AQA GCSE Mathematics: Algebra (8300)

This guide covers Topic 2 Algebra, the second of six topic areas in AQA GCSE Mathematics (8300), first teaching September 2015. Like every GCSE maths specification, this content matches the Department for Education’s Mathematics GCSE subject content and assessment objectives document, so the same four sub-sections – and most of the same statements – appear, in some form, on every UK exam board’s GCSE maths course. It sits directly after Topic 1 Number and is assessed across all three papers; any topic can be examined on any paper, and questions frequently combine algebra with number, ratio or geometry content rather than testing it in isolation.

Syllabus coverage

AQA GCSE MATHEMATICS (8300) – TOPIC 2 ALGEBRA

• 3.2.1 Notation, vocabulary and manipulation – using and interpreting algebraic notation (ab, 3y, a², 1/a, in place of the longer expressions they abbreviate); substituting numerical values into formulae and expressions, including scientific formulae; understanding the vocabulary of expressions, equations, formulae, inequalities, terms and factors (and, at Higher tier, identities); simplifying and manipulating expressions by collecting like terms, expanding brackets, factorising, and – at Higher tier – expanding products of two or more binomials and factorising quadratics of the form ax² + bx + c; understanding and using standard formulae, including rearranging a formula to change the subject; and, at Higher tier, interpreting simple expressions as functions with inputs and outputs, including inverse and composite functions.
• 3.2.2 Graphs – working with coordinates in all four quadrants; plotting straight-line graphs and, at Higher tier, using y = mx + c to identify parallel and perpendicular lines and to find the equation of a line; identifying gradients and intercepts of linear functions both graphically and algebraically; identifying roots, intercepts and turning points of quadratic functions; recognising, sketching and interpreting graphs of linear, quadratic, cubic, reciprocal, exponential and (Higher tier) trigonometric functions; and, at Higher tier, calculating or estimating gradients of graphs and areas under graphs, including in kinematics and financial contexts, plus the equation of a circle centred at the origin and the tangent to a circle at a given point.
• 3.2.3 Solving equations and inequalities – solving linear equations in one unknown algebraically, including the unknown on both sides and equations involving brackets; at Higher tier, solving quadratic equations by factorising, completing the square and the quadratic formula; solving simultaneous equations in two variables, including linear/linear at Foundation tier and linear/quadratic at Higher tier; finding approximate solutions using a graph in all cases; at Higher tier, solving equations numerically by iteration; translating situations into equations or formulae and interpreting the solution; and solving linear inequalities (and, at Higher tier, quadratic inequalities), representing solution sets on a number line and, at Higher tier, using set notation.
• 3.2.4 Sequences – generating terms of a sequence from a term-to-term or position-to-term rule, including from patterns and diagrams; recognising and using triangular, square and cube number sequences and simple arithmetic progressions, plus, at Higher tier, Fibonacci-type, quadratic and simple geometric progressions (including where the common ratio is a surd); and deducing expressions for the nth term of linear sequences, extending at Higher tier to quadratic sequences.

How the four sub-sections connect

Algebra is the topic area most likely to appear woven into other parts of the paper, so it helps to see how its four sub-sections build on each other rather than treating them as separate mini-topics. Notation and manipulation (3.2.1) is the toolkit everything else depends on – you cannot solve an equation, plot a graph correctly, or find the nth term of a sequence without being fluent in expanding, factorising and rearranging first. Graphs (3.2.2) is largely manipulation made visual: a straight-line graph is y = mx + c in picture form, and a quadratic graph’s roots are exactly the solutions you would get by factorising or using the quadratic formula in 3.2.3. Solving equations and inequalities (3.2.3) is where manipulation gets used to find an actual answer, and the specification deliberately expects you to be able to solve the same equation two ways – algebraically and by reading a graph – because exam questions test both. Sequences (3.2.4) can feel separate, but the nth-term formulae are themselves algebraic expressions built and rearranged the same way as everything in 3.2.1.

Foundation versus Higher tier

All content can be assessed on any paper, but a meaningful share of Topic 2 is Higher-tier-only: quadratic factorising beyond the simplest case, the quadratic formula and completing the square, function notation (f(x), fg(x), f⁻¹(x)), circle equations and tangents, quadratic and geometric sequences, and quadratic inequalities are all reserved for Higher tier. A Foundation-tier student should not spend revision time on these; a Higher-tier student should treat them as the questions most likely to separate grades 7-9 from grade 6, since they build directly on Foundation-tier content rather than replacing it.

Common mistakes

• Losing marks on notation conventions. Writing “a × b” instead of “ab,” or leaving an answer as “2 × x + 3 × x” instead of “5x,” loses marks even when the underlying method is correct – the specification explicitly expects simplest form without being told.
• Confusing an equation with an identity. An equation is only true for specific values of the unknown; an identity is true for every value. This distinction is tested directly at Higher tier.
• Mixing up gradient and y-intercept in y = mx + c, especially when a question gives the equation in a rearranged form such as 2y = 4x + 6, where the gradient is 2, not 4.
• Forgetting to check both an algebraic and a graphical method when a question allows either – graphical solutions are usually approximate and algebraic ones exact, and mixing them up under time pressure is a common source of lost accuracy marks.
• Treating the nth-term formula as something to memorise per question rather than derive: for a linear sequence, the coefficient of n is always the common difference, which can be checked quickly against the first few terms.

How to approach it

Because Topic 2 sits between Number and the more visual topics (Geometry, Ratio, Statistics), the most efficient revision order is to consolidate notation and manipulation first, since weaknesses there surface as errors throughout graphs, equations and sequences rather than as isolated mistakes. Practise solving the same equation both algebraically and graphically so the connection between 3.2.2 and 3.2.3 becomes automatic rather than something you have to reason out in the exam. Keep a running list of which specific statements are Higher-tier-only, since misjudging this wastes revision time on content you will never be asked (Foundation) or leaves genuine gaps (Higher). Finally, because algebra is the topic most often blended into contextual, multi-step problems on this specification, practise past-paper questions that combine algebra with another topic area rather than only questions labelled “Algebra,” since that is closer to how AQA actually assesses it.

Related resources

• Algebra revision notes
• Algebra practice questions

Official syllabus

AQA, GCSE Mathematics (8300) Specification, for first teaching 2015, subject content section 3.2 Algebra, https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300/specification/subject-content/3.2-algebra, fetched and verified in full 2026-09-02.