DfE statement A11 · Algebra
Roots, intercepts and turning points of quadratics
Roots, intercepts and turning points of quadratics is content statement A11 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: "Identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square." (statement A11). 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: "and turning points by completing the square". 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 roots off the y-axis. The roots are where the curve crosses the x-axis, so y = 0 there.
- Reading the turning point of y = (x − 3)² + 2 as (−3, 2) instead of (3, 2) — the sign inside the bracket flips.
- Giving only one root when the curve crosses the x-axis twice.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is roots, intercepts and turning points of quadratics on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "and turning points by completing the square" — are Higher only; the rest is Foundation content.
Can I use a calculator for roots, intercepts and turning points of quadratics?
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?
Reading the roots off the y-axis. The roots are where the curve crosses the x-axis, so y = 0 there.
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.