IB Maths AI SL 5.8 Trapezoidal rule Question Bank

Practise IB Mathematics SL/HL 5.8 by applying trapezoidal rule methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 3]

A type of dog food is sold in cylindrical containers. A new label for the container is being considered. The label will be a rectangle that is 5 cm wide and 7 cm high.
The design on the label is a curve, as shown on the following axes, where one unit represents 1 cm for both axes.

Figure for Question SL 5.8—Trapezoidal rule question 1 — IB Maths AI SL

The values in the table approximate points on the curve, correct to one decimal place.

Table for Question SL 5.8—Trapezoidal rule question 1 — IB Maths AI SL

Use the trapezoidal rule with five intervals, and the values given in the table, to estimate the shaded area below the curve.

The curve used in the label design can be modelled by:

y=-\frac{x^{3}}{3}+3 x^{2}-7 x+6, \text { for } 0 \leq x \leq 5

$\frac{1}{2} \times 1 \times((6+4.3)+2(1.7+1.3+3+4.7))$ $=15.9(15.85)\left(\mathrm{cm}^{2}\right)$

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SL 5.8—Trapezoidal rule question 1