How important is the Algebra area in AQA GCSE Mathematics?

Algebra is one of the two largest areas of the course and is assessed on every paper. It is the strand that most separates grades, because higher grades depend on confident manipulation, solving and graph work. Weak algebra leaks marks across ratio, geometry and statistics too, so it rewards early and thorough practice.

Which Algebra topics are Higher tier only?

Completing the square, the quadratic formula in full, simplifying algebraic fractions, solving a linear and quadratic pair simultaneously, quadratic inequalities, function notation and harder graph transformations are weighted to Higher tier. Foundation tier covers manipulation, linear equations, linear simultaneous equations, simple sequences, straight line graphs and linear inequalities.

What does AQA give on the formulae sheet for Algebra?

AQA provides the quadratic formula on the formulae sheet, so you do not have to memorise it, but you must know how to use it accurately, including the discriminant $b^2 - 4ac$. Most other algebra, such as expanding, factorising, completing the square and the index laws, must be carried out from memory.

What is the most common Algebra mistake?

Sign errors are by far the most common, especially when expanding double brackets, moving terms across an equals sign, or using the quadratic formula. Forgetting the $\pm$ in the quadratic formula and cancelling terms instead of factors in algebraic fractions are also frequent. Showing every step protects the method marks.

How should I revise the Algebra area?

Build manipulation first, then linear equations, then simultaneous and quadratic equations, then sequences, then graphs, then inequalities. Drill each technique until it is automatic, always show full working so method marks are secure, and practise reading graph shapes from equations. Finish with mixed problems that combine algebra with other areas.

EnglandMaths

AQA GCSE Mathematics Algebra: a complete overview of manipulation, equations, sequences, graphs and inequalities

A deep-dive AQA GCSE Mathematics guide to the Algebra area. Covers algebraic manipulation, solving linear and simultaneous equations, quadratic equations, sequences, straight line graphs, other graphs and functions, and inequalities, with the techniques and exam patterns AQA repeats.

Generated by Claude Opus 4.818 min read8300Updated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What the Algebra area demands
Manipulation and linear equations
Simultaneous and quadratic equations
Sequences
Graphs and functions
Inequalities
How the Algebra area is examined
Check your knowledge

What the Algebra area demands

Algebra is the language of the rest of mathematics. It takes the number skills you already have and generalises them, so that you can manipulate expressions, solve equations, describe sequences and read the behaviour of graphs. AQA tests fluent manipulation, accurate solving, and the ability to connect algebra to graphs and real situations.

This guide walks through the eight Algebra topics in specification order, then sets out the exam patterns AQA repeats. Each topic has a matching dot-point page with practice questions; this overview ties them together.

Manipulation and linear equations

The area opens with algebraic manipulation: collecting like terms, expanding single and double brackets, factorising, and at Higher tier simplifying algebraic fractions. This feeds directly into solving linear equations, including equations with brackets, fractions and the unknown on both sides, and changing the subject of a formula.

Simultaneous and quadratic equations

Simultaneous equations are solved by elimination or substitution, and at Higher tier this extends to a linear and quadratic pair. Quadratic equations are a major topic: solving by factorising, by the quadratic formula, and at Higher tier by completing the square, and interpreting the roots and turning point.

Sequences

Sequences covers continuing patterns, finding the nth term of linear and (at Higher tier) quadratic sequences, and recognising geometric, triangular and Fibonacci sequences. The nth term connects sequences to straight-line and quadratic graphs.

Graphs and functions

Straight line graphs uses $y = mx + c$ to read gradient and intercept, find equations through points, and apply the parallel and perpendicular rules. Other graphs and functions covers recognising and sketching quadratic, cubic, reciprocal and exponential curves, reading roots and turning points, and function notation at Higher tier.

Inequalities

Inequalities covers solving linear inequalities, showing solutions on a number line, solving quadratic inequalities at Higher tier, and shading regions on a graph. The key extra rule is reversing the inequality sign when multiplying or dividing by a negative.

