DfE statement A22 · Algebra
Linear and quadratic inequalities
Linear and quadratic inequalities is content statement A22 of the DfE GCSE mathematics subject content, in the algebra area. It is on both tiers, with a Higher-only part, and it is examined without a calculator. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graph." (statement A22). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "or two", "and quadratic inequalities in one variable", "using set notation and on a graph". Everything else in the statement is Foundation content.
Calculator
This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.
Common mistakes
- Not reversing the inequality sign when multiplying or dividing by a negative number.
- Using a filled circle for a strict inequality on a number line. < and > take an open circle; ≤ and ≥ take a filled one.
- Giving the solution of a quadratic inequality as two separate outer regions when the parabola is below the axis between the roots — sketch the curve and read off the region asked for.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is linear and quadratic inequalities on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "or two", "and quadratic inequalities in one variable", "using set notation and on a graph" — are Higher only; the rest is Foundation content.
Can I use a calculator for linear and quadratic inequalities?
Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.
What is the single most common mistake here?
Not reversing the inequality sign when multiplying or dividing by a negative number.
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Algebra at Foundation or at Higher.