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.
💡 Exam Tips for Area Under Curves
- 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
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.