## Algebra and Complex numbers

These handy PDF guides can be viewed electronically or printed.

- Algebra 1: Using letters for numbersUsing letters for number

Substitution

Simplification of expressions

Indices - Algebra 2: Expanding brackets & factorisationExpanding brackets

Simple factorisation

Quadratic factorisation

Completing the square - Algebra 3: Simple equationsSolving simple equations

Evaluation and transposition of formulae - Algebra 4: Quadratic & simultaneous equationsSolving quadratic equations

Solving simultaneous equations - Algebra: Factorising and Long Division 1Revision of multiplying brackets

Factorisation

Long division in algebra - Algebra - Factorising and Long Division 2Revision of multiplying brackets

Factorisation

Long Division in Algebra - Algebraic FractionsSimplification

Multiplication & Division

Addition & Subtraction - Complex numbersIntroduction

Argand diagram

The four rules

Modulus-Argument form

Roots

- Resources in the libraryIn addition to the handy online guides above, there are a range of books and ebooks available from the university library.

## Graphs, Logarithms, matrices, integration and vectors

These handy PDF guides can be viewed electronically or printed.

- Graphs 1Introduction

Straight line graphs

Graphs of quadratics

Common types of graph - Graphs 2Revision of straight line graphs and quadratics

Cubics

Quartics

Higher powers

Fractional functions

Modulus functions - LogarithmsRevision of indices

What are logarithms?

Rules for manipulation

Solving equations using logs

The straight line law

Graph of Inx and its inverse - MatricesIntroduction

Order, addition and subtraction

Equality

Multiplication

Identity and invers

Echelon method - Partial fraction & integrationPartial fractions

Integration using partial fractions - Vectors 1: Operations, scalar/vector productsWhat is a vector?

Arithmetic operations on vectors

Scalar (dot) product

Vector (cross) product - Vectors 2Recap on vectors

Unit vectors, normals and bases

Vector equations of straight lines and planes

Intersections of lines and planes

Div, grad, curl & the laplacian - Inequalities & ModulusIntroduction

Inequalities: (basic facts, solution, fractional functions)

Modulus: (meaning, solution of equation