| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Year | 2018 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | ln(y) vs ln(x) linear graph |
| Difficulty | Moderate -0.8 This is a highly structured, step-by-step question that guides students through a standard logarithmic linearization technique. Each part explicitly tells students what to do (write the power law, take logs, complete a table, find gradient/intercept, substitute back). The calculations are straightforward with only two data points, requiring basic log rules and simultaneous equations. This is easier than average as it's essentially a textbook exercise with extensive scaffolding and no problem-solving required. |
| Spec | 1.02r Proportional relationships: and their graphs1.06f Laws of logarithms: addition, subtraction, power rules1.06h Logarithmic graphs: reduce y=ax^n and y=kb^x to linear form |
| \(x\) | \(y\) | |
| Mercury | 0.3075 | 14400 |
| Jupiter | 4.950 | 55.8 |
I notice that the extracted content you've provided appears to be incomplete or corrupted. It shows only question headers and labels (11(i) through 11(vii)) without any actual marking criteria, answer guidance, or point allocations.
To properly clean this up and convert unicode symbols to LaTeX notation, I would need the actual mark scheme content that includes:
- Marking points (M1, A1, B1, etc.)
- Expected answers or methods
- Any mathematical notation or symbols to convert
- Guidance notes or follow-through marks
Could you please provide the complete mark scheme content for Question 11? Once you share the full text, I'll clean it up and format it according to your specifications.11 The intensity of the sun's radiation, $y$ watts per square metre, and the average distance from the sun, $x$ astronomical units, are shown in Fig. 11 for the planets Mercury and Jupiter.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | l | c | c | }
\hline
& $x$ & $y$ \\
\hline
Mercury & 0.3075 & 14400 \\
\hline
Jupiter & 4.950 & 55.8 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Fig. 11}
\end{center}
\end{table}
The intensity $y$ is proportional to a power of the distance $x$.\\
(i) Write down an equation for $y$ in terms of $x$ and two constants.\\
(ii) Show that the equation can be written in the form $\ln y = a + b \ln x$.\\
(iii) In the Printed Answer Booklet, complete the table for $\ln x$ and $\ln y$ correct to 4 significant figures.\\
(iv) Use the values from part (iii) to find $a$ and $b$.\\
(v) Hence rewrite your equation from part (i) for $y$ in terms of $x$, using suitable numerical values for the constants.\\
(vi) Sketch a graph of the equation found in part (v).\\
(vii) Earth is 1 astronomical unit from the sun. Find the intensity of the sun's radiation for Earth.
\hfill \mbox{\textit{OCR MEI AS Paper 1 2018 Q11 [13]}}