| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2006 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | log(y) vs x: convert and interpret |
| Difficulty | Moderate -0.5 This is a straightforward two-part question on exponential modelling via log-linear graphs. Part (i) requires reading gradient and intercept from a graph to write a linear equation (standard C2 skill). Part (ii) requires converting from logarithmic to exponential form using basic log laws. Both parts are routine applications of standard techniques with no problem-solving or novel insight required, making it slightly easier than average. |
| Spec | 1.06h Logarithmic graphs: reduce y=ax^n and y=kb^x to linear form |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\log_{10} y = 0.5x + 3\) | B3 | B1 for each term scored in either part o.e. g. \(y = 1000 \times 10^{y_x}\) |
| (ii) \(y = 10^{0.5x + 3}\) isw | 2 marks | 5 marks total |
(i) $\log_{10} y = 0.5x + 3$ | B3 | B1 for each term scored in either part o.e. g. $y = 1000 \times 10^{y_x}$
(ii) $y = 10^{0.5x + 3}$ isw | 2 marks | 5 marks total9
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{15b8f97b-c058-409f-907f-cb0a6102abc4-4_591_985_312_701}
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\caption{Fig. 9}
\end{center}
\end{figure}
The graph of $\log _ { 10 } y$ against $x$ is a straight line as shown in Fig. 9 .\\
(i) Find the equation for $\log _ { 10 } y$ in terms of $x$.\\
(ii) Find the equation for $y$ in terms of $x$.
Section B (36 marks)\\
\hfill \mbox{\textit{OCR MEI C2 2006 Q9 [5]}}