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Measuring What You Cannot Calculate Directly

Part of Area Under Curves — GCSE Mathematics

This introduction covers Measuring What You Cannot Calculate Directly 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 1 of 11 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 11

Practice

9 questions

Recall

10 flashcards

Measuring What You Cannot Calculate Directly

A car's speedometer tells you how fast you are going right now. But how far did you travel during a journey where the speed was constantly changing — speeding up, slowing down, stopping? You cannot simply multiply speed by time because the speed was not constant. Instead, you find the area under the speed-time graph. Even if the graph is curved, the area still gives the total distance. Estimating this area using the trapezium rule is one of the most practically useful techniques in GCSE mathematics.

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.

Area Under a Curve — Core PrinciplesThe Trapezium Rule — How It WorksThe Trapezium Rule Formula

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 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).

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Area Under a Curve — Core Principles