A-LevelMathematicsCircular measure9709/12 · Oct/Nov 2015 · Q57 Marks
The diagram shows a metal plate OABC, consisting of a right-angled triangle OAB and a sector OBC of a circle with centre O. Angle AOB = 0.6 radians, OA = 6 cm and OA is perpendicular to OC.
- (i)Show that the length of OB is 7.270 cm, correct to 3 decimal places.[1]
- (ii)Find the perimeter of the metal plate.[3]
- (iii)Find the area of the metal plate.[3]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [M1] Length of OB = 6 / cos 0.6 = 7.270 (ag Any valid method)
- [B1] AB = 6 tan 0.6 or 4.1 (Sight of in (ii))
- [M1] Arc length = 7.27 × (1.5π – 0.6) = (7.06) (Use of s=rθ with sector angle)
- [A1] Perimeter = 6 + 7.27 + 7.06 + 6 tan 0.6 = 24.4
- [M1] Area of AOB = (1/2) × 6 × 7.27 × sin 0.6 (Use of any correct area method)
- [M1] Area of OBC = (1/2) × 7.27² × (1.5π – 0.6) (Use of 1/2r²θ)
- [A1] → area = 12.31 + 25.65 = 38.0
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