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Manipulating Expressions
Collecting like terms
The language of algebra
Multiplying out brackets
Multiplying out harder brackets
Expanding two sets of brackets
Adding and subtracting algebraic fractions
Expanding brackets in more complex situations
Solving Linear Equations
Simple linear equations
Linear equations including fractional coefficients
Unknowns on both sides of a simple equation
Simplifying to aid solving
Slightly more complex equations
Unknowns on both sides - a bit more complex
Simplifying to aid solving - a bit more complex
Constructing equations and then solving them
Graphical representation of equations
Algebraic fractions
Solving Linear Inequalities
Linear inequalities in one variable and solutions on a number line
Inequalities in two variables and solutions on a graph
Solving Simultaneous Equations
Eliminating a variable to solve simultaneous linear equations
Graphical representation of simultaneous equations
No solutions and infinite solutions
Solving by substitution when one equation is quadratic
Graphical representations of cases involving a circle
Tinkering with Formulae
Substituting numbers into formulae
Changing the subject of a formula
Considering the dimensions of a formula
Deriving and using complex formulae
Changing the subject of a formula in more complex cases
Investigating Graphs I
Plotting simple linear graphs
Recognising straight line graphs
Plotting graphs of functions in implicit cases
Finding the gradient of a straight line from its formula
Interpreting real-life graphs
Gradients and intercepts
Recognising cubic and reciprocal graphs
Recognising circular graphs
Exponential and trigonometric graphs
Investigating Graphs II
Generating and plotting simple quadratic functions
Identifying parallel lines
Inverse functions and their graphs
Exploring parallel and perpendicular lines
Finding equations of perpendicular lines
Transforming graphs
Solving Quadratic Equations
Finding approximate solutions of a quadratic equation by using a graph
Solving simple quadratic equations by factorising
Identifying cases where factorising should be used
Equations involving harder algebraic fractions
Using the formula to solve quadratic equations
Using graphs to find approximate solutions to quadratic equations
Identifying the number of solutions to a quadratic equation
Using the formula to solve quadratic equations in more complex cases
Using completing the square to solve quadratic equations
Deriving the formula for solving quadratic equations
Using completing the square to solve problems
Tinkering with Expressions
Taking out common factors
Using laws of indices in algebraic cases
Factorising quadratic expressions
Simplifying rational expressions
Establishing identities
More complex cases of completing the square
Pattern Sniffing
Generating simple sequences
Finding the nth term for linear sequences
Finding the nth term for quadratic sequences
Key
Appropriate for all students studying the GCSE Higher Tier course
Appropriate for students aiming to get a grade C or higher
Appropriate for students aiming to get a grade B or higher
Appropriate for students aiming to get a grade A or higher
Appropriate for students aiming to get a grade A*