GCSE Further Mathematics (AQA)
Further Mathematics is studies in class for the top set in Year 10 & 11. The qualification can help to bridge the gap between GCSE and A Level. We enter the AQA specification
A list of the topics covered is listed below.
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
Quadratic Identities
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 Quadratic Functions
Graphs of functions with up to 3 domains
Chapter 4: Algebra 4 Quadratic Equations
Simultaneous Equations
Factor Theorem
Linear Inequalities
Quadratic 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