| Section | Topic | Page | |---------|-------|------| | 1 | Mathematical Induction | 3 | | 2 | Binomial Theorem | 6 | | 3 | Trigonometry (General Solutions & Identities) | 9 | | 4 | Limits & Continuity | 13 | | 5 | Differentiation – Rules & Techniques | 18 | | 6 | Differentiation – Applications | 24 | | 7 | Indefinite Integration | 30 | | 8 | Definite Integration & Applications | 35 | | 9 | Matrix Algebra (2×2 & 3×3) | 40 | | 10 | System of Linear Equations | 45 | | 11 | Vectors in 2D & 3D | 50 | | 12 | Past Exam Trend Analysis | 56 | | 13 | Formula Sheet | 60 |

Fundamental Rules:

Derivatives of Elementary Functions:

Implicit Differentiation: Used when $y$ cannot be isolated. Differentiate both sides with respect to $x$, treating $y$ as a function of $x$ (use chain rule for terms with $y$).

Applications of Differentiation:

Key Content:

Worked Examples:

Key Content:

Worked Example: Find ( A^-1 ) for ( A = \beginpmatrix 1 & 2 \ 3 & 4 \endpmatrix )

Key Observations:

Question Style Table: Show which year tested which topic.

Disclaimer: These notes are a summary for revision purposes. Please refer to the HKEAA Curriculum and Assessment Guide for the full syllabus details.

DSE Mathematics (Extended Part) Module 2 (M2) is an advanced mathematics elective for Hong Kong secondary students. It focuses on algebra (e.g., mathematical induction, binomial theorem, matrices, determinants, system of linear equations, vectors) and calculus (limits, differentiation, integration, and their applications). Many students seek PDF notes for efficient revision, portability, and structured learning.

Key Content:

Worked Example: Find the maximum volume of a cylinder inscribed in a cone.