A-level maths / Pure 1 / Quadratics
Quadratics
Solve equations, understand their graphs and use them to model a situation.
Choose the skill you need, or follow the lessons in order. The written working stays visible; animations and interactive models are there when they help.
- Solving quadratic equationsSolve quadratics by factorising, taking square roots and using the formula. Recognise hidden quadratics and check for lost or extra solutions.
- Completing the squareUnderstand the correction with an area model, then find turning points and solve equations.
- Quadratic graphs, functions and rangeUnderstand function notation, sketch quadratic graphs, find intercepts and turning points, and work out the range from the allowed inputs.
- The discriminantUse b² − 4ac to count real roots, solve parameter questions, explain tangency and prove when roots must exist.
- Quadratic modellingBuild quadratic models from a context or data, find sensible roots and maxima, and explain the assumptions and limits of the answer.
Where to begin
If expanding or factorising is slowing you down, revisit expanding and factorising. To revise a specific skill, open a lesson and choose any section directly.