Algebra — domain overview

Algebra accounts for roughly 30% of the marks in AQA GCSE Maths 8300. It spans 25 specific points (A1–A25) and tests your ability to manipulate symbols, model real situations, and interpret graphs.

The five algebra strands

Strand	Key spec points	Core skill
Notation & manipulation	A1–A6	Writing, simplifying, expanding, factorising expressions
Functions & equations	A7, A17–A22	Solving linear, quadratic, simultaneous; inequalities
Graphs	A8–A16	Plotting, interpreting gradients, sketching function families
Sequences	A23–A25	Term-to-term, nth-term (linear and quadratic)
Modelling	A21	Forming and solving equations in context

Calculator vs non-calculator

Most algebra questions are non-calculator (Papers 1 and 2 combined have one non-calc paper). Exact surd answers, factorising quadratics and algebraic proof all tend to be non-calc.

What examiners look for

1. Show working — an incorrect final answer can still earn method marks if your algebra is visible
2. Check by substitution — substitute your solution back into the original equation
3. Factorise before cancelling — never cancel individual terms; only common factors of the whole numerator/denominator
4. Use the formula sheet wisely — the quadratic formula is given; you don't need to memorise it, but you must be able to use it accurately

The must-know techniques

Expanding and factorising

• Single bracket: $a(b + c) = ab + ac$
• Double bracket: $(x + 2)(x - 3) = x^2 - x - 6$
• Difference of two squares: $a^2 - b^2 = (a+b)(a-b)$
• Perfect square: $(a pm b)^2 = a^2 pm 2ab + b^2$

Solving quadratics

Three methods — know when to use each:

1. Factorising — works when integer roots exist
2. Completing the square — best for deriving the vertex form $a(x-h)^2 + k$
3. Quadratic formula — always works; use when roots are irrational

Simultaneous equations

• Elimination — multiply to align coefficients, then add/subtract
• Substitution — required for linear/quadratic pairs

Inequalities

Treat like equations except: dividing or multiplying by a negative flips the sign.

Common exam mistakes

1. Sign errors in expanding — $(x - 3)^2 e x^2 - 9$; it equals $x^2 - 6x + 9$
2. Incorrect factorisation — always check by re-expanding
3. Forgetting ± when square-rooting — if $x^2 = 16$, then $x = pm 4$
4. Dividing inequalities by negatives — must flip the sign
5. Graph reading precision — use a ruler; read intercepts at axis crossings

Grade boundaries (approximate)

Grade	Algebra expectation
4 (pass)	Expand brackets, solve linear equations, plot linear graphs, nth term of arithmetic sequences
6	Factorise quadratics, solve quadratic by formula/factorising, simultaneous (linear), inequalities
8–9	Complete the square, iteration, proof, linear/quadratic simultaneous, circle equations, sketching