| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2006 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Transformation of specific function type |
| Difficulty | Standard +0.3 This question tests understanding of inverse sine function properties and basic transformations (horizontal shift and reflection). Part (a) requires recall of the domain and range of arcsin, while part (b) applies standard transformation rules. The transformations are straightforward with no complex composition or novel insight required, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\left(1, \frac{\pi}{2}\right)\) | B1 | Or for \(-1\) and \(1\) |
| \(\left(-1, -\frac{\pi}{2}\right)\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Translation in \(+ve\) \(x\) direction | M1 | |
| Correct shape | M1 | |
| Correct graph through \((1,0)\) touching \(y\)-axis | A1 |
## Question 7:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\left(1, \frac{\pi}{2}\right)$ | B1 | Or for $-1$ and $1$ |
| $\left(-1, -\frac{\pi}{2}\right)$ | B1 | |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Translation in $+ve$ $x$ direction | M1 | |
| Correct shape | M1 | |
| Correct graph through $(1,0)$ touching $y$-axis | A1 | |7
\begin{enumerate}[label=(\alph*)]
\item The sketch shows the graph of $y = \sin ^ { - 1 } x$.\\
\includegraphics[max width=\textwidth, alt={}, center]{908f530c-076d-47b1-90dd-38dbfe44f898-05_835_834_447_587}
Write down the coordinates of the points $P$ and $Q$, the end-points of the graph.
\item Sketch the graph of $y = - \sin ^ { - 1 } ( x - 1 )$.
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2006 Q7 [5]}}