CAIE A-Level Mathematics AS 2.5.3 Trapezium Rule Questions

Practise applying the trapezium rule with the correct interval width and endpoint weighting and judging over- or under-estimation from the curve's position relative to chords.

Exam points

use vector notation and operations
solve geometric problems with vectors
interpret vector relationships

[Maximum number: 3]

Figure for Question CAIE A-Level Mathematics AS 2.5.3 Trapezium Rule Questions question 1 — CAIE A-Level Mathematics AS

The diagram shows the curve with equation $y=\sqrt{\sin 2 x+\sin ^{2} 2 x}$ for $0 \leqslant x \leqslant \frac{1}{6} \pi$ . The shaded region is bounded by the curve and the straight lines $x=\frac{1}{6} \pi$ and y=0.

Use the trapezium rule with two intervals to find an approximation to the area of the shaded region. Give your answer correct to 2 significant figures.

Use y-values ( 0 ), $\quad \sqrt{\sin \frac{1}{6} \pi+\sin ^{2} \frac{1}{6} \pi}, \quad \sqrt{\sin \frac{1}{3} \pi+\sin ^{2} \frac{1}{3} \pi}$ or decimal equivalents
(0), $\sqrt{0.75}$ or 0.866, $\sqrt{1.616}$ or 1.271.

Use correct formula, or equivalent, with $h=\frac{1}{12} \pi$
Must be using ' y ' values.

May do as 2 separate trapezia ( 0.113359+ 0.27976).

Obtain 0.39
Marking guidance:

Allow 0.393 but not greater accuracy.

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CAIE A-Level Mathematics AS 2.5.3 Trapezium Rule Questions question 1