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Algebra is the largest part of GCSE Maths syllabus. So it’s important that you know your Algebra! Here we cover everything from the basic of Expanding brackets, grouping like terms, to solving simultaneous equations.

Expanding brackets

Expanding a single bracket

Expanding two or more brackets

Squaring brackets

Forming expressions

How to form expressions and equations from information

Solving linear equations

Terms in expressions and equations

Linear Equations with a positive x term

Linear Equations with a negative x term

Linear Equations with a two x terms

Linear Equations with brackets

Linear Equations that are fractions

Simultaneous equations

Solve by elimination

Same x terms

Same y terms but opposite signs

Same y terms but both signs are negative

Same y terms but both signs are positive

Neither x term nor y term are the same

Substitution methods (Quadratic SImultaneous)

Indices Introduction

Introduction to indices (exponents)

Multiplication rules for indices

Division rule for indices

Negative indices

Fractions raised to a negative index

Rational (fractional) indices

Simplifying terms with negative powers

Expressing terms in the form axn

Equations in which the power has to be found

Summary of indices

Surds

Surds- Introduction & simplifying

Addition and subtraction of surds

Multiplying surds

Dividing Surds

Rationalising surds

Exam Questions

Functions

f(x) notation

Composite functions

The inverse of a function

Factorising

Introduction to factorising

Highest common factor (HCF)

Factorising by grouping

Factorising quadratic expressions

Mixed Exercise – Factorising

Completing the square

Completing the square

Applications of completing the square

Exam Questions – Completing the square

Quadratic Equations

Solve by factorising

Solve by completing the square

Solve by the quadratic formula

Exam Questions – Solved by the quadratic formula

Gradient

Line segment

Parallel lines

Perpendicular lines

Equation of a straight line

Equation of a straight line: y=mx+c

Equation of a line given the gradient and point

Distance between two points

Mid-point of a line segment

Equation of a parallel line

Equation of a perpendicular bisector

Intersection of Graphs

Intersection of two straight lines

Intersection of a straight line and a parabola

Intersection of a straight line and a hyperbola

Quadratic Graphs

Sketching quadratic graphs

Inequalities

Rules for reversing the inequality sign

Solving a linear type

Quadratic inequalities

Graphing inequalities

Graph Transformations

Basic graphs used in transformations

Translations of graphs

Reflections of graphs

Circles

Equation of a circle

Finding the centre and radius

Equation of a circle and tangent

Rational Expressions

Simplifying algebraic fractions

Exam Questions – Simplifying a rational expression

Addition and subtraction of algebraic fractions

Exam Questions – Addition & subtraction

Multiplication of algebraic fractions

Simplifying algebraic fractions NEW (All operations)

Sequences and Series

Definition and finding the nth term

Recurrence relationships

Fibonacci sequences

Quadratic sequences

Exam Questions – Recurrence relationships

Iteration

Iteration

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