 ## GCSE Further Mathematics

Further Mathematics Content

Chapter 1:   Number & Algebra 1              Numbers & the Number System

Simplifying Expressions

Solving Linear Equations

Algebra & Number

Expanding Brackets

Manipulating Surds

Chapter 2:   Algebra 2                                   Factorising

Rearranging Formulae

Simplifying Algebraic Fractions

Solving Equations involving Fractions

Chapter 3:   Algebra 3                                  Function Notation

Domain & Range of a Function

Graphs of Functions

Graphs of Linear Functions

Finding the Equation of a Line

Graphs of functions with up to 3 domains

Chapter 4:   Algebra 4                                  Quadratic Equations

Simultaneous Equations

Factor Theorem

Linear Inequalities

Index Laws

Algebraic Proof

Sequences

Chapter 5:   Geometry 1                               Parallel & Perpendicular Lines

The Distance between 2 points

The midpoint of a line joining 2 points

Equation of a straight line

The Intersection of two lines

Dividing of a line in  given ratio

Equation of a Circle

Chapter 6:   Co-ordinate Geometry           Mensuration

Pythagoras' Theorem

Angle Facts

Circle Theorems

Geometric Proofs

Trigonometry in 2D

Angles of 30, 45 & 60

Problems in 3D

Lines and Planes in 3D

Chapter 7:   Geometry 2                               Trigonometrical functions for angles of any size

The Sine and Cosine Graphs

The Tangent Graphs

The Area of a Triangle

The Sine & Cosine Rules

Solution of Trigonometrical Equations

Trigonometrical Identities

Chapter 8:   Calculus                                    The Gradient of a Curve

Differentiation

Differentiation using Standard Results

Tangents and Normals

Increasing & Decreasing Functions

Stationary Points

Chapter 9:   Matrices                                    Multiplying Matrices

Transformations

Identity Matrix

Transformations of the Unit Square

Combining Transformations

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