HKDSE Maths M2 study guide
HKDSE Maths M2 · Work through your exam, one topic at a time.
The Hong Kong Diploma of Secondary Education (HKDSE) is the public examination taken by senior secondary school candidates in Hong Kong. Mathematics is one of the four Category A core subjects, alongside Chinese Language, English Language and Citizenship and Social Development. Mathematics has a Compulsory Part plus two Extended Parts; Extended Part Module 2 (Algebra and Calculus) is the strand this page supports, aimed at candidates who need stronger algebraic manipulation and calculus for university study in mathematics, engineering, the physical sciences or economics. The HKEAA publishes the assessment framework for each Senior Secondary subject, so candidates should confirm the Module 2 syllabus, paper structure and any school-based assessment arrangements there rather than relying on memory. Topics on this exam: Algebra (Extended Part Module 2) and Calculus (Extended Part Module 2). The HKDSE Maths M2 study guide has 2 sections and about 856 words.
01Algebra (Extended Part Module 2): Proof, Binomial Coefficients, Matrices and Vectors
The Algebra domain of HKDSE Mathematics Extended Part Module 2 tests symbolic manipulation, proof, and structure. Questions often combine topics-mathematical induction with binomial coefficients, logarithms with exponential equations, or matrices with systems of linear equations. Precise notation matters: n!, C(n,r), M^(-1), det M, and the scalar product a·b. Binomial theorem: (a+b)^n = Σ {r=0}^{n} C(n,r) a^(n-r) b^r.
459 words, about 2 min02Calculus (Extended Part Module 2): Limits, Derivatives and Integrals
The Calculus domain tests limits, differentiation, integration, and applications. HKDSE M2 questions ask you to choose the correct rule, justify a limit, and interpret a derivative or integral. Typical tasks include finding a tangent, locating a maximum, evaluating a definite integral, and using the result to find an area. Limit: lim {x→a} f(x) exists only if left- and right-hand limits agree; for rational functions, factor and cancel before substituting.
397 words, about 2 min