IB Maths AI HL Sl 5 8 Trapezoidal Rule Questions

Practise applying the trapezoidal rule to tables or functions, choosing interval widths and bounds, and interpreting approximate area, units and possible error.

Exam points

Apply the trapezoidal rule with equal-width intervals to a table or function.
Calculate an approximate area and choose the correct bounds, interval width and function values.
Interpret the approximation, including units, rounding and the direction/size of possible error.

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Linda owns a field, represented by the shaded region R. The plan view of the field is shown in the following diagram, where both axes represent distance and are measured in metres.

Figure for Question IB Maths AI HL Sl 5 8 Trapezoidal Rule Questions question 1 — IB Maths AI HL

The segments [AB], [CD] and [AD] respectively represent the western, eastern and southern boundaries of the field. The function, f(x), models the northern boundary of the field between points B and C and is given by

f(x)=\frac{-x^{2}}{50}+2 x+30, \text { for } 0 \leq x \leq 70

Suggest how Linda might be able to reduce the error whilst still using the trapezoidal rule.

Linda would like to construct a building on her field. The square foundation of the building, EFGH , will be located such that $[\mathrm{EH}]$ is on the southern boundary and point F is on the northern boundary of the property. A possible location of the foundation of the building is shown in the following diagram.

The area of the square foundation will be largest when $[\mathrm{GH}]$ lies on $[\mathrm{CD}]$ .

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IB Maths AI HL Sl 5 8 Trapezoidal Rule Questions question 1