Moderate -0.8 This is a straightforward graph sketching question requiring knowledge that arccos x has domain [-1,1] and range [0,π], so 2arccos x has range [0,2π]. Students need only apply a vertical stretch and mark key points ((-1,2π), (0,π), (1,0)). No problem-solving or manipulation required, just direct application of inverse function properties.
Passes through \((-1,\,2\pi)\), \((0,\,\pi)\) and \((1,\,0)\)
B1
Good sketch — curve reasonably vertical at \((-1,\,2\pi)\) and \((1,\,0)\), negative gradient at \((0,\,\pi)\); domain and range clearly marked and correct
A1 [3]
## Question 7:
| Reasonable shape (condone extra range) | M1 | Can use degrees or radians |
|---|---|---|
| Passes through $(-1,\,2\pi)$, $(0,\,\pi)$ and $(1,\,0)$ | B1 | |
| Good sketch — curve reasonably vertical at $(-1,\,2\pi)$ and $(1,\,0)$, negative gradient at $(0,\,\pi)$; domain and range clearly marked and correct | A1 [3] | |
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