M2 (Algebra and Calculus): Important notes and tips

M2 (Algebra and Calculus)
The examination will consist of one paper of 2.5 hours’ duration.
The paper will be divided into two 2 sections in which all the questions are to be attempted.
Section A (50 marks) will consist of 8-12 short questions.
Section B (50 marks) will consist of 3-5 long questions.

Surds

Mathematical induction

Binomial Theorem

Trigo (**very important for M2)

The number e

Limits

Differentiation (need to know how to differentiate trigo functions!)

Application of differentiation (curve sketching!)

Indefinite integration (integration of trigo functions and integration by parts!)

Definite integration (even, odd and periodic functions!)

Application of definite integration (area and VOLUME!)

Determinants

Matrices

System of linear equations

Introduction to vectors

Scalar product and vector product

Application of vectors