The diagram shows a semicircle with centre O and radius 6 cm. The radius OC is perpendicular to the diameter AB. The point D lies on AB, and DC is an arc of a circle with centre B. [Figure X.X]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

1. Pythagoras → r = √72 OE or cos45 = 6/r → r = 6/√2 = 6√2 (M1) Correct method leading to r =
2. Arc DC = √72 × ¼π = (3√2)/2 π, 2.12π, 6.66 (M1A1) Use of s=rθ with their r (NOT 6) and ¼π
3. Area of sector-BDC is ½ × 72 × ¼π (= 9π or 28.274...) (*M1) Use of ½r²θ with their r (NOT 6) and ¼π
4. Area Q = 9π – 18 (10.274...) (DM1) Subtracts their ½ × 6 × 6 from their ½r²θ
5. Area P is (¼π6² – area Q) = 18 (M1) Uses {¼π6² – (their area Q using √72)}
6. Ratio is 18 / (9π-18) (10.274) → 1.75 (A1)