O-LevelMathematicsTrigonometry4024/21 · May/June 2017 · Q912 Marks
(b) [Figure: Pentagon ABCDE with angles and lengths] ABCDE is a pentagon. AB = 18 cm, BC = 16 cm, CD = 11 cm and EA = 7 cm. EAB = 115° and BDC = 28°.
- (a)Calculate the interior angle of a regular nine-sided polygon.[2]
- (b)(i)Show that BE = 21.9 cm, correct to 3 significant figures.[3]
- (b)(ii)Calculate angle DBC.[3]
- (b)(iii)The perimeter of the pentagon is 62 cm. Given that the area of triangle BDE is 109 cm², calculate the obtuse angle DEB.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [2] 140°
- [2] M1 for 180 – (360 ÷ 9) or 180(9 – 2) ÷ 9
- [3] 21.89.... with at least 7² + 18² – 2 × 7 × 18 × cos 115 seen
- [1] M1 for 7² + 18² – 2 × 7 × 18 × cos 115
- [1] A1 for 479.5 or 373 + 106.49.. or 373 + 106.5
- [3] 18.8° to 19°
- [2] M2 for sin B = 11sin28/16
- [1] M1 for sin B/11 = sin28/16 oe
- [4] 95.47° to 95.5°
- [3] B3 for 84.5 to 84.6
- [2] M2 for sin E = 109×2 / their DE × 21.9
- [1] M1 for 109 = 1/2 × 21.9 × their DE × sin E
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