CAIE IGCSE Additional Mathematics 14.8 Maxima & Minima Question Bank

Practise forming a one-variable model and using stationary points to optimise areas, volumes, dimensions and practical designs.

Exam points

use a constraint to eliminate one variable before differentiating the target expression
set the first derivative to zero and verify whether the stationary value is a maximum or minimum
substitute the optimal value back to calculate the requested dimension, area or volume

[Maximum number: 4]

A circle, centre O and radius $r\text{ cm}$ , has a sector OAB of fixed area $10\text{ cm}^2$ . Angle AOB is $\theta$ radians and the perimeter of the sector is $P\text{ cm}$ .

(a)

Find the value of r for which P has a stationary value.

[ 3 ]

$\frac{dP}{dr}=2-\frac{20}{r^2}$
M1
When $\frac{dP}{dr}=0$ :
$r=\sqrt{10}$
M1 dependent for equating and solving; A1 cao.

(b)

Find the value of $\theta$ at this stationary value.

[ 1 ]

$\theta=2$
B1

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14.8. Apply differentiation to maxima and minima question 1

Question (a)

Question (b)