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Improving Trapezium Rule Accuracy (Higher)

Part of Area Under Curves · GCSE GCSE Mathematics revision

This deep dive covers Improving Trapezium Rule Accuracy (Higher) 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 7 of 11 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 7 of 11

Practice

9 questions

Recall

10 flashcards

Improving Trapezium Rule Accuracy (Higher)

The more strips you use, the closer the estimate is to the true area. Halving the strip width h roughly halves the error.

To decide whether a trapezium rule answer is an over- or underestimate, look at the shape of the curve between each pair of strip boundaries:

Concave up (∪ shape between boundaries): the straight-line tops of the trapeziums lie BELOW the curve — the estimate is an underestimate
Concave down (∩ shape between boundaries): the straight-line tops lie ABOVE the curve — the estimate is an overestimate
Mixed curvature: some strips underestimate and some overestimate — state which effect dominates or that it is not possible to tell overall

Key note: if the curve dips below the x-axis, the area of that region contributes a negative value to the total. On a speed-time graph this would be unusual (negative speed), but on other graphs you may need to consider the sign of each region separately.

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).

Improving Trapezium Rule Accuracy (Higher)

Improving Trapezium Rule Accuracy (Higher)

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Practice Questions for Area Under Curves

Quick Recall Flashcards

9 questions on Area Under Curves — practise free