DSE Mathematics Syllabus: 18 Units, Papers & M1/M2 Guide

The DSE Mathematics Syllabus is the curriculum framework examined by the Hong Kong Diploma of Secondary Education. It is deliberately split into two parts. The Compulsory Part is the mathematics every candidate must study and be examined on. The Extended Part is optional and sits on top of it, giving students who need heavier mathematical machinery a further module to prove it with.

The Compulsory Part is organised around three strands, and each strand is broken into numbered learning units:

• Number and Algebra (Units 1–9)—the backbone of the subject: quadratic equations in one unknown, functions and graphs, equations of straight lines, more about polynomials, exponential and logarithmic functions, more about equations, variations, and arithmetic and geometric sequences and their summations.
• Measures, Shape and Space (Units 10–14)—measures, shape and space topics such as areas and volumes, coordinate geometry, trigonometry, and the geometry of circles and 3-D figures.
• Data Handling (Units 15–18)—organising and presenting data, measures of central tendency and dispersion, probability, and uses and abuses of statistics.

Together these 18 units carry a suggested total of 250 lesson hours, roughly 10% to 12.5% of the entire senior secondary curriculum. Two further learning units are described alongside them — Further Applications and Inquiry and Investigation — which are treated in the next section because they are structured differently from the numbered topics.

Teachers and tutors plan the whole two-year or three-year sequence around the 18 learning units, so it is worth knowing how much weight each strand really carries in class time and in revision.

Two further learning units complete the Compulsory Part. Further Applications (Unit 19, about 14 suggested hours) asks students to solve more complex real-life and mathematical application problems, looking for information that gives a clue to the solution and exploring different solution strategies or combining different areas of mathematics. The curriculum documents list examples such as simple financial applications including tax and instalment payments; analysing and interpreting data from a survey; investigating Ptolemy’s theorem and Ceva’s theorem and their applications; exploring the relationship between the Fibonacci sequence and the golden ratio; appreciating applications of cryptography; and analysing mathematical games. Inquiry and Investigation (Unit 20, about 10 suggested hours) asks students to discover and construct knowledge through activities, strengthening exploration, communication, thinking and concept formation. The curriculum emphasises that this is not a separate, isolated unit — teachers may use the suggested time for activities inside other units, such as mathematical modelling and STEAM-related tasks.

The Compulsory Part has no school-based assessment. Everything rides on the two written papers, and their weightings decide how revision time should be divided.

The scope of the questions is stated precisely in the assessment framework. Paper 1 Section A draws on the foundation topics of the Compulsory Part plus foundation topics from the S1–S3 mathematics curriculum; Section B covers both foundation and non-foundation topics, which is why Section B is where the distinction between a steady pass and a top grade is usually decided. Paper 2 follows the same logic inside a multiple-choice format: Section A is built on foundation topics, while Section B reaches into the non-foundation topics.

• Paper 1 question scope—Section A is limited to foundation topics of the Compulsory Part and of the S1–S3 curriculum; Section B spans foundation and non-foundation topics, so it is the real testing ground for the harder material.
• Paper 2 question scope—Section A (about two-thirds of the paper) is foundation topics; Section B (about one-third) covers foundation and non-foundation topics. All items are multiple-choice, roughly 45 in total.
• Exam-room conventions—questions will not involve lengthy computation; answers must be reasonably accurate; approved calculators and mathematical drawing instruments may be used; SI and metric units appear where appropriate and candidates should be familiar with the symbols commonly used in mathematics papers.
• No school-based assessment—the two papers together produce the whole subject result. School marks cannot cushion the outcome, which is exactly why the 65% and 35% split should drive the revision timetable.

The Extended Part is an optional addition to the Compulsory Part, made up of two modules. Students may take at most one, and the module result is reported as part of the mathematics subject result.

Module 1 is the better fit when the destination is a statistics-heavy or applied field, and Module 2 when university courses expect calculus and algebra as working tools. Because the choice is reported in the same subject result and cannot be swapped later, it is worth confirming the entry requirements of the programmes a student actually intends to apply for before committing.

The revised senior secondary mathematics curriculum has been rolled out progressively from Secondary 4 since the 2023/24 school year, and the first cohort examined under it sat the HKDSE in 2026. Three changes matter most to candidates:

• Polar coordinates removed—polar coordinates have been deleted from the Compulsory Part, so questions set on that topic will no longer appear.
• Hexadecimal notation moved to enrichment—the topic is no longer part of the compulsory content and is now enrichment material that students may explore out of interest rather than an examination focus.
• Theorem of three perpendiculars added—a new learning focus that gives 3-D geometry one more examinable element, and a detail worth noting when revising solid geometry.

