DfE statement A15 · Algebra

Gradients and areas under graphs

Higher onlyEither paper

Gradients and areas under graphs is content statement A15 of the DfE GCSE mathematics subject content, in the algebra area. It is Higher tier only, and it appears on both the calculator and the non-calculator papers. 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: "Calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts." (statement A15). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement A15

Tier

Higher tier only. A Foundation entry is never asked for this, so if you are sitting Foundation you can leave it out of your revision entirely.

Calculator

This turns up on both the non-calculator and the calculator papers, so practise it both ways — the written method for Paper 1 and the efficient calculator route for Papers 2 and 3.

Common mistakes

Treating the gradient of a velocity-time graph as the distance. The gradient is the acceleration; the area underneath is the distance.
Estimating the area under a sloping graph with rectangles only, when splitting it into a rectangle and a triangle — or using trapezia — is both easier and more accurate.
Giving the answer without units, or with the wrong compound unit, when the axes make the units plain.

Formulae for this statement

Kinematics: velocity from accelerationv = u + atGiven in the exam Kinematics: displacement from times = ut + ½at²Given in the exam Kinematics: velocity from displacementv² = u² + 2asGiven in the exam

Sample questions (10 of 30)

A15 · Gradients and areas under graphsQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Algebra

A15

Advanced

The area under a speed-time graph between t = 0 and t = 6 seconds is estimated using three strips of equal width, using the speeds, in m/s, at t = 0, 2, 4 and 6: 0, 5, 9 and 12. Using the trapezium rule with these three trapezia, estimate the distance travelled.

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