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Area Under Curves

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 be part of a solid GCSE revision cycle.

Study this topic

1

Measuring What You Cannot Calculate Directly

Introduction2

Area Under a Curve — Core Principles

Key Facts3

The Trapezium Rule — How It Works

Diagram4

The Trapezium Rule Formula

Deep Dive5

Step-by-Step Process

Deep Dive6

Overestimate or Underestimate?

Deep Dive7

Integration for Exact Area (Higher)

Deep Dive8

Exam Tips for Area Under Curves

Exam Tips9

Worked Examples

Notes10

Common Misconceptions

Misconceptions11

Topic Summary: Area Under Curves

Summary

Sample Flashcards

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.
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).

Sample Questions

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

9

exam-style questions

10

revision flashcards

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Gradients of Curves