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This topic covers the three main methods for solving quadratic equations — factorising, completing the square and the quadratic formula — and choosing the most efficient for a given equation. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Rearrange to equal zero, then factorise if possible. If not, use the quadratic formula or complete the square. Check whether both solutions make sense in context — a negative length or time is usually rejected.
Before you start
The prerequisite is factorising and the quadratic formula. It is Pure 1 content. You will lean on this again for the discriminant and quadratic inequalities.
What you learn
The skill is spotting the hidden quadratic, substituting, solving, and rejecting any invalid value before finishing. After a substitution, back-substitute and check each value is valid — e.g. The course works through factorising & solving, the formula & exact roots, disguised quadratics, exponential & index-form quadratics and simultaneous: a line meets a curve. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Solving Quadratics is a Algebra topic in the A-level syllabus, covered here at the AS year. The course is built from 5 concept sections, 5 worked examples and 5 check points before the exam-style set. Students often pair it with Transformations of Graphs, Algebraic Division and Algebraic Fractions. Endless extra practice on this strand is available on the Algebra revision engine, which generates a fresh question each time.
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