DfE statement A12 · Algebra
Recognising and sketching graphs
Recognising and sketching graphs is content statement A12 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: "Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/x with x ≠ 0, exponential functions y = kˣ for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size." (statement A12). 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: "exponential functions y = kˣ for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size". 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
- Drawing the reciprocal graph y = 1/x touching or crossing the axes. It approaches both without ever reaching them.
- Drawing y = kˣ crossing the x-axis. An exponential graph with k positive never reaches zero.
- Sketching a cubic as a parabola, so the S-shape and the possibility of three roots are lost.
- Starting y = cos x at the origin. cos 0° is 1; it is sin x that starts at 0.
Sample questions (10 of 15)
Nearby statements
Questions people ask
Is recognising and sketching graphs on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "exponential functions y = kˣ for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size" — are Higher only; the rest is Foundation content.
Can I use a calculator for recognising and sketching graphs?
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?
Drawing the reciprocal graph y = 1/x touching or crossing the axes. It approaches both without ever reaching them.
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.