What topics are in DSE M2?

Seventeen learning units: odd and even functions, mathematical induction, the binomial theorem, more about trigonometric functions, introduction to e, limits, differentiation, applications of differentiation, indefinite integration, definite integration, applications of definite integration, determinants, matrices, systems of linear equations, introduction to vectors, scalar and vector products, and applications of vectors.

What is the format of the DSE M2 exam?

One paper of 2 hours 30 minutes with 100 marks. Section A (50 marks) has 8 to 12 short questions and Section B (50 marks) has 3 to 5 long questions. Every question must be answered.

Is there a free way to get step-by-step help with M2 questions?

Yes. You can type or photograph an M2 question in SketchMath Chat and get a worked solution with a GeoGebra graph. There is a free daily allowance; a paid plan removes the limit.

Should I take M1 or M2?

M2 is the more algebraic and abstract module, with vectors, matrices and calculus that includes trigonometric functions. M1 replaces the algebra with statistics. Compare them in detail on the M1 vs M2 page and check the requirements of the university programmes you are considering.

DSE M2 (Algebra and Calculus): Notes, Formulas and Interactive Graphs for Every Topic

DSE M2 is Module 2 (Algebra and Calculus) of the HKDSE Mathematics Extended Part. It has 17 learning units in three areas: Foundation Knowledge, Calculus and Algebra (matrices, systems of linear equations and vectors). This page links to notes for every unit, each with formulas, worked examples and an interactive graph.

Ask an M2 question and see the graph

A typical M2 vector picture: the projection of b onto a, with the dashed perpendicular from B to the line OA. Try it yourself →

What Is in DSE M2?

The curriculum allocates about 125 hours to Module 2:

Foundation Knowledge (5 units): odd and even functions, mathematical induction, the binomial theorem, more about trigonometric functions, and the number e.
Calculus (6 units): limits, differentiation and its applications, indefinite and definite integration, and areas and volumes of revolution.
Algebra (6 units): determinants, matrices, systems of linear equations, and three units on vectors.

The examination is a single paper of 2 hours 30 minutes. Section A has 8 to 12 short questions worth 50 marks and Section B has 3 to 5 long questions worth 50 marks. All questions are to be answered. See the full M2 syllabus and exam format and time management.

Instant Help for M2 Questions, With the Graph Drawn for You

SketchMath is built on GeoGebra. Type an M2 question, or upload a photo of it, and you get a step-by-step solution together with the diagram: vectors, planes and solids of revolution in a 3D view you can rotate; tangents, shaded areas and curve sketches in 2D.

You do not construct the graph yourself. It is generated from the question, then you can drag and rotate it.
Choose "DSE M2" in the curriculum menu so the answer uses M2 methods and notation and stays inside the syllabus.
Generate practice questions for any of the 17 units and check your working step by step.

Guides: exam skills and common problems

Past paper solutions with video, by year

Algebra

Calculus

Foundation Knowledge

"Basically every 3D topic (Core and M2) is a real help, and for some of the more complicated 2D questions and the four centres of a triangle it is pretty good too. With Desmos I often move something by accident and have to start again to change it, which is inconvenient and wastes time, and it cannot give you the whole graph just from typing in the question the way SketchMath does. The M2 vectors part will definitely bring in more users, because every one of those questions is genuinely tricky."

— A DSE student who uses SketchMath (user feedback, translated from Cantonese)