IB Maths AI SL Topic 5: Calculus questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1 Paper 2

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Question 1

Paper 2Easy6 marks

A surveyor estimates the area of an irregular lake by measuring its width at equal intervals along a straight line through the lake. The measured widths are shown below.

Distance along the line, $x$ (m)	0	25	50	75	100
Width of lake (m)	0	18	24	17	0

(a)

Using the trapezoidal rule, show that the estimated area of the lake between $x=0$ and $x=50$ is $750\text{ m}^2$

[3]

(b)

Using your answer to part (a) and the remaining measurements, calculate an estimate of the total area of the lake.

[3]

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