2. Algebra and Graphs

E2.1 Introduction to Algebra

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Introduction to Solving Equations

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Linear Equations

Prof. Keith Ball, Warwick University

E2.2 Algebraic Manipulation

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Quadratic Equations By Factorising

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Quadratic Equations By Completing the Square

Prof. Keith Ball, Warwick University

ALGEBRA AND FUNCTIONS I – EDEXCEL (9MA0)

Expanding Brackets and Factorising

Dr Niki Kalaydzhieva, UCL

E2.3 Algebraic Fractions

ALGEBRA AND FUNCTIONS I – EDEXCEL (9MA0)

Rationalising the Denominator

Dr Niki Kalaydzhieva, UCL

E2.4 Indices II

ALGEBRA AND FUNCTIONS I – EDEXCEL (9MA0)

Indices

Dr Niki Kalaydzhieva, UCL

ALGEBRA AND FUNCTIONS I – EDEXCEL (9MA0)

Fractional and Negative Indices

Dr Niki Kalaydzhieva, UCL

E2.5 Equations

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Introduction to Solving Equations

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Linear Equations

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Quadratic Equations By Factorising

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Quadratic Equations By Completing the Square

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

The Quadratic Formula

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Extension: Deriving the Quadratic Formula

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Quadratic Equations By Graphing

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Introduction

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Simultaneous Linear Equations By Substitution

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Simultaneous Linear Equations By Cancellation

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Simultaneous Linear and Quadratic Equations

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Equations Using Iteration

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Mathematical Formulae in Applications

Prof. Keith Ball, Warwick University

SOLVING EQUATIONS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Equations in Applications

Prof. Keith Ball, Warwick University

E2.6 Inequalities

SOLVING INEQUALITIES – EDEXCEL GCSE (1MA1): HIGHER TIER

Introduction to Inequalities

Prof. Keith Ball, Warwick University

SOLVING INEQUALITIES – EDEXCEL GCSE (1MA1): HIGHER TIER

Solving Linear Inequalities

Prof. Keith Ball, Warwick University

SOLVING INEQUALITIES – EDEXCEL GCSE (1MA1): HIGHER TIER

Graphing Linear Inequalities in Two Variables

Prof. Keith Ball, Warwick University

SOLVING INEQUALITIES – EDEXCEL GCSE (1MA1): HIGHER TIER

Quadratic Inequalities

Prof. Keith Ball, Warwick University

E2.7 Sequences

SEQUENCES – EDEXCEL GCSE (1MA1): HIGHER TIER

Introduction to Sequences

Prof. Keith Ball, Warwick University

SEQUENCES – EDEXCEL GCSE (1MA1): HIGHER TIER

Generating Sequences

Prof. Keith Ball, Warwick University

SEQUENCES – EDEXCEL GCSE (1MA1): HIGHER TIER

Famous Sequences: Squares and Triangle Numbers

Prof. Keith Ball, Warwick University

SEQUENCES – EDEXCEL GCSE (1MA1): HIGHER TIER

Famous Sequences: Cubes and Fibonacci

Prof. Keith Ball, Warwick University

SEQUENCES – EDEXCEL GCSE (1MA1): HIGHER TIER

Linear and Quadratic Sequences

Prof. Keith Ball, Warwick University

SEQUENCES – EDEXCEL GCSE (1MA1): HIGHER TIER

Geometric Sequences

Prof. Keith Ball, Warwick University

SEQUENCES – EDEXCEL GCSE (1MA1): HIGHER TIER

Formulae for Geometric Sequences

Prof. Keith Ball, Warwick University

SEQUENCES – EDEXCEL GCSE (1MA1): HIGHER TIER

Formulae for Linear Sequences

Prof. Keith Ball, Warwick University

SEQUENCES – EDEXCEL GCSE (1MA1): HIGHER TIER

Formulae for Quadratic Sequences

Prof. Keith Ball, Warwick University

E2.8 Proportion

RATIO, PROPORTION, AND RATES OF CHANGE II – EDEXCEL GCSE (1MA1)

