A-Level Algebra & Functions Revision
Algebra and functions revision for A-Level and International A-Level Maths
Algebra is the topic every other A-Level topic depends on. Marks lost in calculus, trigonometry or coordinate geometry are very often algebra marks in disguise — a surd mishandled, a discriminant sign reversed, a fraction not simplified before it was differentiated. This free revision engine covers the algebra and functions content of Edexcel A-Level Maths and the International A-Level Pure 1 to Pure 4 papers, from indices and surds in the first weeks of Year 12 through to partial fractions in Year 13. It generates a new question every time and marks your answer as you go.
What the algebra revision engine covers
Indices and surds — the index laws, simplifying surds and rationalising a denominator Quadratic functions and the discriminant — using b² − 4ac to determine the nature of the roots Completing the square — writing a quadratic as (x + p)² + q and reading off the minimum Solving quadratics — factorising, the formula, and answers left in surd form Inequalities — linear and quadratic, including sketching to find the correct region Transformations of graphs — translations, stretches and reflections of y = f(x) The factor and remainder theorems — testing factors and finding unknown coefficients Algebraic division — dividing polynomials and factorising a cubic fully The modulus function — solving equations and inequalities involving |x| Functions, domain and range — what a function accepts and what it produces Composite and inverse functions — fg(x), gf(x), and finding f⁻¹(x) Algebraic fractions — simplifying, adding and solving Improper algebraic fractions — dividing out to a quotient plus a remainder Partial fractions — splitting a rational function into simpler pieces
Algebra formulas and results you need to know
The discriminant. For ax² + bx + c = 0, the discriminant is b² − 4ac. Positive gives two distinct real roots, zero gives one repeated root, negative gives no real roots. The quadratic formula. x = (−b ± √(b² − 4ac)) / 2a. Completing the square. x² + bx + c becomes (x + b/2)² + c − (b/2)², and the minimum value is the constant left outside. The factor theorem. (x − a) is a factor of f(x) exactly when f(a) = 0. The remainder theorem. Dividing f(x) by (x − a) leaves a remainder of f(a). The modulus function. |A| = B means A = B or A = −B. |A| < B means −B < A
How to use it
Choose a topic or a whole exam module. The engine generates a question, you type your answer, and it marks it straight away — accepting any equivalent form, so a surd, a fraction or a decimal all count where they are genuinely equal. If you get stuck there are two hints: one to name the technique, one to nudge you through it. Signing in saves your accuracy per topic to your A-Level skill tree.
More A-Level Maths revision
If algebra is where you are losing marks, it is worth being fluent here before moving on — partial fractions feed directly into integration, and transformations of graphs into trigonometry. Every topic and your progress across all of them is on the revision hub. All of our revision engines are free to use.