Practice IB Mathematics Applications & Interpretation (AI) Topic SL 5.8—trapezoid Rule with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.8—trapezoid Rule and mirrors Paper 1, 2, 3 style where relevant.
Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.
A farmer is planning a new orchard. The shape of one section is defined by the region bounded by the curve , the -axis, and the vertical line , where and are measured in metres.
(a) Divide the interval into 4 equal sub-intervals and the -values of the endpoints.
(b) the value of at each endpoint.
A garden bed has one straight boundary of length m. Its width, measured perpendicular to this boundary, is recorded at regular intervals. The two endpoint widths are known to be exactly zero, but two interior measurements have been lost.
| Distance along the straight boundary (m) | |||||||
|---|---|---|---|---|---|---|---|
| Recorded width (m) |
Using only the recorded widths at , a surveyor obtained a trapezoidal area estimate of . Using all seven recorded widths, the estimate was .
Give
…
An irrigation channel is m wide. Its water depth , in metres, is measured at equally spaced horizontal positions , measured in metres from one vertical bank. The water surface is horizontal. One depth reading is missing.
| Depth |
Using all five readings, an engineer obtained a trapezoidal estimate of square metres for the water's cross-sectional area. Treat this estimate and the tabulated values as exact for parts (a)–(d).
Give exact answers where possible, and other numerical answers to three significant figures.
…
(e) Use your answers to parts (b) and (d) to find the width- trapezoidal approximation to . Hence why the approximation to in part (d) is exact, even though neither half of the calculation is exact.
(e) the approximation with the exact value and the difference.
(c) Use the trapezoidal rule with these 4 sub-intervals to approximate the area of the orchard section, giving your answer in .
(e) the approximation with the exact value and the difference.
The function is defined by for . Let and .
Give exact values unless an approximation is requested. In the trapezoidal rule, use equally spaced strips of the stated width.
(b) Use the trapezoidal rule with strip width to approximate . Show the ordinates used.
(d) Show that . Hence, without carrying out another integration or a full trapezoidal sum, find the exact value of and its trapezoidal approximation using strip width .
An architect is designing a glass panel. The shape of the panel is defined by the region bounded by the curve , the -axis, and the vertical line , where and are measured in metres.
(c) Use the trapezoidal rule with these 4 sub-intervals to approximate the area of the panel, giving your answer in .
(d) the exact area of the orchard section by integrating from 0 to 4, giving your answer in .
(a) the graph of on its domain, labelling the -intercept, the stationary points and the domain endpoints. Hence why for .
(c) Find the exact value of and the percentage error of the approximation in part (b). geometrically why the approximation is an overestimate.
(a) Divide the interval into 4 equal sub-intervals and the -values of the endpoints.
(b) the value of at each endpoint.
(d) the exact area of the panel by integrating from 0 to 4, giving your answer in .
