| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Change of base or reciprocal relationship |
| Difficulty | Easy -1.2 This question tests basic understanding of exponential functions and inverse functions through reflection in y=x. Part (i) requires sketching y=3^x and identifying the y-intercept (0,1), which is routine recall. Part (ii) asks students to recognize that reflection in y=x gives the inverse function, so f(x)=log₃(x), which is a standard textbook exercise with no problem-solving required. The multi-part structure adds minimal difficulty as each part is straightforward. |
| Spec | 1.02v Inverse and composite functions: graphs and conditions for existence1.06a Exponential function: a^x and e^x graphs and properties |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Correct shape in both quadrants [graph shown] | B1 (AO1.2) | Correct shape in both quadrants; condone touching the \(x\)-axis, but not cutting it |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((0,1)\) | B1 (AO1.1) | Do not allow just \(y=1\) |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((f(x)=)\log_3 x\) | B1 (AO1.1) | Allow e.g. \(\frac{\log x}{\log 3}\) |
| [1] |
## Question 5(i) A:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct shape in both quadrants [graph shown] | B1 (AO1.2) | Correct shape in both quadrants; condone touching the $x$-axis, but not cutting it |
| **[1]** | | |
## Question 5(i) B:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(0,1)$ | B1 (AO1.1) | Do not allow just $y=1$ |
| **[1]** | | |
## Question 5(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(f(x)=)\log_3 x$ | B1 (AO1.1) | Allow e.g. $\frac{\log x}{\log 3}$ |
| **[1]** | | |
---5
\begin{enumerate}[label=(\roman*)]
\item (A) Sketch the graph of $y = 3 ^ { x }$.\\
(B) Give the coordinates of any intercepts.
The curve $y = \mathrm { f } ( x )$ is the reflection of the curve $y = 3 ^ { x }$ in the line $y = x$.
\item Find $\mathrm { f } ( x )$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2018 Q5 [3]}}