CAIE IGCSE Mathematics Extended Bounds of Calculation Results

Practise selecting input bounds that maximise or minimise a formula and calculating rigorous bounds for perimeter, area, speed and rates.

Exam points

derive each input interval from its stated rounding accuracy before using the formula
maximise a positive quotient with the numerator's upper bound and denominator's lower bound
choose all upper or lower dimensions appropriately for sums, products, areas and perimeters

[Maximum number: 3]

A rectangle has an area of $9400 \mathrm{~cm}^{2}$ , correct to the nearest $100 \mathrm{~cm}^{2}$ .

The length of the rectangle is 80 cm , correct to the nearest 10 cm .
Calculate the upper bound of the width of the rectangle.

126 nfww
M2 for $\frac{9400+50}{70\text{ to }80}$ or $\frac{9400\text{ to }9500}{80-5}$
or M1 for 9350 or 9450 or 75 or 85 seen

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E1.10.2 Find upper and lower bounds of the results of calculations which have question 1