Standard +0.3 This question requires sketching a transformed cotangent graph, which involves understanding the phase shift and identifying asymptotes. While cotangent is less commonly encountered than sine/cosine, this is a straightforward application of graph transformations with no problem-solving required—students need only recall the basic cot(x) shape and apply a horizontal shift of π/2.
Either a decreasing branch; condone translations; do not allow end points turning to intersect asymptote
Sketches three branches within \([0, 2\pi]\)
M1
Condone overlapping branches; asymptotes need not be drawn
Fully correct sketch with asymptotes at approximately \(x = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi\)
A1
Labelling not required; ignore anything after \(2\pi\) or left of \(O\)
## Question 7:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Sketches one correct section of $y = \cot x$ | B1 | Either a decreasing branch; condone translations; do not allow end points turning to intersect asymptote |
| Sketches three branches within $[0, 2\pi]$ | M1 | Condone overlapping branches; asymptotes need not be drawn |
| Fully correct sketch with asymptotes at approximately $x = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi$ | A1 | Labelling not required; ignore anything after $2\pi$ or left of $O$ |
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