Algebra
Algebra helps us generalise patterns and solve problems where values are unknown. It forms the foundation for many GCSE Maths topics including equations, graphs, functions and formulae. These lessons cover key Foundation and Higher topics needed for GCSE Maths exams.
What you’ll learn in Algebra
Expressions and sequences
Build confidence with notation, patterns and algebraic manipulation.
1. Introduction to Algebra
Read algebraic notation, substitute values into expressions and formulae, and understand basic equations.
View Lesson →Foundation & Higher2. Simplifying Algebraic Expressions
Collect like terms, simplify products and powers, and use algebra to explain and justify results.
View Lesson →Foundation & Higher3. Sequences and nth Terms
Recognise linear, quadratic and geometric patterns; find linear nth terms, then derive quadratic nth terms at Higher.
View Lesson →Foundation & Higher4. Expanding Brackets
Expand single and double brackets, then explore Higher three-bracket expansion and algebraic proof.
View Lesson →Foundation & Higher5. Factorising
Take out common factors and factorise quadratics, including a Higher extension with a coefficient before x².
View Lesson →Equations, functions and numerical methods
Solve equations, work with functions and extend into Higher numerical methods.
6. Solving Linear Equations
Solve equations with one unknown using inverse operations, step by step.
View Lesson →Foundation & Higher7. Inequalities
Solve linear inequalities, show number-line solutions and explore Higher quadratics and regions.
View Lesson →Foundation & Higher8. Quadratic Equations
Solve quadratics by factorising, then progress to the formula and completing the square.
View Lesson →Foundation & Higher9. Rearranging Formulae
Change the subject of a formula by rearranging algebraic expressions correctly.
View Lesson →Higher10. Algebraic Fractions
Simplify and calculate with algebraic fractions, track restrictions and solve fraction equations.
View Lesson →Foundation & Higher11. Solving Simultaneous Equations
Solve pairs by substitution and elimination, interpret intersections, and try a Higher linear–quadratic example.
View Lesson →Foundation & Higher12. Functions
Start with function machines, then learn Higher function notation, composite rules and inverse functions.
View Lesson →Higher13. Numerical Methods and Iteration
Approximate roots using sign changes, decimal search and iterative formulae.
View Lesson →Graphs and coordinate mathematics
Start with straight lines, then explore graph families, transformations and circle equations.
14. Linear Graphs
Plot straight lines, find their equations, identify parallel lines and explore Higher perpendicular lines.
View Lesson →Foundation & Higher15. Quadratic Graphs and Graphical Solutions
Plot quadratics, read roots and turning points, and solve equations using crossings.
View Lesson →Foundation & Higher16. Cubic, Reciprocal and Exponential Graphs
Explore cubic and reciprocal graphs, with Higher exponential growth and decay.
View Lesson →Higher17. Trigonometric Graphs
Recognise sine, cosine and tangent graphs, periods and graphical solutions in degrees.
View Lesson →Higher18. Graph Translations and Reflections
Translate and reflect graphs, track coordinates and write transformed equations.
View Lesson →Higher19. Circle Equations and Tangent Lines
Use origin-centred circle equations and find tangents with perpendicular gradients.
View Lesson →