| Exam Board | OCR MEI |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Critique single model appropriateness |
| Difficulty | Moderate -0.3 This question involves straightforward exponential substitution (parts a,c,e), basic reasoning about model limitations (part b), and interpreting graphical features like asymptotes and inflection points (parts d,e). While it requires understanding of exponential growth and curve interpretation across multiple parts, each individual step is routine with no complex calculations or novel problem-solving required—slightly easier than a typical A-level question due to its largely qualitative nature. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06i Exponential growth/decay: in modelling context |
| Answer | Marks | Guidance |
|---|---|---|
| \(0.3\) [MWh] | B1 [1] | AO 3.4 |
| Answer | Marks | Guidance |
|---|---|---|
| \(27\) [MWh] | B1 [1] | AO 3.4; \(P = 0.3e^{0.5\times9} = 27.0051...\) |
| Answer | Marks | Guidance |
|---|---|---|
| Reason why model is not suitable, e.g. the model is only based on data up to 2009; the model predicts unlimited growth in solar energy and that is not possible | B1 [1] | AO 3.5b; Very large prediction in 2025 (80 501MWh) is unrealistic; "Extrapolation" alone does not score, needs explaining/clarifying |
| Answer | Marks | Guidance |
|---|---|---|
| The graph gives a value close to 27 when \(t = 9\) | E1 [1] | AO 3.2b; Correct reasoning (answer given) |
| Answer | Marks | Guidance |
|---|---|---|
| [Sketch: gradient increasing from near zero to maximum, then decreasing to near zero] | B1, B1 [2] | AO 2.2a; Gradient increasing from near zero to maximum for value of \(t\) somewhere between 10 and 20; gradient decreasing to near zero from max value |
| Answer | Marks | Guidance |
|---|---|---|
| \(14\) | B1 [1] | AO 1.2; Answer in range 13 to 15 |
| Answer | Marks | Guidance |
|---|---|---|
| This is when the rate of increase of electricity production is greatest | E1 [1] | AO 3.2a |
| Answer | Marks | Guidance |
|---|---|---|
| \(300\) [MWh] | B1 [1] | AO 2.2a; Accept answer in range 300 to 305 |
## Question 9(a)(i):
$0.3$ [MWh] | B1 [1] | AO 3.4
## Question 9(a)(ii):
$27$ [MWh] | B1 [1] | AO 3.4; $P = 0.3e^{0.5\times9} = 27.0051...$
## Question 9(b):
Reason why model is not suitable, e.g. the model is only based on data up to 2009; the model predicts unlimited growth in solar energy and that is not possible | B1 [1] | AO 3.5b; Very large prediction in 2025 (80 501MWh) is unrealistic; "Extrapolation" alone does not score, needs explaining/clarifying
## Question 9(c):
The graph gives a value close to 27 when $t = 9$ | E1 [1] | AO 3.2b; Correct reasoning (answer given)
## Question 9(d)(i):
[Sketch: gradient increasing from near zero to maximum, then decreasing to near zero] | B1, B1 [2] | AO 2.2a; Gradient increasing from near zero to maximum for value of $t$ somewhere between 10 and 20; gradient decreasing to near zero from max value
## Question 9(d)(ii):
$14$ | B1 [1] | AO 1.2; Answer in range 13 to 15
## Question 9(d)(iii):
This is when the rate of increase of electricity production is greatest | E1 [1] | AO 3.2a
## Question 9(e):
$300$ [MWh] | B1 [1] | AO 2.2a; Accept answer in range 300 to 305
---9 A small country started using solar panels to produce electrical energy in the year 2000. Electricity production is measured in megawatt hours (MWh).
For the period from 2000 to 2009, the annual electrical energy produced using solar panels can be modelled by the equation $\mathrm { P } = 0.3 \mathrm { e } ^ { 0.5 \mathrm { t } }$, where $P$ is the annual amount of electricity produced in MWh and $t$ is the time in years after the year 2000.
\begin{enumerate}[label=(\alph*)]
\item According to this model, find the amount of electricity produced using solar panels in each of the following years.
\begin{enumerate}[label=(\roman*)]
\item 2000
\item 2009
\end{enumerate}\item Give a reason why the model is unlikely to be suitable for predicting the annual amount of electricity produced using solar panels in the year 2025.
An alternative model is suggested; the curve representing this model is shown in Fig. 9.
\begin{figure}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Fig. 9}
\includegraphics[alt={},max width=\textwidth]{20639e13-01cc-4d96-b694-fb3cf1828f4d-08_702_1587_1265_230}
\end{center}
\end{figure}
\item Explain how the graph shows that the alternative model gives a value for the amount of electricity produced in 2009 that is consistent with the original model.
\item \begin{enumerate}[label=(\roman*)]
\item On the axes given in the Printed Answer Booklet, sketch the gradient function of the model shown in Fig. 9.
\item State approximately the value of $t$ at the point of inflection in Fig. 9.
\item Interpret the significance of the point of inflection in the context of the model.
\end{enumerate}\item State approximately the long term value of the annual amount of electricity produced using solar panels according to the model represented in Fig. 9.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 3 2023 Q9 [8]}}