Quadratic equations

AQA GCSE Maths

8 ready-made resources for teaching Quadratic equations, written for AQA GCSE Maths. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where students usually go wrong, free to read whether or not you sign up.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Tiered worksheetWord, editable
Worksheet mark schemeWord, editable

Foundation tier

Solve quadratic equations by factorising when the coefficient of x² is 1 (e.g. x² + 5x + 6 = 0).
Recognise and apply the zero product rule (if ab = 0, then a = 0 or b = 0).
Solve simple quadratics of the form x² = a, including both positive and negative roots.
Substitute values into a given quadratic formula to find solutions (calculator use).

Higher tier, in addition

Factorise quadratics where the coefficient of x² is not 1 (e.g. 2x² + 7x + 3).
Complete the square for a quadratic expression, and use this to find the turning point or solve the equation.
Recall and use the quadratic formula unaided, from 2028 onward (see policy note below).
Solve quadratic equations arising from worded/contextual problems, including simultaneous equations that combine a linear and a quadratic equation.
Rearrange an equation into standard form (ax² + bx + c = 0) before solving.

Where students go wrong

Forgetting the negative root when square-rooting (e.g. solving x² = 9 and giving only x = 3).
Sign errors when factorising expressions with a negative constant term.
Substituting a, b, c incorrectly into the quadratic formula, especially when a term is missing or negative.
Persisting with factorising when an equation doesn't factorise into nice integers, instead of switching method.
Sign errors when completing the square.

How it gets asked in the exam

"Solve", "Factorise", "Show that...", "Find the values of x", "Hence solve", "Solve by completing the square".

Key vocabulary

Quadratic, coefficient, root, factorise, expand, turning point, completing the square, quadratic formula, zero product rule, discriminant (Higher).

Assumed prior knowledge

Expanding double brackets and factorising simple linear expressions.
Solving linear equations confidently.
Understanding of square roots, including that a positive number has two square roots.
Basic surd manipulation (Higher only, for non-integer solutions).

How Speca scaffolds this topic

Use a consistent factor-pair grid/box method as the default visual for factorising, repeated across every worked example.
Provide a simple decision flowchart ("does it factorise? → try the formula; is it x² = number? → square root directly") to reduce the cognitive load of choosing a method.
Colour-code the a, b, c values consistently when substituting into the quadratic formula.
Break completing the square into discrete, visually separated steps (e.g. using algebra-tile-style diagrams) rather than one dense algebraic line.

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