What this topic covers
Algebra has 4 subtopics:
- Notation, vocabulary and manipulation
- Graphs
- Solving equations and inequalities
- Sequences
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GCSE Edexcel Higher Maths · Topic 2 of 6
Algebra – GCSE Edexcel Higher Maths revision notes
Choose a subtopic. Algebra covers Notation, vocabulary and manipulation, Graphs, Solving equations and inequalities, and Sequences in GCSE Edexcel Higher Maths. 39 lessons in 4 subtopics.
Revise Algebra for GCSE Edexcel Higher Maths, including Notation, vocabulary and manipulation, Graphs, Solving equations and inequalities, and Sequences.
39
Lessons
4
Subtopics
Algebra lessons by subtopic
39 lessons, grouped by subtopic.
Notation, vocabulary and manipulation
- Substituting Values into Formulae and Expressions
- Understanding Algebraic Language
- Expanding and Factorising Expressions
- Collecting Like Terms and Basic Algebraic Operations
- Advanced Algebraic Manipulation
- Substituting into and Interpreting Formulae
- Changing the Subject of a Formula
- Equations vs Identities and Algebraic Arguments
- Algebraic Proofs
- Interpreting Expressions as Functions
Graphs
- Working with Coordinates in All Four Quadrants
- Plotting Straight-Line Graphs
- Gradients and Intercepts of Linear Functions
- Turning Points and Symmetry of Quadratics
- Quadratic Graphs - Roots and Intercepts
- Recognising and Sketching Linear and Quadratic Graphs
- Straight-Line Graph Skills and Gradients
- Transformations of Linear and Quadratic Graphs
- Interpreting Real-World Graphs
- Interpreting Gradients and Areas Under Graphs
- Circle Equations and Properties
- Tangents to Circles
Solving equations and inequalities
- Solving Linear Equations Algebraically
- Finding Approximate Solutions Using Graphs
- Completing the Square and the Quadratic Formula
- Solving Quadratic Equations by Factorising
- Solving simultaneous equations algebraically
- Graphical solutions to simultaneous equations
- Solving Quadratics, Simultaneous Equations and Rearranging Formulae: Solve quadratic equations by factorising, completing the square and the quadratic formula, use the discriminant, solve linear–quadratic simultaneous equations and rearrange complex formulae.
- Numerical Solutions Using Iteration
- Solving Linear Equations with Brackets and Unknowns on Both Sides
- Creating Algebraic Expressions from Situations
- Solving Equations from Real Problems
- Representing Solution Sets
- Advanced Inequalities
- Solving Linear Inequalities
Sequences
Revise Right Mocks '26
Edexcel GCSE Maths mock draft, 26–31 Oct. Draft coverage: Maths Paper 1 (Higher tier). Reviewed for an original-practice sitting; check student availability before registering. Marking and results will follow later, after separate approval. Eligible new accounts receive a five-day Pro trial when signup email verification completes. Previous trials keep their original expiry. After expiry, new papers need Pro unless you have an explicitly confirmed free sitting offer for this event. That offer adds no Pro time or AI learning. Saved attempts and released results remain readable. No card or automatic charge.
More in this course
Go back to the full GCSE Edexcel Higher Maths topic list, or practise this topic with past-paper questions.
Frequently asked questions
What is Algebra?
Algebra covers Notation, vocabulary and manipulation, Graphs, Solving equations and inequalities, and Sequences in GCSE Edexcel Higher Maths. 39 lessons in 4 subtopics.
How do you use the quadratic formula?
The quadratic formula, x = (-b ± √(b² - 4ac)) ÷ 2a, solves any quadratic in the form ax² + bx + c = 0. The Completing the Square and the Quadratic Formula notes cover this in full.
What is the equation of a circle?
The equation of a circle with centre at the origin is x² + y² = r², where r is the radius. The Circle Equations and Properties notes cover this in full.
How do you substitute into the area of a trapezium formula?
The area of a trapezium is A = 1/2(a + b)h, where a and b are the parallel sides and h is the perpendicular height. The Substituting into and Interpreting Formulae notes cover this in full.
How do you use the trapezium rule?
The trapezium rule estimates the area under a curve using equal strips, where the first and last y-values appear once and the middle values are doubled. The Interpreting Gradients and Areas Under Graphs notes cover this in full.
How do you expand and simplify brackets?
To expand and simplify, expand each bracket, write out all the terms, then collect like terms. The Collecting Like Terms and Basic Algebraic Operations notes cover this in full.
What are triangular numbers?
Triangular numbers are the totals of stacked rows of dots, with one dot in the first row, then two, then three, and so on: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55. The Triangular, Square and Cube Numbers and Arithmetic Progressions notes cover this in full.
What is an expression in maths?
An expression is a mathematical phrase made up of one or more terms connected by operations such as +, -, × and ÷. The Understanding Algebraic Language notes cover this in full.
How do you expand triple brackets?
To expand three brackets, expand two first, then multiply the result by the third. The Expanding and Factorising Expressions notes cover this in full.