1. Introduction to indices (exponents)
2. Multiplication rules for indices
3. Division rule for indices
4. Negative indices
5. Fractions raised to a negative index
6. Rational (fractional) indices
7. Simplifying terms with negative powers
8. Expressing terms in the form axⁿ
9. Equations in which the power has to be found
10. Summary of indices
11. Exam Questions - Indices

Algebra Basics

1. Expanding a single bracket
2. Expanding two or more brackets
3. Squaring a bracket
4. Terms in expressions and equations
5. Identity or equation - what is the difference?
6. Linear Equations with a positive x term
7. Linear equations with a negative x-term
8. Linear equations with two x-terms
9. Linear equations with brackets
10. Fractional linear equations
11. f(x) notation
12. Polynomials

Polynomials

1. Polynomials

Pythagoras’ Theorem

1. Pythagoras' theorem

Trigonometry Introduction

1. Introduction to trigonometry
2. Finding the length of a side
3. Finding an angle
4. Mixed Exercise - Pythagoras and Trigonometry

1. Surds - introduction & simplifying
2. Addition and subtraction of surds
3. Multiplying surds
4. Dividing surds
5. Rationalising surds
6. Exam Questions - Surds

1. f(x) notation

Factorising

1. Introduction to factorising
2. Highest common factor (HCF)
3. Factorising by grouping
4. Factorising quadratic expressions
5. Mixed Exercise - Factorising
6. Exam Questions - Factorising

Completing the Square

1. Completing the square
2. Applications of completing the square
3. Exam Questions - Completing the square

Simultaneous Equations

1. Elimination method for linear equations
2. Substitution method for linear and non-linear equations
3. Exam Questions - Simultaneous equations

1. Solve by factorising
2. Solve by completing the square
3. Solve by the quadratic formula
4. Exam Questions - Solved by the quadratic formula
5. Solving quadratic equations in some function of x

Quadratic Equations – Roots and Discriminant

1. Roots and discriminant of a quadratic equation
2. Exam Questions - Roots and discriminant

Quadratic Graphs

1. Sketching quadratic graphs

1. Linear inequalities
2. Rules for reversing the inequality sign
3. Solving a linear type
4. Solving a double inequality
5. Exam Questions - Solving a double inequality
6. Quadratic inequalities
7. Exam Questions - Quadratic inequalities
8. Exam Questions - Simultaneous inequalities

1. Algebraic long division

Factor and Remainder Theorems

1. The factor theorem
2. How to solve a cubic equation
3. Exam Questions - Factor theorem
4. The remainder theorem
5. Exam Questions - Remainder theorem

1. Sketching cubic curves
2. Sketching reciprocal curves of the form y = k/x

1. Line segment
2. Parallel lines
3. Perpendicular lines

Lines

1. Equation of a straight line: y=mx+c
2. Equation of a line given the gradient and point
3. Distance between two points
4. Mid-point of a line segment
5. Equation of a parallel line
6. Equation of a perpendicular bisector

Intersection of Graphs

1. Intersection of two straight lines
2. Intersection of a straight line and a parabola
3. Intersection of a straight line and a hyperbola
4. Nature of the intersection

Circles

1. Equation of a circle
2. Finding the centre and radius
3. Circle properties
4. Equation of a tangent to a circle
5. Equation of a circle through 3 points
6. Exam Questions - Circles

1. The gradient function dy/dx
2. Differentiation - terms of the form axⁿ
3. The second derivative
4. Exam Questions - Differentiation: introduction

Tangents and Normals

1. Equations of tangents and normals
2. Exam Questions - Tangents and normals

Stationary Points

1. Stationary points
2. Nature of a stationary point
3. Exam Questions - Stationary points
4. Applications of stationary points
5. Exam Questions - Applications of stationary points

Increasing and Decreasing functions

1. Increasing and decreasing functions
2. Exam Questions - Increasing and decreasing functions

1. Integration - Terms of the form axⁿ
2. Exam Questions - Integration: introduction

Equations of Curves

1. Finding the equation of a curve given the gradient function
2. Exam Questions - Equations of curves

Definite Integration

1. Definite integration
2. Convergent and Divergent Integrals

Applications of Integration – Area bound by a curve

1. Area bound by a curve and x-axis
2. Exam Questions - Area bound by a curve and x-axis