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Area Under a Curve — Core Principles

Part of Area Under Curves — GCSE Mathematics

This key facts covers Area Under a Curve — Core Principles 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 2 of 11 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 2 of 11

Practice

9 questions

Recall

10 flashcards

Area Under a Curve — Core Principles

  • Speed-time graph: area under the curve = distance travelled
  • Rate-of-change graph: area = total accumulated quantity
  • Trapezium rule: estimates the area by dividing into trapezium-shaped strips
  • More strips = more accurate estimate
  • Exact area: found by integration (calculus) — gives a precise answer

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.

Measuring What You Cannot Calculate DirectlyThe Trapezium Rule — How It WorksThe Trapezium Rule FormulaStep-by-Step Process

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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Measuring What You Cannot Calculate Directly

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The Trapezium Rule — How It Works