| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2012 |
| Session | June |
| Marks | 3 |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch single standard trig graph (sin/cos/tan) |
| Difficulty | Easy -2.0 This is a routine sketching question requiring only basic knowledge of sine function transformations. Part (i) is trivial recall, and part (ii) involves a simple horizontal translation—both are standard textbook exercises with no problem-solving or novel insight required. The low mark allocation (1+2=3 marks total) confirms this is well below average A-level difficulty. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05f Trigonometric function graphs: symmetries and periodicities |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Sine wave through the origin, showing intersections with the \(x\)-axis at \(0\), \(\pi\) and \(2\pi\) | B1 [1] | |
| (ii) Sine wave translated in the negative \(x\)-direction; \(x\)-intercepts \(\frac{2}{5}\pi\), \(\frac{11}{5}\pi\); \(y\)-intercept \(0.5\) and symmetrical about the \(x\)-axis | M1, A1 [2] | [3] |
**(i)** Sine wave through the origin, showing intersections with the $x$-axis at $0$, $\pi$ and $2\pi$ | B1 [1] |
**(ii)** Sine wave translated in the negative $x$-direction; $x$-intercepts $\frac{2}{5}\pi$, $\frac{11}{5}\pi$; $y$-intercept $0.5$ and symmetrical about the $x$-axis | M1, A1 [2] | [3]Sketch, on separate diagrams, the graphs of the following functions for $0 \leqslant x \leqslant 2\pi$ giving the coordinates of all points of intersection with the axes.
\begin{enumerate}[label=(\roman*)]
\item $y = \sin x$. [1]
\item $y = \sin\left(x + \frac{1}{6}\pi\right)$. [2]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2012 Q5 [3]}}