| Exam Board | OCR MEI |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Inverse function with exponentials |
| Difficulty | Moderate -0.8 Part (a) requires straightforward manipulation of logarithms (exponentiating both sides, then rearranging) to get y = k + 2^x. Part (b) is a standard exponential graph sketch with vertical translation. Both parts are routine applications of basic techniques with no problem-solving or novel insight required, making this easier than average. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\log_{10}(y-k) = \log_{10} 2^x\) | M1 | Correct use of one of the laws of logs – award if \(2^x\) seen or if \((y-k) = 10^{x\log 2}\) |
| \(y = k + 2^x\) | A1 | LHS must be \(y=\). Allow \(y = k + 10^{x\log 2}\) |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| General shape correct | B1 | Positive and negative values of \(x\) should be seen. FT their exponential (a) |
| \(y\)-intercept at \(k+1\) on positive \(y\)-axis | B1 | \(y\)-intercept at \(k+1\) on positive \(y\)-axis. FT their exponential (a) provided in terms of \(k\) |
| Asymptote at \(k\) | B1 | Asymptote at \(k\). Horizontal line need not been seen provided the intention is clear |
| [3] |
## Question 5:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\log_{10}(y-k) = \log_{10} 2^x$ | M1 | Correct use of one of the laws of logs – award if $2^x$ seen or if $(y-k) = 10^{x\log 2}$ |
| $y = k + 2^x$ | A1 | LHS must be $y=$. Allow $y = k + 10^{x\log 2}$ |
| [2] | | |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| General shape correct | B1 | Positive and negative values of $x$ should be seen. FT their exponential (a) |
| $y$-intercept at $k+1$ on positive $y$-axis | B1 | $y$-intercept at $k+1$ on positive $y$-axis. FT their exponential (a) provided in terms of $k$ |
| Asymptote at $k$ | B1 | Asymptote at $k$. Horizontal line need not been seen provided the intention is clear |
| [3] | | |
---5
\begin{enumerate}[label=(\alph*)]
\item Make $y$ the subject of the formula $\log _ { 10 } ( y - k ) = x \log _ { 10 } 2$, where $k$ is a positive constant.
\item Sketch the graph of $y$ against $x$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 1 2024 Q5 [5]}}