O-LevelMathematicsTrigonometry4024/22 · May/June 2014 · Q510 Marks

The diagram shows a framework ABCD supporting a shop sign. The framework is fixed to a vertical wall AB with CD horizontal. AC = 64 cm and CD = 80 cm. BẬC = 35°, BCA = 90° and ACD = 125°. [Figure of framework ABCD]

(a)Calculate AB.[2]
(b)Calculate AD.[3]
(c)Calculate ADC.[3]
(d)On the sign CDEF, FE is parallel to CD and is 40 cm below it. FE = 65 cm. Calculate the area of the sign CDEF.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

[2] (a) 78.1 to 78.13
[2] (a) M1 for cos 35 = 64/AB or better
[3] (b) 127.9 to 128
[3] (b) M1 for 64² + 80² + or – (2) × 64 × 80 cos 125 M1 for AD² = 64² + 80² – 2 × 64 × 80 cos 125
[3] (c) 24.1 to 24.2°
[3] (c) M1 for sin ADC / 64 = sin 125 / their128 oe M1 for sin ADC = (64 x sin 125) / their128
[2] (d) 2900
[2] (d) M1 for 0.5 × (80 + 65) × 40

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