Circular measure — AS & A Level Mathematics (9709) questions by topic
Finding the perimeter of a coin-shaped figure built from arcs of three equal circles, working out areas and perimeters for metal plates made of sectors and semicircles, and comparing two arcs bounding a shaded region are typical of the 13 circular measure questions from 2023 to 2025, worth 4 to 10 marks.
Find, state and show are the only three command words tracked here, each requiring arc length and sector area formulae applied in radians rather than degrees. Because mixing radians and degrees is the single most common error in this topic, submit your working for instant marking, so a wrongly converted angle is caught the moment it is used, rather than after an entire perimeter or area has been built on it.
May–June 2025, Paper 13
The diagram shows a square ABCD where each side has length 12 cm. Points E and F lie on the sides BC and CD respectively and are such that BE = (1/3)BC and DF = (1/3)DC. The arc…
Answer this question and get it marked →May–June 2025, Paper 15
The diagram shows a sector ABD of a circle with centre A and radius 10 cm. The perpendicular bisector of AB passes through D. (In the diagram, A and B are the ends of a horizontal…
Answer this question and get it marked →May–June 2024, Paper 12
It is given that r = 0.4 cm. Show that the length EF = 2.4 cm.
Answer this question and get it marked →May–June 2024, Paper 13
The diagram shows a sector of a circle with centre C. The radii CA and CB each have length r cm and the size of the reflex angle ACB is θ radians. The sector, shaded in the…
Answer this question and get it marked →October–November 2024, Paper 11
The diagram shows a sector of a circle, centre O, where OB = OC = 15 cm. The size of angle BOC is (2/5)π radians. Points A and D on the lines OB and OC respectively are joined by…
Answer this question and get it marked →October–November 2024, Paper 12
The diagram shows a metal plate OABCDEF consisting of sectors of two circles, each with centre O. The radii of sectors AOB and EOF are r cm and the radius of sector COD is 2r cm.…
Answer this question and get it marked →October–November 2024, Paper 13
The diagram shows a metal plate ABCDEF consisting of five parts. The parts BCD and DEF are semicircles. The part BAFO is a sector of a circle with centre O and radius 20 cm, and D…
Answer this question and get it marked →May–June 2023, Paper 11
The diagram shows a sector ABC of a circle with centre A and radius 8 cm. In the diagram C is at the top, B is at the lower left with a right angle marked at B, and A is at the…
Answer this question and get it marked →May–June 2023, Paper 12
The diagram shows a sector OAB of a circle with centre O. Angle AOB = θ radians and OP = AP = x, where P lies on OB. Show that the arc length AB is 2xθ cos θ.
Answer this question and get it marked →May–June 2023, Paper 13
The diagram shows a sector OAB of a circle with centre O and radius r cm. Angle AOB = θ radians. It is given that the length of the arc AB is 9.6 cm and that the area of the…
Answer this question and get it marked →October–November 2023, Paper 11
Given that angle ACB = kπ radians, state the value of the fraction k.
Answer this question and get it marked →October–November 2023, Paper 12
The diagram shows the shape of a coin. The three arcs AB, BC and CA are parts of circles with centres C, A and B respectively. ABC is an equilateral triangle with sides of length…
Answer this question and get it marked →October–November 2023, Paper 13
The diagram shows points A, B and C lying on a circle with centre O and radius r. Angle AOB is 2.8 radians. The shaded region is bounded by two arcs. The upper arc is part of the…
Answer this question and get it marked →Other AS & A Level Mathematics topics
- Differentiation (95)
- Algebra, logarithmic and exponential functions (87)
- Trigonometry (57)
- Series (37)
- Integration (33)
- Kinematics (33)
- The normal distribution (32)
- Energy, work and power (31)
- The Poisson distribution (31)
- Complex numbers (28)
- Sampling and estimation (28)
- Permutations and combinations (27)