O-LevelMathematicsGeometry4024/21 · Oct/Nov 2014 · Q1012 Marks
A, B, C and D are points on the circumference of a circle, centre O. The diameter AC intersects BD at E. BDC = 2x°.
- (a)(i)(a)Find an expression, in terms of x, for BAC,[1]
- (a)(i)(b)BOC,[1]
- (a)(i)(c)OCB.[1]
- (a)(ii)Calculate x when OBE = x° and DEC = 123°.[3]
- (b)(i)The cross-section of a prism is a sector of a circle, radius 8 cm and angle 40°. The prism is 20 cm long. Calculate the area of the cross-section,[2]
- (b)(ii)the total surface area of the prism.[4]
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 2014). The mark or mark type is shown in brackets.
- [1] 2x
- [1] 4x
- [1ft] 90-2x oe
- [3] 19
- [3] M2 for 180 - 3x = 123 oe or B1 for BE0 = (180 - 123)
- [2] 22.3
- [2] M1 for 40/360 × π × 8²
- [4] 476 to 477
- [4] M1 for 40/360 × π × 16 and M1 for 2 × their 22.3 and B1 for 8 × 20
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