O-LevelMathematicsGeometry4024/21 · Oct/Nov 2021 · Q37 Marks

3 (a) [Figure geometry diagram with circle, tangent, and angles] Points A, B and C are on the circle, centre O. AOC and OBE are straight lines. DE is a tangent to the circle at C. ABO = 34°. (i) Explain why triangle AOB is isosceles. (ii) Find BÊC. BÊC = (b) [Figure geometry diagram with two sectors] OPS and OQR are sectors of circles each with centre O. OPQ and OSR are straight lines. OP = 7.4 cm, PQ = 1.2 cm and QÔR = 96°. Calculate the shaded area. cm²

(a)(i)Explain why triangle AOB is isosceles.[1]
(a)(ii)Find BÊC.[3]
(b)OPS and OQR are sectors of circles each with centre O. OPQ and OSR are straight lines. OP = 7.4 cm, PQ = 1.2 cm and QÔR = 96°. Calculate the shaded area.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[1] (a)(i) AO and BO are radii, so 2 equal sides
[3] (a)(ii) [ BÊC = ] 22° nfww
[3] B1 for ∠BOC = 68° soi or for ∠BOA = 112° soi or ∠OBC = 56° soi
[3] B1 for ∠OCE or ∠ACE = 90° soi
[3] (b) 16.1 or 16.08 to 16.09
[3] M2 for 96/360 × π × ((7.4+1.2)² -7.4²) oe or M1 for 96/360 × π × (7.4+1.2)² or 96/360 × π × 7.4²

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