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Exam Tips for Area Under Curves

Part of Area Under Curves — GCSE Mathematics

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.

Integration for Exact Area (Higher)Worked ExamplesMeasuring What You Cannot Calculate DirectlyArea 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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Worked Examples