Expanding, factorising, and inequalities

AQA GCSE Maths

8 ready-made resources for teaching Expanding, factorising, and inequalities, 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

Expand a single bracket, including where the multiplier is negative or algebraic.
Expand and simplify an expression containing two or more brackets.
Factorise an expression by taking out the highest common factor.
Expand a pair of binomials (double brackets).
Solve a linear inequality and represent the solution set on a number line.
Solve a linear inequality and write the solution using inequality notation.

Higher tier, in addition

Expand three binomials.
Factorise a quadratic expression where the coefficient of x² is greater than 1.
Recognise and factorise a difference of two squares.
Factorise an expression by grouping terms in pairs.
Solve a quadratic inequality and represent the solution set.
Solve a linear inequality in two variables and represent the region that satisfies it on a graph.

Where students go wrong

Making a sign error when expanding a bracket with a negative multiplier.
Multiplying only some of the terms inside a bracket rather than every term.
Factorising incompletely, leaving a common factor still inside the bracket.
Forgetting to reverse the inequality sign when multiplying or dividing both sides by a negative number.
Using a closed circle instead of an open circle on a number line (or vice versa) for strict versus non-strict inequalities.
Confusing the intersection ("and") region with the union ("or") region when combining two-variable inequalities.

How it gets asked in the exam

"Expand and simplify...", "Factorise...", "Solve the inequality...", "Show the solution set on a number line", "Shade the region that satisfies...".

Key vocabulary

Expand, factorise, bracket, term, common factor, binomial, inequality, solution set, difference of two squares, region.

Assumed prior knowledge

Solving linear equations.
Factorising and solving quadratic equations.
Collecting like terms and working with negative numbers.
Plotting straight-line graphs, needed for two-variable inequality regions.

How Speca scaffolds this topic

Use a consistent "expand checklist", an arrow drawn from the term outside the bracket to every term inside it, with a dedicated sign-tracking box, so no term is missed and no sign is dropped.
Provide a fixed open/closed circle reference card (< and > → open circle; ≤ and ≥ → filled circle) shown alongside every number-line inequality question.
Use a consistent highlighted "flip the sign" alert box wherever an inequality is multiplied or divided by a negative number, so the rule is visually flagged every time it applies rather than only stated once.

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