O-LevelMathematicsTrigonometry4024/21 · May/June 2016 · Q912 Marks

(a) [Figure 9.1] ABCD represents the rectangular sloping surface of a triangular prism. ABEF is a horizontal rectangle. CE and DF are vertical. CBE = 15°, DC = 5 m and AD = 2 m. (b) [Figure 9.2] A triangle has sides of 10 cm, 9 cm and 6 cm, and an angle of θ°, as shown in the diagram. Calculate θ. (b)(ii) [Figure 9.3] The triangle KGH has sides of a cm, b cm and c cm as shown in the diagram. It is given that KGH is an obtuse angle. Complete the statement below using one of the symbols < < = > >. c² ..... (a² + b²)

(a)(i)Calculate AC.[2]
(a)(ii)Calculate CE.[2]
(a)(iii)Calculate FÂE.[4]
(b)(i)A triangle has sides of 10cm, 9 cm and 6 cm, and an angle of θ°, as shown in the diagram. Calculate θ.[3]
(b)(ii)The triangle KGH has sides of a cm, b cm and c cm as shown in the diagram. It is given that KGH is an obtuse angle. Complete the statement below using one of the symbols < < = > >. c² ..... (a² + b²)[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

[2] (a)(i) 5.38 to 5.39 or √29
[2] (a)(i) M1 for (AC²) = 2^2 + 5^2
[2] (a)(ii) 0.517 to 0.518
[2] (a)(ii) M1 for (CE/2) = sin15 oe
[4] (a)(iii) 68.8 to 68.9
[4] (a)(iii) M1 for (AF/2) = cos15 oe or BC^2 = BE^2 + (their CE)^2 or any complete alternative method
[4] (a)(iii) A1 for 1.932 and
[4] (a)(iii) M1 for tan FAE = (5 / (2 cos15)) oe or (5 / their(AF))
[3] (b)(i) 80.9(4.... Or 81
[3] (b)(i) B1 for 10^2 = 6^2 + 9^2 – 2×6×9×cos θ or
[3] (b)(i) B2 for cos θ = (9^2 + 6^2 - 10^2) / (2×9×6)
[1] (b)(ii) >

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