O-LevelMathematicsTrigonometry4024/21 · May/June 2015 · Q712 Marks

Section B [48 marks] Answer four questions in this section. Each question in this section carries 12 marks. (a) (i) Evaluate (8 sin 54°) / (sin 18°).

(a)(i)Evaluate (8 sin 54°) / (sin 18°).[1]
(a)(ii)Evaluate √4.73² – 1.65 sin 43°.[1]
(b)[Figure ABC] In the triangle ABC, BC = 16 cm and BẬC = 60°. AB = x cm and AC = 2x + 3 cm.
(b)(i)Form an equation in x and show that it simplifies to 3x² + 9x - 247 = 0.[4]
(b)(ii)Solve the equation 3x² + 9x - 247 = 0, giving your answers correct to 2 decimal places.[3]
(b)(iii)Hence write down the lengths of AB and AC.[1]
(b)(iv)Find the area of triangle ABC.[2]

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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.

[1] 20.9 to 21(.0)
[1] 4.6(0) to 4.61
[4] 3x² + 9x − 247 (= 0) correctly obtained; B3 for 16² = x² + 4x² +12x+9-2x²-3x; Or M2 for 16² = x² + (2x+3)² −2x(2x+3) cos 60; Or M1 for (16² =)x² + (2x+3)² ±(2)x(2x+3) cos60
[3] 7.70 and -10.70; B2 for one correct solution; Or 7.69 to 7.70 and -10.69 to -10.70; Or if in the form (p±√q)/r, B1 for p = – 9 and r = 6 or for q = 3045 (55.18)
[1] 7.70; 18.40; 1ft
[2] 61.3 to 62(.0); M1 for (1/2)×their 7.70 × their 18.40 × sin60

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