O-LevelMathematicsTrigonometry4024/21 · May/June 2015 · Q510 Marks
[Figure ABCDEF] In the framework ABCDEF, BCD is a straight line, and CA is parallel to DF. ABD, BÔIDE and DÊF are right angles. AB = 4m, DE = 11 m and EF = 4 m.
- (a)FDE = x°. Show that x = 20.0 correct to 3 significant figures.[2]
- (b)BẬC = y°. Stating your reasons, explain why y = x.[1]
- (c)Calculate AC.[3]
- (d)The perpendicular distance between the parallel lines CA and DF is 7 m. Calculate the area of ACDF.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.
- [2] Correctly shown; M1 for tan x = 4/11
- [1] Complete explanation; BĈA = CDF corresponding and y + BCA = 90 = x + CDF
- [3] 4.256 to 4.26(0); M2 for (AC =) 4/cos y; Or M1 for 4/cosy; AC
- [4] 55.8 to 55.9; M3 for (1/2)(their (c) + their FD)×7; Or B2 for (FD =) 11.7 or √137 or √4²+11²; Or B1 for (DF²) = 4² + 11²
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