A-LevelMathematicsCircular measure9709/12 · Oct/Nov 2016 · Q68 Marks

[Figure 6.1] The diagram shows a metal plate ABCD made from two parts. The part BCD is a semicircle. The part DAB is a segment of a circle with centre O and radius 10 cm. Angle BOD is 1.2 radians.

(i)Show that the radius of the semicircle is 5.646 cm, correct to 3 decimal places.[2]
(ii)Find the perimeter of the metal plate.[3]
(iii)Find the area of the metal plate.[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 (Oct/Nov 2016). The mark or mark type is shown in brackets.

[M1] r/10 = sin 0.6 or r/10 = cos 0.97 Or other valid alternative. or BD = √200-200cos1.2 (=11.3)
[A1] → r = 5.646 AG
[M1] Major arc = 10(0) (= 50.832) θ = 2π− 1.2 (= 5.083) θ = 2π – 1.2 or π – 1.2 Implied by 5.1
[B1] Semicircle = 5.646π (= 17.737)
[A1] Major arc + semicircle = 68.6
[M1] Area of major sector = ½10²(θ) (= 254.159) θ = 2π – 1.2 or π – 1.2
[M1] Area of triangle OBD = ½10²sin1.2 (= 46.602) Use of ½absinC or other complete method
[A1] Area = semicircle + sector + triangle (= 50.1 + 254.2 + 46.6) = 351

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.