A-LevelMathematicsCircular measure9709/12 · Oct/Nov 2014 · Q26 Marks
The diagram shows a triangle AOB in which OA is 12 cm, OB is 5 cm and angle AOB is a right angle. Point P lies on AB and OP is an arc of a circle with centre A. Point Q lies on AB and OQ is an arc of a circle with centre B. [Figure with triangle AOB, O at origin, A on y-axis, B on x-axis, arcs OP and OQ]
- (i)Show that angle BAO is 0.3948 radians, correct to 4 decimal places.[1]
- (ii)Calculate the area of the shaded region.[5]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.
- [1] tanθ = 5/12 → ( θ = 0.3948 ). Any valid trig method ag
- [1] Other angle in triangle = π/2 - 0.3948. Unsimplified OK
- [1] Area of triangle AOB = ½×12×5 (= 30). co
- [1] Use of ½r²θ once. With θ in radians and r = 5 or 12
- [1] Shaded area = sector + sector - triangle = ½×12²×0.3948 + ½×5²θ - 30. Sum of 2 sectors – triangle or any other valid method using the given angle and a different one.
- [1] = 28.43 + 14.70 - 30 = 13.1. co
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →