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.
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
- Estimate vs exact: the trapezium rule gives an approximation — more strips means a closer estimate
Practice questions for Area Under Curves
On a velocity-time graph, what does the area under the curve represent?
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.
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.