A-LevelMathematicsFunctions9709/12 · May/June 2020 · Q98 Marks
Functions f and g are such that f(x) = 2 - 3 sin 2x for 0 ≤ x ≤ π, g(x) = -2f(x) for 0 ≤ x ≤ π. The diagram below shows the graph of y = f(x). [Figure 9.1]
- (a)State the ranges of f and g.[3]
- (b)Sketch, on this diagram, the graph of y = g(x).[2]
- (c)Describe fully a sequence of transformations that maps the curve y = f(x) on to y = h(x).[3]
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 (May/June 2020). The mark or mark type is shown in brackets.
- [B1 B1] f(x) from -1 to 5
- [B1FT] g(x) from -10 to 2 (FT from part (a))
- [B2, 1] Correct shape. Amplitude of 6, minimum at -10, maximum at 2. Correct period. Reflects f(x) in x-axis then stretch by factor 2.
- [B1] Reflect in x-axis
- [B1] Stretch by factor 2 in the y direction
- [B1] Translation by –π in the x direction OR translation by (-π, 0)
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