IB Maths AI HL 1.6 Approximation, bounds and error analysis Question Bank

Practise IB Maths AI HL 1.6 by analysing approximation error, bounds and the effect of rounding in applied models.

Exam points

Calculate and interpret percentage error when an approximation is used in a multi-step model.
Propagate upper and lower bounds through a calculation and justify the resulting interval.
Evaluate whether the precision of an approximation is sufficient for the stated practical decision.

[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 SL 1.6—Approximation and error 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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SL 1.6—Approximation and error question 1