Revision NotesExam QuestionsPast Papers
O LevelAdditional MathsCambridgeExam QuestionsTrigonometryCircular Measure

Circular Measure (Cambridge O Level Additional Maths)

Exam Questions

1 hour10 questions
Medium
Hard
Very Hard
1
Sme Calculator4 marks

A circle has a radius of 6 cm. A sector of this circle has a perimeter of 2 open parentheses 6 plus 5 pi close parentheses space cm. Find the area of this sector.

How did you do?

Did this page help you?

2
Sme Calculator3 marks

q6b-0606-m20-qp-22-additional-maths

The diagram shows the sector A O B of a circle with centre O and radius 7 cm.
Angle A O B space equals pi over 4 radians. Find the perimeter of the shaded region.

How did you do?

Did this page help you?

3a
Sme Calculator1 mark

q7-0606-s20-qp-13-additional-maths
The diagram shows an isosceles triangle O A B such that O A space equals space O B space equals space 12 cm and angle A O B space equals space theta space radians.
Points C and D lie on O A and O B respectively such that C D is an arc of the circle, centre O, radius 10 space cm. The area of the sector O C D space equals space 35 cm squared .

Show that theta space equals space 0.7.

How did you do?

3b
Sme Calculator4 marks

Find the perimeter of the shaded region.

How did you do?

3c
Sme Calculator3 marks

Find the area of the shaded region.

How did you do?

Did this page help you?

1a
Sme Calculator5 marks

q9-2025-specimen-paper-2-cie-igcse-additional-maths

The diagram shows a rectangle A B C D and an arc A X B of a circle with centre at O, the midpoint of D C.
The length of B C is 8 space cm and the length of D C is 30 space cm. Angle A O B is theta radians.

Find the perimeter of the shape A D O C B X.

How did you do?

1b
Sme Calculator2 marks

Find the area of the shape A D O C B X.

How did you do?

Did this page help you?

2a
Sme Calculator2 marks

In this question all lengths are in centimetres.

q10a-june-2021-cie-igcse-additional-maths

The diagram shows a shaded shape. The arc A B is the major arc of a circle, centre O, radius 10. The line A B is of length 15, the line O C is of length 25 and the lengths of A C and B C are equal.

Show that the angle A O B is 1.70 radians correct to 2 decimal places.

How did you do?

2b
Sme Calculator4 marks

Find the perimeter of the shaded shape.

How did you do?

2c
Sme Calculator5 marks

Find the area of the shaded shape.

How did you do?

Did this page help you?

3a
Sme Calculator5 marks

In this question all lengths are in centimetres and all angles are in radians.

q11-0606-w20-qp-12-additional-maths

The diagram shows the rectangle A D E F, where A F space equals space D E space equals space r. The points B and C lie on A D such that A B equals C D equals r . The curve B C is an arc of the circle, centre O, radius r and has a length of 1.5 r.

Show that the perimeter of the shaded region is left parenthesis 7.5 plus 2 space sin space 0.75 right parenthesis r .

How did you do?

3b
Sme Calculator4 marks

Find the area of the shaded region, giving your answer in the form k r squared, where k is a constant correct to 2 decimal places.

How did you do?

Did this page help you?

1a
Sme Calculator1 mark

q7-0606-s20-qp-11-additional-maths

The diagram shows an isosceles triangle O A B such that O A space equals space O B and angle A O B space equals space theta radians. The points C and D lie on O A and O B respectively. C D is an arc of length 9.6 cm of the circle, centre O, radius 12 cm. The arc C D touches the line A B at the point M.

Find the value of theta.

How did you do?

1b
Sme Calculator4 marks

Find the total area of the shaded regions.

How did you do?

1c
Sme Calculator3 marks

Find the total perimeter of the shaded regions.

How did you do?

Did this page help you?

2a
Sme Calculator4 marks

q11-0606-s20-qp-22-additional-maths

The circles with centres C subscript 1 and C subscript 2 have equal radii of length r space cm. The line C subscript 1 C subscript 2 is a radius of both circles. The two circles intersect at A and B.

Given that the perimeter of the shaded region is 4 straight pi space cm, find the value of r. [4]

How did you do?

2b
Sme Calculator4 marks

Find the exact area of the shaded region.

How did you do?

Did this page help you?

3a
Sme Calculator1 mark

In this question all lengths are in centimetres.

q8-0606-w20-qp-13-additional-maths

The diagram shows the figure A B C. The arc A B is part of a circle, centre O, radius r, and is of length 1.45 space r. The point O lies on the straight line C B such that C O space equals space 0.5 space r.

Find, in radians, the angle A O B.

How did you do?

3b
Sme Calculator3 marks

Find the area of A B C, giving your  in the form k r squared, where k is a constant.

How did you do?

3c
Sme Calculator4 marks

Given that the perimeter of A B C is 12 space cm, find the value of r.

How did you do?

Did this page help you?

4a
Sme Calculator2 marks

q12-0606-w20-qp-21-additional-maths

The diagram shows a shape consisting of two circles of radius 3 cm and 4 cm with centres A and B which are 5 cm apart. The circles intersect at C and D as shown. The lines A C and B C are tangents to the circles, centres B and A respectively. Find the angle C A B in radians.

How did you do?

4b
Sme Calculator4 marks

Find the perimeter of the whole shape.

How did you do?

4c
Sme Calculator4 marks

Find the area of the whole shape.

How did you do?

Did this page help you?