How the Algebra area is examined

A typical AQA profile for Algebra:

Manipulation. Expanding, factorising, simplifying and substituting into expressions.
Solving. Linear, simultaneous and quadratic equations, with full working for method marks.
Graphs. Plotting and interpreting straight lines and curves, finding gradients, intercepts, roots and turning points.
Reasoning and problem solving. Forming equations from words, using sequences, and combining algebra with ratio and geometry.

Check your knowledge

A mix of recall and solving questions covering the Algebra area. Attempt them under timed conditions, then check against the solutions.

Expand and simplify $(x + 4)(x - 1)$ . (2 marks)
Solve $5x - 2 = 3x + 8$ . (2 marks)
Solve $x^2 + 2x - 8 = 0$ by factorising. (2 marks)
Find the nth term of $7, 11, 15, 19, \ldots$ . (2 marks)
State the gradient and $y$ -intercept of $y = 3x - 4$ . (2 marks)
Solve the inequality $4x + 1 < 13$ . (2 marks)
Solve simultaneously $x + y = 10$ and $x - y = 4$ . (3 marks)
Write $x^2 + 6x + 7$ in completed-square form. (2 marks)

Solutions

Step 1: Expand and simplify double brackets

Multiply every term in the first bracket by every term in the second using FOIL, then collect like terms. This is the foundation for factorising in reverse and for working with quadratics.

(x + 4)(x - 1) = x^2 - x + 4x - 4 = x^2 + 3x - 4

Final answer: $x^2 + 3x - 4$ .

Step 2: Solve a linear equation by balancing

Collect variable terms on one side and constant terms on the other by performing the same operation to both sides. Showing each step secures the method marks even if an arithmetic slip occurs.

5x - 2 = 3x + 8 \Rightarrow 2x - 2 = 8 \Rightarrow 2x = 10 \Rightarrow x = 5

Final answer: $x = 5$ .

Step 3: Solve a quadratic equation by factorising

Set the equation equal to zero, factor it into two brackets, then apply the zero-product property: each bracket set to zero gives one solution. The solutions are opposite in sign to the constants in the brackets.

x^2 + 2x - 8 = 0 \Rightarrow (x + 4)(x - 2) = 0

x = -4 \text{ or } x = 2

Final answer: $x = -4$ or $x = 2$ .

Step 4: Find the nth term of a linear sequence

The common difference between consecutive terms is the coefficient of $n$ in the nth term. Substituting $n = 1$ into the expression and comparing with the first term determines the constant to add or subtract.

Common difference $= 4$ , so the nth term starts as $4n$ . When $n = 1$ , $4n = 4$ but the first term is $7$ , so add $3$ .

Final answer: $4n + 3$ .

Step 5: Read the gradient and y-intercept from slope-intercept form

The equation $y = mx + c$ reveals the gradient $m$ and y-intercept $c$ directly by comparison. No calculation is needed; the values are read off by matching the structure.

$y = 3x - 4$ has gradient $3$ and y-intercept $-4$ .

Final answer: Gradient $3$ , y-intercept $-4$ .

Step 6: Solve a linear inequality

Solve a linear inequality using the same steps as a linear equation. The one extra rule is that multiplying or dividing both sides by a negative number reverses the inequality sign.

4x + 1 < 13 \Rightarrow 4x < 12 \Rightarrow x < 3

Final answer: $x < 3$ .

Step 7: Solve simultaneous equations by elimination

When adding the two equations eliminates one variable, you can solve immediately for the remaining one. Back-substitute to find the eliminated variable.

Adding: $(x + y) + (x - y) = 10 + 4 \Rightarrow 2x = 14 \Rightarrow x = 7$ .

Substituting: $7 + y = 10 \Rightarrow y = 3$ .

Final answer: $x = 7$ , $y = 3$ .

Step 8: Complete the square

Completing the square rewrites $x^2 + bx + c$ in the form $(x + p)^2 + q$ by halving the coefficient of $x$ for the bracket and then adjusting the constant. This is useful for finding the vertex of a parabola and for solving quadratics.

Half of $6$ is $3$ ; $(x + 3)^2 = x^2 + 6x + 9$ , which is $2$ more than $x^2 + 6x + 7$ .

(x + 3)^2 - 2

Final answer: $(x + 3)^2 - 2$ .

Sources & how we know this

AQA GCSE Mathematics (8300) specification — AQA (2015)