| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2010 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Sequence of transformations order |
| Difficulty | Moderate -0.3 This is a straightforward transformations question requiring application of standard rules. Part (i) involves two basic transformations of ln x (reflection then translation), and part (ii) requires working backwards from a transformed equation to identify the sequence. Both parts are routine C3 material with no problem-solving insight needed, making it slightly easier than average. |
| Spec | 1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
The transformations R, S and T are defined as follows.
\begin{align}
\text{R} &: \text{ reflection in the } x\text{-axis} \\
\text{S} &: \text{ stretch in the } x\text{-direction with scale factor 3} \\
\text{T} &: \text{ translation in the positive } x\text{-direction by 4 units}
\end{align}
\begin{enumerate}[label=(\roman*)]
\item The curve $y = \ln x$ is transformed by R followed by T. Find the equation of the resulting curve. [2]
\item Find, in terms of S and T, a sequence of transformations that transforms the curve $y = x^3$ to the curve $y = \left(\frac{1}{3}x - 4\right)^3$. You should make clear the order of the transformations. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 2010 Q2 [4]}}