IB Maths AI HL Sl 1 6 Approximation and Error Questions

Practise rounding and estimating accuracy, using bounds and percentage error to judge whether a measurement or approximation supports the stated decision.

Exam points

Round values to decimal places or significant figures and state an appropriate level of accuracy for the calculation.
Use upper and lower bounds for rounded measurements to find an interval or bound for a derived quantity.
Calculate percentage error or percentage change from exact, measured, estimated or rounded values.
Judge whether the approximation, precision or uncertainty is sufficient for the stated practical decision and report the result appropriately.

[Maximum number: 3]

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 1 6 Approximation and Error 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

Calculate the percentage error in Linda's estimate.

$\frac{11.4}{4713.33 \ldots} \times 100 \%$ OR $\left|\frac{4701.93 \ldots-4713.33 \ldots}{4713.33 \ldots}\right| \times 100 \% \quad$ (M1)

Note: Award (M1) for their correct substitution into the percentage error formula.
$0.242 \%(0.241867 \ldots \%)$ A1
Note: Percentage sign is required. Accept $0.242038 \ldots \%$ if 4710 is used.

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IB Maths AI HL Sl 1 6 Approximation and Error Questions question 1