DSE M2 Syllabus: Every Topic, and What Is Not Required
The DSE M2 syllabus has 17 learning units plus an inquiry unit, about 125 lesson hours. Several things students often revise are not in it: complex numbers, equations of lines and planes, the scalar triple product, the shell method, induction on divisibility or inequalities, and the subsidiary angle form.
DSE M2 Topics by Area
| Learning unit | Hours | Not required |
|---|---|---|
| 1. Odd and even functions | 2 | Rules such as odd + odd = odd |
| 2. Mathematical induction | 3 | Inequalities; divisibility |
| 3. The binomial theorem | 3 | Trinomials; greatest coefficient or term; numerical approximation |
| 4. More about trigonometric functions | 15 | Subsidiary angle form |
| 5. Introduction to e | 2 | Proof that (1 + 1/n)ⁿ converges |
| 6. Limits | 3 | Rigorous definition; judging continuity from graphs |
| 7. Differentiation | 13 | Testing differentiability; third and higher derivatives |
| 8. Applications of differentiation | 14 | — |
| 9. Indefinite integration | 15 | Integrands with sin⁻¹x, cos⁻¹x, tan⁻¹x; by parts more than twice |
| 10. Definite integration | 10 | Sum to infinity by integration; other absolute-value integrands |
| 11. Applications of definite integration | 4 | Shell method |
| 12. Determinants | 2 | Properties of determinants |
| 13. Matrices | 10 | General proof of |AB| = |A||B| |
| 14. Systems of linear equations | 6 | — |
| 15. Introduction to vectors | 5 | Direction cosines |
| 16. Scalar product and vector product | 5 | Scalar triple product; "parallelepiped" |
| 17. Applications of vectors | 6 | — |
Source: Education Bureau, Explanatory Notes to Senior Secondary Mathematics Curriculum: Module 2 (Algebra and Calculus), 2009 with updates in August 2018. The remaining 7 hours are for the inquiry and investigation unit.
Topics Often Mistaken for M2
- Complex numbers, the Argand diagram and De Moivre’s theorem. Not in the M2 learning units. Basic complex-number arithmetic belongs to the Compulsory Part.
- Vector and Cartesian equations of lines and planes. M2 vectors stop at parallelism, orthogonality, division of a segment, projection, angle and area.
- The binomial theorem for negative or fractional powers. Only positive integral indices are covered.
- Maclaurin series, partial fractions as a technique, differential equations. None is a listed learning objective.
Older past papers and overseas textbooks contain some of these. Selecting "DSE M2" in SketchMath keeps answers within the current syllabus and tells you when a question goes beyond it.
Frequently Asked Questions
Seventeen learning units across Foundation Knowledge (5), Calculus (6) and Algebra (6), plus a further unit on inquiry and investigation that is not examined as separate content.
No. Complex numbers do not appear among the M2 learning units in the EDB explanatory notes. Basic operations with complex numbers are part of the Compulsory Part.
More about trigonometric functions and indefinite integration (15 hours each), applications of differentiation (14) and differentiation (13). Calculus as a whole takes 59 of the 118 content hours.