Pure Maths

• Algebra
• Functions
• Series and Sequences
• Matrices
• Proof

Trigonometry

• Sine, Cosine and Tangent
• Radians
• Pythagoras' Theorem
• SOHCAHTOA
• The Sine and Cosine Rules
• Area of a Triangle
• Trigonometric Identities and Formulae
• Cosecant, Secant and Cotangent
• Hyperbolic Functions
• Euler's Formula and Euler's Identity

Plane Geometry

• Equation of a Straight Line
• Properties of Straight Line Segments
• Tangents and Normals
• Geometry of a Circle
• Equation of a Circle
• Arc Length and Area of a Sector
• Polar Coordinates

Vectors

• Vectors in Cartesian Coordinates
• Dot Product
• Cross Product
• Differentiating Vectors

Differentiation

• Differentiation
• Chain Rule
• Product Rule
• Quotient Rule
• Differentiation from First Principles
• Parametric Differentiation
• Implicit Differentiation
• Differentiation using Inverse Functions
• Partial Derivatives
• Tangents and Normals
• Stationary Points

Integration

• Indefinite Integration
• Definite Integration
• Integration by Parts
• Integration by Substitution
• Integration using Partial Fractions
• Integration using Trigonometric Identities
• Integration by Reduction
• Double and Triple Integrals

Fundamental Theorem of Calculus

• Fundamental Theorem of Calculus

Ordinary Differential Equations

First Order ODEs

• Separable ODEs
• Integrating Factor
• Homogeneous First Order Differential Equations

Second Order ODEs

• Homogeneous Second Order Differential Equations
• Forced Second Order Differential Equations

Series Expansions

• Taylor Series
• Maclaurin Series