Topical Revision Paper 13 Unit 13 Circular Measure Students

Topical Revision Paper 13 Term 3 Unit 13: Circular Measure Question 1: The diagram shows two circles with centres A and B, intersecting at points C and D. The radii of the circles are 8 cm and 12 cm respectively, and angle ACB = angle ADB = 2  radians. (i) Show that angle CBD is approximately 1.18 radians. [2] The shaded region is bounded by minor arcs CD with centres A and B respectively. (ii) Find the perimeter of the shaded region. [3] (iii) Find the area of the shaded region. [3] Answer: (ii) 29.9 cm (iii) 51.6 cm2 Question 2: The diagram shows a quadrant inscribed in the square ABCD of sides 6 cm. ACE is a sector centred at A. F is the point of intersection of the diagonal AC and the arc DB. FG is perpendicular to AE. P1 D C A B

Find (i) the area of the shaded region BCE, [3] (ii) the perimeter of FGBECF. [4] Answer : (i) 10.3 cm2 (ii) 17.6 cm Question 3: The diagram below shows a tangent RST to two semi-circles with centre P and Q. The point R, A, P, B, Q and C lie on the same straight line. It is also given that AB = 2 cm and AC = 8 cm. (i) Show that RA = 1 cm. [2] (ii) Find QRT in radian. [2] (iii) Calculate the perimeter of the shaded region. [4] (iv) Calculate the area of the shaded region. [4]

Answer : (ii) 6  (iii) 8.70 cm (iv) 1.17 cm2 Question 4: The diagram below shows a semicircle ADB with centre O and a radius of 6 m. ACE is a sector of a circle with centre C and a radius of 9.8 m. CE intersects the semicircle at D such that CD is 6 m. (i) Show that 1.89AOD radians. [2] (ii) Calculate the area of the shaded region. [4] Answer: (ii) 15.1 m2 E D AOB C 9.8 m 6 m 6 m