Proportionality

Dr Thomas Woolley, Cardiff University

RATIO, PROPORTION, AND RATES OF CHANGE III – EDEXCEL GCSE (1MA1): HIGHER TIER

Direct Proportion

Dr Thomas Woolley, Cardiff University

RATIO, PROPORTION, AND RATES OF CHANGE III – EDEXCEL GCSE (1MA1): HIGHER TIER

Inverse Proportion

Dr Thomas Woolley, Cardiff University

RATIO, PROPORTION, AND RATES OF CHANGE III – EDEXCEL GCSE (1MA1): HIGHER TIER

Extending Proportion

Dr Thomas Woolley, Cardiff University

E2.9 Graphs in Practical Situations

GRAPHS III – EDEXCEL GCSE (1MA1): HIGHER TIER

Straight-Line Graphs in Real Contexts

Prof. Keith Ball, Warwick University

GRAPHS III – EDEXCEL GCSE (1MA1): HIGHER TIER

Distance-Time Graphs

Prof. Keith Ball, Warwick University

GRAPHS III – EDEXCEL GCSE (1MA1): HIGHER TIER

Velocity and Acceleration in Distance-Time Graphs

Prof. Keith Ball, Warwick University

GRAPHS III – EDEXCEL GCSE (1MA1): HIGHER TIER

Exponential Graphs in Real Contexts

Prof. Keith Ball, Warwick University

GRAPHS III – EDEXCEL GCSE (1MA1): HIGHER TIER

Finding Equations From Exponential Graphs

Prof. Keith Ball, Warwick University

GRAPHS III – EDEXCEL GCSE (1MA1): HIGHER TIER

Gradient and Area Under the Curve

Prof. Keith Ball, Warwick University

E2.10 Graphs of Functions

GRAPHS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Introduction

Prof. Keith Ball, Warwick University

GRAPHS I – EDEXCEL GCSE (1MA1): HIGHER TIER

The Coordinate Plane

Prof. Keith Ball, Warwick University

GRAPHS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Straight-Line Graphs

Prof. Keith Ball, Warwick University

GRAPHS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Slopes and Intercepts

Prof. Keith Ball, Warwick University

GRAPHS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Other Equations of Lines

Prof. Keith Ball, Warwick University

GRAPHS I – EDEXCEL GCSE (1MA1): HIGHER TIER

Finding Equations of Lines

Prof. Keith Ball, Warwick University

GRAPHS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Graphing Quadratic Functions

Prof. Keith Ball, Warwick University

GRAPHS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Intercepts and Roots of Quadratic Equations

Prof. Keith Ball, Warwick University

GRAPHS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Turning Points of Quadratic Functions

Prof. Keith Ball, Warwick University

E2.11 Sketching Curves

GRAPHS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Graphing Quadratic Functions

Prof. Keith Ball, Warwick University

GRAPHS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Graphing Cubic Functions

Prof. Keith Ball, Warwick University

GRAPHS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Graphing the Reciprocal Function

Prof. Keith Ball, Warwick University

GRAPHS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Graphing Exponential Functions

Prof. Keith Ball, Warwick University

GRAPHS II – EDEXCEL GCSE (1MA1): HIGHER TIER

Graphing Trigonometric Functions

Prof. Keith Ball, Warwick University

E2.12 Differentiation

DIFFERENTIATION I

Straight Lines and Gradients

Prof. Samir Siksek, Warwick University

DIFFERENTIATION I

Defining the Gradient of the Tangent to a Curve

Prof. Samir Siksek, Warwick University

DIFFERENTIATION I

Defining the Derivative

Prof. Samir Siksek, Warwick University

DIFFERENTIATION I

Differentiation From First Principles

Prof. Samir Siksek, Warwick University

DIFFERENTIATION I

Derivatives of Common Functions

Prof. Samir Siksek, Warwick University

DIFFERENTIATION II

Differentiation Rules

Prof. Samir Siksek, Warwick University

DIFFERENTIATION II

Applying Differentiation Rules to Trigonometric Functions

Prof. Samir Siksek, Warwick University

DIFFERENTIATION II

Stationary Points, Local Maxima, and Local Minima

Prof. Samir Siksek, Warwick University

E2.13 Functions

WHAT ARE NUMBERS?

Functions

Prof. Kevin Buzzard, Imperial College London

Contents

E2.1 Introduction to Algebra

E2.2 Algebraic Manipulation

E2.3 Algebraic Fractions

E2.4 Indices II

E2.5 Equations

E2.6 Inequalities

E2.7 Sequences

E2.8 Proportion

E2.9 Graphs in Practical Situations

E2.10 Graphs of Functions

E2.11 Sketching Curves

E2.12 Differentiation

E2.13 Functions