CAIE IGCSE Additional Math 9.1 Solve Arc Length and Sector Area Problems Questions

Practise Cambridge IGCSE Additional Mathematics by calculating sector areas, arc lengths, perimeters and composite shaded regions.

Exam points

Calculate arc lengths, sector perimeters and sector areas using radians.
Find shaded-region perimeters and areas by combining sectors, triangles and composite shapes.
Form and solve exact or numerical relationships involving radius, angle and shaded mensuration.

[Maximum number: 7]

(a)

Figure for Question (a) — CAIE IGCSE Additional Math

The diagram shows an isosceles triangle.
Find the value of $\theta$ in radians.

[ 2 ]

$2\sin^{-1}\left(\frac{4}{5}\right)$ or $\cos^{-1}\left(\frac{64-25-25}{-2(5)(5)}\right)$ oe
1.85 or 1.854 to 1.855

(b)

Figure for Question (b) — CAIE IGCSE Additional Math

This diagram shows a shape made of two arcs.
Each arc is part of a circle with radius 5 cm.
The height of the shape is 8 cm.
Use your answer to part (a) to find

[ 5 ]

(i)

the perimeter of the shape

[ 2 ]

$5\times\text{their }1.85\times 2$
M1 FT their 1.85 providing it is less than $2\pi$ .
18.5 or 18.54 to 18.55
A1

(ii)

the area of the shape.

[ 3 ]

$\frac{1}{2}\times5^2\times\text{their }1.85$
M1 FT their 1.85 providing it is less than $2\pi$ .
Correct plan, e.g. $[2\times\frac{1}{2}\times]5^2(\text{their }1.85-\sin(\text{their }1.85))$
M1 dep on previous M1.
22.4 or 22.21 to 22.38 nfww
A1

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CAIE IGCSE Additional Math 9.1 Solve Arc Length and Sector Area Problems Questions question 1

Question (a)

Question (b)

Question (i)

Question (ii)