O-LevelMathematicsTrigonometry4024/22 · May/June 2024 · Q107 Marks
The diagram shows a pentagon. [Figure 10.1]
- (a)Calculate the interior angle B.[2]
- (b)In the pentagon, AE = 8 cm and AD = 15 cm. Calculate the length ED. Show your working and give your answer correct to 1 decimal place.[5]
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Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [2] 87
- M1 for B+106+120+79+148 = 3 × 180 oe soi or 74+60+101+32+180-B = 360 oe soi
- [5] 9.3 nfww
- M2 for x² + 8x – 161 [= 0]
- M1 for 15² = 8² + x² - 2 × 8 × x × cos120 oe
- M2 for sqrt(8² - 4×1×(-161))
- M1 for (-8±sqrt(8² - 4×1×(-161))) / (2×1) oe or (-8±sqrt(p)) / (2×1) oe
- M1 for 8 sin120 / sinADE oe or 15 sin(60 - their 27.5) / sin120 oe
- M1 for sin120 / 15 = sin(60 - their 27.5) / ED oe or 8 sin(60 - their 27.5) / sin(their 27.5) oe
- B1 for 9.3 nfww
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