A-LevelMathematicsCircular measure9709/12 · May/June 2016 · Q66 Marks
The diagram shows a circle with radius r cm and centre O. The line PT is the tangent to the circle at P and angle POT = α radians. The line OT meets the circle at Q. [Figure 6.1]
- (i)Express the perimeter of the shaded region PQT in terms of r and α.[3]
- (ii)In the case where α = 1/3 π and r = 10, find the area of the shaded region correct to 2 significant figures.[3]
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 (May/June 2016). The mark or mark type is shown in brackets.
- [B1] PT = r tanα
- [B1] QT = OT – OQ = r/cos α – r or √(r² + r²tan²α) - r
- [B1] Perimeter = sum of the 3 parts including rα
- [M1] Area of triangle = ½ × 10 × 10 tan(π/3) Correct formula used, 50√3, 86.6
- [M1] Area of sector = ½ × 10² × 1/3π Correct formula used, 50π/3, 52.36
- [A1] Shaded region has area 34 (2sf) allow 17.7 or 17.8.
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