functions — appears in nearly every Paper 1, both A(2) and B.
• Functions and graphs (transformations, vertex form, completing the square).
• Exponential and logarithmic functions — usually one Paper 1 question on log laws / change of base, plus 2-3 Paper 2 items.
• Variations (direct, inverse, joint, partial) — at least one MC question every year.
• Sequences (arithmetic and geometric, sums to infinity).
• Inequalities and linear programming — one B-section question is common.
• More about polynomials (factor theorem, remainder theorem, division).

Measures, Shape and Space (≈ 35-40%)

• Coordinate geometry of straight lines and circles — heavy weight, often the longest Section B question.
• Locus — appears in roughly 60% of recent papers.
• Mensuration (3-D solids, similar figures, scale-factor laws for area and volume).
• Trigonometry — sine rule, cosine rule, area formula, 3-D problems with bearings and angles of elevation/depression.
• Properties of circles (chords, tangents, cyclic quadrilaterals).
• Transformations and tessellation — lower yield, mostly in Paper 2.

Data Handling (≈ 15-20%)

• Statistics — measures of central tendency, dispersion, box-and-whisker plots, standard deviation, weighted mean.
• Probability — including conditional probability, with-replacement vs without-replacement, and tree diagrams.
• Permutations and combinations — usually one Paper 2 item, occasionally embedded inside a Paper 1 probability question.

If you have limited revision time, the highest-yield topics by past-paper frequency are: quadratic functions, coordinate geometry of circles, 3-D trigonometry, sequences, and probability. Weak spots in any of these will cap your grade at Level 3.

Level cut-offs and what they mean for university entry

The 2024 HKEAA grading thresholds (as a percentage of total marks) ran approximately as follows for Mathematics Compulsory Part. Year-on-year drift is usually within ±3 percentage points:

• Level 2: ~30%
• Level 3: ~44%
• Level 4: ~58%
• Level 5: ~72%
• Level 5*: ~80%
• Level 5**: ~87%

Practical implications:

• To meet the 3322 baseline (the minimum entry to a JUPAS-funded degree), you need Level 2 in Math — about 30% of the total mark.
• To be competitive for business, social science and most arts programmes, target Level 4 — that’s roughly 58% of the total.
• For engineering, computing, science, architecture, target Level 5 — ~72%.
• For medicine, dentistry, BBA + Law double degrees, quantitative finance, target Level 5* or 5** — 80% and above.

Translating to raw marks: Paper 1 + Paper 2 together carry around 150 raw marks (after scaling by HKEAA). To hit Level 5 you need to consistently score in the 108-120 raw mark range across mock exams.

Calculator policy: what is allowed in 2026

Only calculators on the HKEAA-approved list may be used. The most common compliant models in Hong Kong schools are the Casio fx-50FH II, Casio fx-3650P II / fx-3950P, Sharp EL-509W series, and the Citizen SR-260N. Anything graphing, programmable, or capable of symbolic algebra (CAS) is banned and will trigger a Category 1 irregularity report.

Before the exam:

• Replace the battery in February.
• Reset the calculator (SHIFT + 9 + 3 + = on the Casio fx-50FH II) to clear any stored data, otherwise an invigilator can disqualify you.
• Tape over any maker’s instructions printed on the lid if your school requires it (rules vary by school but HKEAA itself only requires the model itself to be approved).

Six common pitfalls that cost grades

1. Memorising methods without understanding why. Many candidates can solve a textbook quadratic but freeze when the same skill is wrapped inside a coordinate geometry question. Drill mixed-topic past papers, not chapter exercises.
2. Skipping Paper 2 multiple choice in revision. MC is treated as “easy” and ignored. But losing 10 of the 45 Paper 2 marks shifts your subject score by roughly 7 percentage points — enough to drop a level.
3. Not writing units. Coordinate geometry and mensuration answers without correct units (cm, cm², cm³) are penalised one A-mark per question.
4. Rounding too early. Internal calculations should be carried to 4 or 5 significant figures and only the final answer rounded to 3 s.f. (unless the question specifies otherwise). Premature rounding in trig is the most common cause of “off by 0.1” errors.
5. Ignoring locus questions. Locus appears regularly but few students drill it. A clean Locus question is often worth 4-6 easy marks.
6. Misreading “give your answer in surd form” or “leave answer in terms of π”. Decimal approximations when surds are required cost a full A-mark.

A six-month revision plan (November to April)

This plan assumes you start in early November of S6 with all topics already taught at school. Adjust earlier if you are behind on syllabus content.

November — diagnostic and gap-filling. Sit one full Paper 1 + Paper 2 from 2022 under timed conditions. Mark it strictly. List the topics where you lost more than 30% of available marks. Spend the rest of November rebuilding those topics from textbook level upward.

December — topic mastery, harder problems. Work through one chapter per week. For each chapter, do the textbook exercise, then 5 to 10 past Section A(2) questions tagged to that topic. Target topics: quadratic functions, coordinate geometry, polynomials, sequences, trigonometry.

January — harder Section B and Paper 2 timed sets. Move to Section B questions for your strongest topics first (you want to lock in those marks). Do two Paper 2s per week under 75-minute conditions.

February — full mock papers. One full Paper 1 + Paper 2 per week, alternating between recent papers (2023, 2024, 2025) and older papers (2017-2019). Mark using the official HKEAA marking scheme — never a “model answer” book that paraphrases. Track your score weekly; you should see steady upward drift.

March — error log review and final-sprint. Compile every mistake from your past mock attempts into a single error log organised by topic. Re-attempt every wrong question without looking at solutions. Continue with one mock per week.

Easter break — pacing and exam-day rehearsal. Sit two full mocks back-to-back to simulate exam stamina. Practise the calculator drill, the marking-scheme handwriting style, and the time budget. Review question wording vocabulary: “express”, “find the exact value”, “hence”, “deduce”.

What is new for 2026

The Compulsory Part curriculum itself has not changed since the 2014 revision; the 2026 paper format follows the same structure as 2025. However, two operational notes matter for 2026 candidates:

• HKEAA continues to enforce the post-pandemic seating layout in most centres, with calculators inspected at the desk. Arrive at least 30 minutes early.
• The front-cover instructions now explicitly remind candidates that graphical answers must be drawn on the supplied answer book, not the question paper. Bring two pencils and a 30 cm ruler.

Bottom line

Mathematics Compulsory Part is the most learnable of the four DSE core subjects. Unlike Chinese or English, where stylistic intuition compounds over years, almost every Math mark is mechanically recoverable through past-paper drilling, error logging, and targeted topic review. A student who starts a structured plan in November and sits at least 12 full mocks before the exam can realistically move from Level 3 to Level 5. The subject rewards consistency, not flair.

For revision resources, prioritise the official HKEAA past papers and marking schemes (free download from the HKEAA website) over commercial mock papers, which often contain off-syllabus questions or marking rubrics that do not match HKEAA conventions.