HKDSE · 試験対策

Mathematics M2 (Algebra and Calculus) 試験対策

The ultimate exam survival and strategy guide for HKDSE Mathematics M2, combining systematic paper structural breakdowns, common marker pitfalls from official examiner reports (2021-2023), and key calculator strategies.

読了時間 2 分更新日: 2026年6月21日

試験の概要

試験数
1
満点
100
制限時間
2時間 30分
出題形式
2
試験時間配点問題数配点比率出題形式
Module 2 (Algebra and Calculus)2時間 30分10012100%Section A (Short Questions), Section B (Structured Questions)
評価段階
5**5*54321
電卓の規定

Use only calculators on the HKEAA Approved List, bearing the 'H.K.E.A.A. APPROVED' (or older 'H.K.E.A. APPROVED') label. Programmable scientific models (e.g. Casio fx-50FH II, fx-3650P II) are allowed, and you MAY keep your own formulas/programs stored in memory — HKDSE does not require you to clear it. Graphic-display (graphing) and CAS/symbolic calculators are not on the approved list and must not be used.

  • AO1: Knowledge and understanding of algebraic and calculus concepts (60%)
  • AO2: Application and problem-solving skills in mathematical context (40%)

過去問と採点基準にもとづいて作成（2021–2023）。

電卓プログラム

2×2 Determinant

Casio fx-50FH II / fx-3650P II (HKEAA-approved programmable)

目的: \(\det\begin{psmallmatrix}a&b\c&d\end{psmallmatrix}=ad-bc\).

使う場面: Determinants, invertibility, and Cramer's rule.

手順
Prompt a, b, c, d; outputs ad−bc.
プログラム
?→A:?→B:?→C:?→D:AD-BC

試験での注意: If the result is 0 the matrix is singular (no inverse).

Cramer's Rule (2 equations)

Casio fx-50FH II / fx-3650P II (HKEAA-approved programmable)

目的: Solves \(ax+by=e,\ cx+dy=f\): \(x=\frac{ed-bf}{ad-bc},\ y=\frac{af-ec}{ad-bc}\).

使う場面: Two linear equations in two unknowns.

手順
Prompt a,b,c,d,e,f; outputs x then y.
プログラム
?→A:?→B:?→C:?→D:?→E:?→F:AD-BC→Z:(E D-B F)÷Z◢(A F-E C)÷Z

試験での注意: If ad−bc = 0 there is no unique solution.

Quadratic Roots & Discriminant

Casio fx-50FH II / fx-3650P II (HKEAA-approved programmable)

目的: \(\Delta=b^2-4ac\); roots \(\frac{-b\pm\sqrt{\Delta}}{2a}\).

使う場面: Any quadratic, or testing the nature of roots.

手順
Prompt a,b,c; outputs \(\Delta\) then the two roots.
プログラム
?→A:?→B:?→C:B²-4AC→D:D◢(-B+√D)÷(2A)◢(-B-√D)÷(2A)

試験での注意: \(\Delta<0\) means no real roots.

よくあるミス

  1. 1high影響する配点: 1Limits (Calculus)

    Missing the limit sign 'lim (h->0)' in intermediate steps of first principles differentiation.

    回避方法: Keep writing '\lim_{h \to 0}' in front of every algebraic expression until you evaluate the limit by substituting h = 0.
  2. 2high影響する配点: 2Definite integration (Calculus)

    Failing to change the lower and upper limits of integration when performing substitution in definite integrals.

    回避方法: Construct a small table relating x and u immediately after defining u. Write the new limits on the integral sign in the very next step.
  3. 3high影響する配点: 1Mathematical induction (Foundation Knowledge)

    Incomplete presentation in Mathematical Induction, such as skipping LHS/RHS separate verification for the base case or omitting the conclusion sentence.

    回避方法: Explicitly state: 'When n = 1, LHS = ... and RHS = ... Since LHS = RHS, the statement is true for n = 1.' Conclude with: 'By the principle of mathematical induction, the statement is true for all positive integers n.'
  4. 4medium影響する配点: 2Systems of linear equations (Algebra)

    Incorrectly applying Cramer's rule formulas when the determinant of the coefficients is zero.

    回避方法: If det(A) = 0, Cramer's rule is inapplicable. You must use Gaussian elimination (augmented matrix) to analyze whether there are infinitely many solutions or no solution.
  5. 5medium影響する配点: 1Matrices (Algebra)

    Assuming matrix multiplication is commutative (i.e. AB = BA) when expanding algebraic matrix identities.

    回避方法: Keep the exact order of multiplication. For example, write (A+B)(A-B) = A^2 - AB + BA - B^2, and only simplify to A^2 - B^2 if the question specifies AB = BA.
  6. 6medium影響する配点: 1Applications of differentiation (Calculus)

    Claiming a coordinate is a point of inflection solely because f''(x) = 0 at that point.

    回避方法: Perform a sign test to show that f''(x) changes its sign (from positive to negative or vice versa) as x passes through that point.

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