- 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
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.
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.