CAIE IGCSE Mathematics Extended E5.3 Circles, arcs & sectors Question Bank

Practise circumference, circle area, arc length and sector area calculations, including exact answers in terms of π.

Exam points

find circle area from a radius or from a diagram that first gives the diameter
calculate major or minor arc length by choosing the correct sector angle
use sector area or perimeter formulae, giving exact answers in terms of π when required

Covered syllabus points

E5.3.1 Carry out calculations involving the circumference and area of a circle.E5.3.2 Carry out calculations involving arc length and sector area as

[Maximum number: 4]

NOT TO SCALE

A, B and C are points on the circle, centre O.
DE is a tangent to the circle at C.
AC=10 cm, AB=9.5 cm and BC=7.7 cm.

Calculate the area of triangle ABC as a percentage of the area of the circle.

38.8 or 38.9 or 38.78 to 38.85
M3 for $\frac{0.5\times9.5\times7.7\times\sin70.2}{\pi(\text{their (c)})^2}\times100$ oe
or lower method marks as in markscheme

[Maximum number: 3]

NOT TO SCALE

The diagram shows a sector of a circle with radius 8 cm and angle $75^{\circ}$ .
Find the perimeter of the sector.
cm

26.5 or 26.47...
B2 for 10.5 or 10.47... or $\frac{10\pi}{3}$
OR M2 for $8+8+\frac{75}{360}\times2\pi\times8$
or M1 for $\frac{75}{360}\times2\pi\times8$

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Covered syllabus points

E5.3 Circles, arcs and sectors question 1

E5.3 Circles, arcs and sectors question 2