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Math with
Mr Hunte

CAPE Pure Mathematics Unit 2
KEY CONCEPTS

These lessons are designed to help you learn mathematics, think mathematically, and review what you already know. Using ideas from Building Thinking Classrooms (BTC) and the Concrete–Pictorial–Abstract (CPA) framework, the lessons move from exploring and making sense of ideas to representing them visually and finally connecting them to formal mathematical methods. Work through each lesson at your own pace, pause when you need to, revisit topics you find challenging, and use the video tutorials for additional support. Check Your Understanding questions are included throughout to help you see how well you have understood each idea. Some questions use an Open Middle-style approach, where there may be more than one way to approach a problem, encouraging you to experiment, reason, and explain rather than simply apply a memorised rule.

Differentiation Notes

Module 1

Differentiation of Implicit Functions

Module 1

Differentiation of Parametric Equations

Module 1

Differentiation of Trigonometric Functions 2

Module 1

Differentiation of Inverse Trig Functions

Module 1

Differentiation of The Natural Logarithm

Module 1

Differentiation of Exponential Functions

Module 1

Partial Derivatives

Module 1

Integration Notes

Module 1

Integration with Exponential Functions

Module 1

Integration Involving Logarithms

Module 1

Integration: Function by Derivative

Module 1

Integration of Trigonometric Functions

Module 1

Partial Fractions

Module 1

Integration by Parts

Module 1

Reduction Formulae

Module 1

Trapezium Rule

Module 1

Complex Numbers Notes

Module 1

Introduction to Complex Numbers

Module 1

Equations and Complex Numbers

Module 1

The Argand Diagram and Modulus-Argument Form

Module 1

De Moivre's Theorem

Module 1

Multiples of Sine and Cosine

Module 1

Euler's Formula

Module 1

Locus on the Argand Diagram

Module 1

Sequences Notes

Module 2

Introduction to Sequences

Module 2

Types of Sequences

Module 2

Recurrence Relations and Mathematical Induction

Module 2

Series and Standard Summation Formulae

Module 2

Method of Differences

Module 2

Arithmetic Progressions

Module 2

Geometric Progressions

Module 2

MaClaurin's Series

Module 2

Taylor's Series

Module 2

Newton-Raphson

Module 2

Matrix Multiplication

Module 3

Determinant of a 3x3 Matrix

Module 3

Transpose of a Matrix

Module 3

Inverse of a 3x3 Matrix

Module 3

Cramer's Rule

Module 3

Row Reduction

Module 3

Separable Differential Equations

Module 3

Integrating Factor

Module 3

Homogeneous Differential Equations

Module 3

Non-Homogeneous Differential Equations

Module 3

Differential Equations Requiring a Substitution

Module 3

Differential Equations and Mathematical Modelling

Module 3

Probability

Module 3

Permutations

Module 3

Combinations

Module 3

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