CAIE IGCSE Additional Math 9. Circular measure Question Bank

Practise radian-based circle measure in diagrams involving arcs, sectors, shaded regions, perimeters and compound areas.

Covered syllabus points

9.1. Solve arc length and sector area problems

[Maximum number: 3]

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 $P\text{ cm}$ .

Find an expression for P in terms of r.

$\frac12r^2\theta=10,\quad \theta=\frac{20}{r^2}$
B1
$P=2r+r\theta$
M1
$P=2r+\frac{20}{r}$
A1

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Covered syllabus points

9. Circular measure question 1