O-LevelAdditional MathematicsTrigonometry4037/12 · Oct/Nov 2012 · Q99 Marks
Using the axes below, sketch for 0 ≤ x ≤ π, the graphs of y = sin 2x and y = 1+cos2x.
- (a)(i)Using the axes below, sketch for 0 ≤ x ≤ π, the graphs of y = sin 2x and y = 1+cos2x.[4]
- (a)(ii)Write down the solutions of the equation sin 2x - cos2x = 1, for 0 ≤ x ≤ π.[2]
- (b)(i)Write down the amplitude and period of 5 cos 4x - 3.[2]
- (b)(ii)Write down the period of 4 tan 3x.[1]
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 2012). The mark or mark type is shown in brackets.
- [B1] B1 for either correct amplitude or period for y = sin2x
- [B1] B1 for y = sin2x all correct
- [B1] B1 for translation of +1 parallel to y-axis or correct period for y = 1 + cos2x
- [B1] B1 for y = 1 + cos2x all correct
- [B1, B1] Allow in degrees
- [B1,B1] B1 for each
- [B1]
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