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Exam Tips for Area Under Curves

Part of Area Under Curves · GCSE GCSE Mathematics revision

This exam tips covers Exam Tips for Area Under Curves within Area Under Curves for GCSE Mathematics. Revise Area Under Curves in Graphs for GCSE Mathematics with 9 exam-style questions and 10 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 8 of 11 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.

Topic position

Section 8 of 11

Practice

9 questions

Recall

10 flashcards

💡 Exam Tips for Area Under Curves

State the y-values clearly in a table before applying the formula — this avoids errors
First and last once, all others twice — the classic memory device for the trapezium rule
Check the strip width h — it must be the same for all strips when using the standard formula
Give units: area on a speed-time graph has units of distance (m, km); always state the units of your answer
Over/underestimate: look at whether the curve bends up (under) or down (over) relative to the trapezium tops
More strips = better estimate — halving h approximately halves the error

Keep building this topic

Read this section alongside the surrounding pages in Area Under Curves. That gives you the full topic sequence instead of a single isolated revision point.

Improving Trapezium Rule Accuracy (Higher)Worked Examples Measuring What You Cannot Calculate Directly Area Under a Curve — Core Principles

Practice Questions for Area Under Curves

On a velocity-time graph, what does the area under the curve represent?

A. The acceleration
B. The average velocity
C. The distance (or displacement) travelled
D. The speed at a given moment

1 markfoundation

Explain whether the trapezium rule gives an overestimate or underestimate for the area under the curve y = x² between x = 0 and x = 3. Justify your answer.

2 markshigher

Quick Recall Flashcards

What does the area under a speed-time graph represent?

Distance travelled. Area under a speed-time graph = distance travelled This works for any speed-time or velocity-time graph. Even if the graph is curved, the area still represents distance. Units: if speed is m/s and time is s, then area has units of metres (m).

What is the trapezium rule used for?

Estimating the area under a curve by dividing it into trapezium-shaped strips. Each strip is a trapezium (not a rectangle or triangle). The more strips used, the more accurate the estimate. It is an approximation — the actual area is slightly different because the tops of the strips are straight lines, not curves.

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Improving Trapezium Rule Accuracy (Higher)

Worked Examples