O-LevelAdditional MathematicsTrigonometry4037/12 · Oct/Nov 2016 · Q78 Marks
The diagram shows part of the graph of y = 2 cos (x - π/6). The graph intersects the y-axis at the point A, has a maximum point at B and intersects the x-axis at the point C. [Figure 7.1]
- (i)Find the coordinates of A.[1]
- (ii)Find the coordinates of B.[2]
- (iii)Find the coordinates of C.[2]
- (iv)Find ∫ 2 cos(x - π/6) dx .[1]
- (v)Hence find the area of the shaded region.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [1] (i) (0, √3) or (0, 1.73) or better B1
- [2] (ii) (π/6, 2) or (0.524, 2) or better B1 for each
- [1] (iii) cos(x - π/6) = 0 M1 for correct attempt to solve trigonometric equation
- [1] (iii) x = 2π/3 oe or 2.09 or better A1
- [1] (iv) 2sin(x - π/6) (+c) B1
- [1] (v) Area = [2sin(x - π/6)] from 0 to 2π/3 M1 for correct use of their limits, in radians, into ksin(x - π/6)
- [1] (v) = 2 + 1 = 3 A1
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