| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2013 |
| Session | June |
| Marks | 3 |
| Topic | Trig Graphs & Exact Values |
| Type | Find period or state transformations |
| Difficulty | Easy -1.2 This is a straightforward question testing basic knowledge of trigonometric transformations. Part (i) requires sketching a standard transformed cosine graph with period π, and part (ii) asks for a simple description of a horizontal stretch by factor 1/2. Both parts are routine recall with minimal problem-solving, making this easier than average A-level content. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05f Trigonometric function graphs: symmetries and periodicities |
**(i)** Two 'cos' curves shown in the range — B1
$+1$ and $-1$ shown on $y$-axis and $x$ values for at least stationary points indicated on fully correct curve. (For the second B1, curves must show the stationary point at $2\pi$ clearly.) — B1 **[2]**
**(ii)** State 'stretch' — B1
parallel to the $x$-axis — B1
scale factor 0.5 — B1 **[3]**6 (i) Sketch the graph of $y = \cos 2 x$ for $0 \leqslant x \leqslant 2 \pi$.\\
(ii) Describe the transformation which maps the graph of $y = \cos x$ onto the graph of $y = \cos 2 x$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2013 Q6 [3]}}