DfE statement A18 · Algebra
Solving quadratic equations
Solving quadratic equations is content statement A18 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 4 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 quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula; find approximate solutions using a graph." (statement A18). 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: "including those that require rearrangement", "by completing the square and by using the quadratic formula". 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
- Reading the solutions of (x − 3)(x + 5) = 0 straight off as x = 3 and x = 5. The signs flip: x = 3 and x = −5.
- Forgetting the negative root. x² = 49 has two solutions, 7 and −7.
- Using the formula or factorising before rearranging the equation to equal zero.
- In the quadratic formula, mishandling −b when b is already negative, or dividing only the square-root part by 2a instead of the whole numerator.
Formulae for this statement
Sample questions (10 of 29)
Nearby statements
Questions people ask
Is solving quadratic equations on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "including those that require rearrangement", "by completing the square and by using the quadratic formula" — are Higher only; the rest is Foundation content.
Can I use a calculator for solving quadratic equations?
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.
When should I complete the square instead of using the formula?
Complete the square when the question asks for the turning point of the curve, for the minimum or maximum value, or explicitly says to. Use the formula when you only need the roots and the quadratic does not factorise. Both methods are Higher tier; Foundation solves quadratics by factorising.
What is the single most common mistake here?
Reading the solutions of (x − 3)(x + 5) = 0 straight off as x = 3 and x = 5. The signs flip: x = 3 and x = −5.
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.