CAIE A-Level Mathematics AS 2.5.3 Trapezium Rule Questions

Practise solving statistical inference problems within the AS mathematics syllabus.

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 $y=\frac{2 \ln x}{3 x+1}$ . The curve crosses the x-axis at the point A and has a maximum point B. The shaded region is bounded by the curve and the lines x=3 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 decimal places.

Use y-values [0], $\frac{2}{7} \ln 2$ or 0.1980 and $\frac{2}{10} \ln 3$ or 0.2197
Use correct formula, or equivalent, with h=1
Obtain 0.31

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