'Extra Maths' - Preview (with examples)

Pure 

Counting Exs 1 2 3 4 5 6 7 

Functions

Convex & Concave Functions (2 pages; 2/6/23)

Rational Functions (5 pages; 12/7/24)

y squared = f(x) (2 pages; 2/6/23)

Mappings & Functions (3 pages; 2/6/23)

Exponential Functions (2 pages; 2/6/23)

Inverse Functions (3 pages; 2/6/23)

Modulus Function (2 pages; 2/6/23)

Geometry

Shortest distance from Origin to line  (7 pages; 6/3/25) 

Groups - Part 1 (10 pages; 22/10/16)

Groups - Part 2 (12 pages; 23/10/16)

Groups Exs 1 2 3 4 

Linear Interpolation (5 pages; 7/2/16)

Linear Interpolation Exs 1

Matrices 

Invariant points & lines - conditions (12 pages; 16/4/20) 

Shears (8 pages; 12/8/18) 

Shears (Exs) (11 pages; 29/3/25)

Eigenvectors (10 pages; 4/9/18)

Eigenvectors & Invariance (6 pages; 16/4/20) 

Eigenvectors (Exs) (38 pages; 29/3/25)

Numbers

Algebraic & Transcendental Numbers (1 page; 5/6/23)

Number Theory (18 pages; 12/11/24)

Primes - Results (3 pages; 21/5/25)

Parametric equations (7 pages; 5/5/21)

Parametric Eq'ns Exs 1 

Recurrence relations (16 pages; 29/4/25)

Taylor Series (5 pages; 23/7/21)

Series - Results (2 pages; 18/5/25)

Trigonometry

Factor Formulae (1 page; 15/4/21)

t=tan(x/2) substitution (4 pages; 24/3/20)

Mechanics 

Circular Motion [Important Ideas] (2 pages; 25/10/20)

Circular Motion - Constant Speed (9 pages; 25/10/20)

Circular Motion - Variable Speed (13 pages; 30/9/15)

Circular Motion Exs 1 2

Frameworks (9 pages; 25/3/21)

Bending moment & shearing force (5 pages; 25/3/21)

Fictitious forces (5 pages; 25/10/20) 

Systems of forces (5 pages; 14/11/18)

Rolling wheel: Friction (14 pages; 31/5/24)

Collisions - reversal of direction (6 pages; 24/6/20) 

Impulses & connected particles (13 pages; 28/8/18) 

Oscillations

Differential equations: Oscillations (11 pages; 29/5/20)

Oscillations Exs 1 2 3 4

Rotating Bodies

Motion of a particle in a rotating frame of reference (27 pages; 29/1/24)

Angular Momentum & Planar Rigid Body Motion (20 pages; 27/11/23)  

Moments of Inertia (7 pages; 1/8/23) 

Rolling wheel - Point on circumference (5 pages; 1/2/21) 

Rolling Wheel - Friction (11 pages; 3/5/23) 

Rotating Bodies Ex 1

Gravitational Potential Energy (3 pages;15/2/19) 

Probability & Statistics

Conditional Probability (2 pages; 1/2/23)

Confidence Intervals - Types (3 pages; 16/4/16)

Geometric & Negative Binomial distributions (5 pages; 11/2/25)

Hypothesis Tests - Types (8 pages; 24/1/20)

Linear Coding (2 pages; 8/7/21)

Normal distribution (9 pages; 21/2/17)

Normal Distribution Exs 1 2

Approximations to Binomial & Poisson (4 pages; 30/1/17)

Probability & Counting Approaches (12 pages; 21/3/24)

Selections (6 pages; 15/3/24)

Probability Exs 1 2 

Probability Generating Functions: Ideas & Exs (16 pages; 27/2/25)

Probability Generating Functions: Further Exs (11 pages; 27/2/25) 

Sampling (4 pages; 7/8/17) 

Uniform distribution (Discrete) (2 pages; 20/3/20)

Uniform Distribution (Discrete) Ex 1 

Sample variance (3 pages; 8/7/21)

Decision Maths

Game Theory Exs 1 2 3 

Graphs & Networks

Directed Edges (incl. Incidence & Distance matrices) (5 pages; 19/11/19)

Planarity Algorithm (5 pages; 30/6/20)

Planarity algorithm Ex 1

Kuratowski's Thm (Ex) 1 

Floyd's Algorithm (21 pages; 17/6/20)

Floyd's Algorithm Exs 1 2 

Hungarian Algorithm  (9 pages; 28/8/17) 

Formulating network problems as LP problems (7 pages; 21/1/20)

Formulate as LP problem (Exs) 3 4 5 6 7 

Travelling Salesman problem (10 pages; 29/6/20)

Travelling Salesman problem Ex 1