GCSE Further Mathematics

At St Joseph's a selected group of students are invited to study for the AQA Further Mathematics exam.  This is a GCSE subject intended to cater for pupils who would like to study beyond the Higher Tier GCSE syllabus in Mathematics and who are capable of working above this level. The syllabus is designed to broaden the mathematical experience of high attaining pupils. The content that is not on the GCSE specification is taught during the Autumn Term during an enrichment session.

Terminal Assessments

AQA Level 2 Certificate in Further Mathematics is linear. Students take two question papers

Paper 1:    105 mins, 80 marks, non-calculator, 50%

Paper 2:    105 mins, 80 marks, calculator, 50%

A mix of question styles, from short, single-mark questions to multi-step problems. The mathematical demand increases as a student progresses through the paper

Further Mathematics Content

You will find links for the vast majority of the Further Maths course below, including Video tutorials for many of the topics. The content in orange is included on the GCSE specification for Mathematics and the content in green is the additional content that is taught during the enrichment hour each week.

Chapter 1:   Number & Algebra 1             

Product Rule for Counting     Video    Practice Questions    Answers

Surds (addition/subtraction)   Video      Practice Questions    Answers

Surds (rationalising denominators)   Video    Practice Questions    Answers

Expanding Brackets     Video   Practice Questions    Answers

Expanding 3 Brackets     Video    Practice Questions    Answers

Expanding Brackets (Pascal’s triangle)   Video    Practice Questions    Answers

Chapter 2:   Algebra 2                                 

Factorisation     Video    Practice Questions    Answers

Factorising Quadratics     Video     Practice Questions    Answers

Algebraic Fractions (add/subtract)    Video    Practice Questions     Answers

Algebraic Fractions (multiply)    Video     Practice Questions      Answers

Algebraic Fractions (divide)    Video     Practice Questions      Answers

Algebraic Fractions (equations)   Video    Practice Questions      Answers

Changing the Subject     Video    Practice Questions    Answers


Chapter 3:   Algebra 3                                 

Sketching Quadratics     Video    Practice Questions    Answers

Function Notation     Video      Practice Questions     Answers

Composite Functions     Video      Practice Questions     Answers

Inverse Functions     Video      Practice Questions     Answers

Domains and Ranges     Video    Practice Questions     Answers

Drawing Functions   Video     Practice Questions        Answers


Chapter 4:   Algebra 4                                 

Completing the Square (x²)     Video    Practice Questions    Answers

Completing the Square (ax²)    Video    Practice Questions    Answers

Solving Quadratics by Factorisation    Video    Practice Questions   Answers

Solving Quadratics (Completing the Square)  Video  Practice Questions   Answers

Solving Quadratics (Quadratic Formula)   Video    Practice Questions       Answers

Factor Theorem     Video      Practice Questions    Answers

Algebraic Long Division     Video      Practice Questions    Answers

Factorising Cubics     Video       Practice Questions    Answers

Solving Cubics     Video     Practice Questions    Answers

Exponential Graphs     Video    Practice Questions   Answers

Simultaneous Equations (both linear)     Video      Practice Questions     Answers

Simultaneous Equations (non-linear)   Video    Practice Questions    Answers

Simultaneous Equations (3 unknowns)   Video    Practice Questions     Answers

Linear Inequalities    Video       Practice Questions     Answers

Quadratic Inequalities   Video      Practice Questions    Answers

Laws of Indices    Video    Practice Questions    Answers

Fractional Indices    Video     Practice Questions     Answers

Negative Indices   Video    Practice Questions     Answers

Equations with indices/roots    Video     Practice Questions    Answers

Algebraic Proof     Video    Practice Questions     Answers

nth Terms     Video    Practice Questions      Answers

Limiting Values    Video    Practice Questions      Answers

Linear Sequences    Video    Practice Questions      Answers

Quadratic Sequences   Video 1   Video 2    Practice Questions        Answers


Chapter 5:   Geometry 1                               

Gradient    Video     Practice Questions     Answers

Parallel Lines    Video     Practice Questions     Answers

Perpendicular Lines    Video     Practice Questions    Answers

Distance between two points   Video    Practice Questions    Answers

Midpoint of a Lines    Video      Practice Questions     Answers

Ratio (Lines)    Video    Practice Questions     Answers

Equation of a Line    Video    Practice Questions     Answers

Equation of a Circle (centre is the origin)    Video     Practice Questions     Answers

Equation of a Circle (centre not the origin)   Video    Practice Questions    Answers

Equation of a Tangent to a Circle     Video     Practice Questions    Answers

Chapter 6:   Co-ordinate Geometry           


Circle Theorems    Video    Practice Questions     Answers

3D Pythagoras    Video       Practice Questions      Answers

3D Trigonometry     Video      Practice Questions    Answers

Exact Trig Values    Video     Practice Questions    Answers

Trig Identities    Video      Practice Questions    Answers

Geometric Proof     Video    Practice Questions    Answers

Chapter 7:   Geometry 2                               

Sine Rule (sides)     Video      Practice Questions   Answers

Sine Rule (angles)     Video      Practice Questions   Answers

Sine Rule (ambiguous case)   Video    Practice Questions    Answers

Cosine Rule (sides)     Video      Practice Questions    Answers

Cosine Rule (angles)   Video      Practice Questions    Answers

Area of a Triangle    Video      Practice Questions    Answers

Trig Graphs   Video   Practice Questions      Answers

Finding other Trig ratios    Video     Practice Questions    Answer

Solving Trigonometric Equations: Introduction    Video

Solving Trigonometric Equations 1     Video    Practice Questions    Answers

Solving Trigonometric Equations 2     Video    Practice Questions    Answers

Chapter 8:   Calculus                                   

Introduction     Video      Practice Questions    Answers

Differentiation      Video         Practice Questions      Answers

Differentiation after Rearranging     Video       Practice Questions    Answers

Gradient of a Curve    Video    Practice Questions      Answers

Equation of a Tangent     Video      Practice Questions    Answers

Equation of a Normal      Video    Practice Questions     Answers

Increasing/Decreasing Function    Video    Practice Questions  Answers

d2y/dx2     Video    Practice Questions      Answers

Stationary Points     Video     Practice Questions     Answers

Application of Differentiation    Video     Practice Questions     Answers

Sketch curve knowing maxima/minima     Video    Practice Questions    Answers

Revision Videos:  Part 1     Part 2     Part 3   


Chapter 9:   Matrices                                  

Multiplying Matrices (by a scalar)   Video      Practice Questions    Answers

Multiplying Matrices (2×2 by 2×1)   Video     Practice Questions     Answers

Multiplying Matrices (2×2 by 2×2)   Video     Practice Questions     Answers

Identity Matrix     Video    Practice Questions      Answers

Transforming the Unit Square    Video     Practice Questions    Answers

Matrix Transformations    Video     Practice Questions      Answers

Revision Videos:  Part 1     Part 2   

Classwiz Guide

Great video guides as to how to get the best out of the Classwiz calculator

Click here and then select Classwiz Guide from the menu on the left