A second timing issue is easy to miss. The revised junior secondary mathematics curriculum has been in place since the 2020/21 school year, which means some cohorts never studied particular topics at primary or junior secondary level — the divisibility test for 3, prime and composite numbers, and short division for the highest common factor and lowest common multiple are the usual examples. Schools arrange bridging teaching for these, but students who meet such a topic for the first time in a Paper 1 Section A question should not assume the gap is their own fault.

Marking schemes reward process as well as the final answer, and the paper structure rewards judgment about where to spend time. Three habits separate candidates who plateau from those who keep climbing:

• Method marks are real marks—writing the correct formula, substitution and intermediate step earns credit even when the arithmetic slips at the end, so present the working in a readable sequence rather than in a single compressed line.
• Foundation first—Section A questions are less likely to cross topics and are the cheapest marks on the paper. Marks lost in Section A are far harder to recover in a difficult Section B.
• Accuracy discipline—questions are designed to avoid long computation, which means careless rounding, unit slips and mis-keyed calculator entries are a larger share of lost marks than most students expect.

The Compulsory Part is not a memory test. It is a test of whether you can select the right mathematical tool quickly, use it cleanly, and still be accurate in minute 130 of a 135-minute paper.

The plan below is the one that repeatedly turns a mid-range score into a strong one, because it attacks the two things the paper punishes most: misallocated time and repeated topic errors.

• Paper 1 time allocation (135 minutes in total)—the widely used plan is roughly 25 minutes for Section A(1), about 45 minutes for Section A(2), and the remainder for Section B with time reserved for checking. Dividing the paper into three equal 45-minute blocks is exactly how long questions end up unfinished.
• Paper 2 pacing (75 minutes, about 45 questions)—that is around 90 seconds per question. Skip a stuck item rather than sinking minutes into it, return once the confident questions are banked, and leave time to check that no answer has been left blank or shifted out of position.
• Bank Section A first—Section A questions cross fewer topics and are easier to control. A mark lost in Section A is worth the same as a mark in Section B, but costs far less to earn.
• Know the recurring topics—teaching write-ups of past papers repeatedly highlight variation, polynomials, area and volume, and coordinate geometry with locus. Students targeting Level 5 or above should also be fluent with completing the square, transformations of graphs, and the four centres of a triangle — in-centre, circumcentre, centroid and orthocentre.
• Later long questions are cross-topic—the final questions of Paper 1 often combine 3-D geometry, coordinate geometry and more than one strand, so practise them as combinations rather than as isolated chapters.
• Draw when there is no diagram—recent papers often omit the figure. Sketch it yourself, and for 3-D geometry fold a piece of rough paper into the solid to make the spatial relationship visible.
• Practise the calculator, not just the maths—approved calculators and drawing instruments are allowed in the exam, so use them throughout practice to verify answers and sketch graphs; unfamiliarity with them costs marks on the day.
• An error log beats blind drilling—sort every wrong question by topic and record why it went wrong (unclear concept, carelessness, running out of time), then redo that exact set two weeks later. This is the single most reliable way to raise a grade.
• Ignore marketplace “cut-off scores”—the HKDSE reports standards-referenced results and the HKEAA does not publish the raw marks behind each level. The numbers circulating online are estimates that shift with the difficulty of each year’s paper.

The Extended Part is optional, so the decision is strategic rather than compulsory. Four situations usually justify taking Module 1 or Module 2:

• Official sources—the Education Bureau’s Mathematics Curriculum and Assessment Guide (Secondary 4–6); the Curriculum Development Council’s Supplement to the Mathematics Education Key Learning Area Curriculum Guide: Learning Content of Senior Secondary Mathematics (2017) and the Explanatory Notes on the Senior Secondary Mathematics Curriculum: Compulsory Part (updated December 2021); and the HKEAA Mathematics assessment framework together with the examination report and question papers with marking schemes. The current curriculum documents and assessment framework are always more reliable than circulating notes.
• Further reading—the mathematics set on this platform: Hong Kong Secondary 3 Mathematics Syllabus (the junior secondary bridge) and Hong Kong Secondary 2 Mathematics Syllabus, plus DSE Maths Tutoring for one-to-one support. The same guide is available in Chinese: DSE數學課程範圍（繁體） and DSE数学科课程范围（简体）.
• Parent tip—set a weekly timed paper with your child and record the error types on the spot; a two-month review of that log stabilises results more reliably than a last-minute sprint. If the same topic keeps failing, arrange targeted remedial practice early instead of continuing to grind through whole papers.
• Need a tutor?—for one-to-one home or online mathematics tutoring, post a free tuition case in the next section and TutorZone will match you by district, level and timing.

Note: The information above is for reference only. Please consult professional education institutions for details.

This article was initially drafted and organised with AI. Editor / Professor Chan Kwok-wai; Managing Editor / Kong Yee-leung