Algebra

Revise collecting like terms, using algebraic notation correctly, simplifying expressions, and multiplying a single term over a bracket. This guide contains video and quizzes.

Revise factorising expressions into one or two brackets. For Higher tier, factorise quadratics when the coefficient of 𝑥 squared doesn't equal 1. This guide has video and quizzes.

Revise how to use algebra to support and construct arguments, show that two expressions are equivalent, and how to find a counterexample. This guide contains video and quizzes.

Revise writing formulae, substituting into expressions and formulae, and how to change the subject of a formula using inverse operations. This guide contains video and quizzes.

Learn about function notation, how to find an inverse function by changing the subject, and how to work with composite functions. This guide contains a quiz.

Learn how to use inverse operations to find the value of an unknown variable in an equation, so that the value is true. This guide contains a quiz.

Learn how to solve equations with brackets, 𝑥 terms on both sides, and fractions using inverse operations in this GCSE maths study guide. This guide contains videos and quizzes.

Inequalities are the relationships between two expressions not equal to one another. The symbols used for inequalities are <, >, ≤, ≥ and ≠. This guide contains video and quizzes.

Revise representing an inequality as a region on one side of a line. Dashed lines on graphs show the line is not included in the region. This guide contains video and quizzes.

Learn about term-to-term rules, 𝑛th term rules and how to work out expressions for 𝑛th terms based on a set of numbers in a quadratic sequence. This guide contains quizzes.

In geometric sequences, the term-to-term rule is to multiply or divide by the same value. Other sequences include square numbers and Fibonacci sequences. This guide has quizzes.

Revise plotting coordinates and creating straight line graphs to show the relationship between two variables. This guide contains video and quizzes.

Learn how to calculate the equation of a line from a graph, work out the gradient from an equation, and visualise intercepts. This guide contains video and quizzes.

Revise finding equations of parallel lines and the gradient of perpendicular lines, and prove that given lines are parallel or perpendicular. This guide contains video and quizzes.

Letters can be used to stand for unknown values or values that can change. Formulas can be written and equations solved to find solutions to a range of problems in science and engineering.

Formulae are used in everyday life, from working out areas and volumes of shapes to converting units of measurement. Knowing how to use and rearrange formulae are very useful skills.

Forming, using and solving equations are skills needed in many different situations. From balancing accounts to making sense of a mobile phone bill, solving equations is a vital skill.

Simultaneous equations require algebraic skills to find the values of letters within two or more equations. They are called simultaneous equations because the equations are solved at the same time.

Solve quadratic equations by factorising, using formulae and completing the square. Each method also provides information about the corresponding quadratic graph.

Algebraic expressions in fraction form are rational. Methods of adding, subtracting, multiplying and dividing fractions plus expanding and factorising can be used to simplify rational expressions.

Inequalities show the relationship between two expressions that are not equal to one another. Inequalities are useful when projecting profits and breakeven figures.

Sequences can be linear, quadratic or practical and based on real-life situations. Finding general rules helps find terms in sequences.

Graphs show the relationship between two variables and are often seen in newspapers and the media. People who work in professions involving maths and science commonly use graphs.

The most commonly occurring graphs are quadratic, cubic, reciprocal, exponential and circle graphs. Their equations can be used to plot their shape.

Functions of graphs can be transformed to show shifts and reflections. Graphic designers and 3D modellers use transformations of graphs to design objects and images.

Using graphs is not just about reading off values. In real-life contexts, the intercept, gradient and area underneath the graph can have important meanings such as a fixed charge, speed or distance.