| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Simple exponential equation solving |
| Difficulty | Moderate -0.8 This is a straightforward C2 exponential question requiring basic sketching skills and routine logarithm manipulation. Part (a) is standard curve sketching, while part (b) involves solving simple exponential equations using logarithms—both are textbook exercises with no problem-solving insight required. The multi-part structure adds marks but not conceptual difficulty. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks |
|---|---|
| (a) Graph showing curve through \((0, \frac{1}{2})\) with correct shape | B2 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(5^{x-1} = 10\) | M1 | |
| \((x-1)\lg 5 = \lg 10 = 1\) | M1 | |
| \(x = \frac{1}{\lg 5} + 1 = 2.43\) | M1 A1 | |
| (ii) \(5^{x-1} = 2^x\) | M1 | |
| \((x-1)\lg 5 = x\lg 2\) | M1 | |
| \(x(\lg 5 - \lg 2) = \lg 5\) | M1 | |
| \(x = \frac{\lg 5}{\lg 5 - \lg 2} = 1.76\) | A1 | (8) |
**(a)** Graph showing curve through $(0, \frac{1}{2})$ with correct shape | B2 |
**(b)**
**(i)** $5^{x-1} = 10$ | M1 |
$(x-1)\lg 5 = \lg 10 = 1$ | M1 |
$x = \frac{1}{\lg 5} + 1 = 2.43$ | M1 A1 |
**(ii)** $5^{x-1} = 2^x$ | M1 |
$(x-1)\lg 5 = x\lg 2$ | M1 |
$x(\lg 5 - \lg 2) = \lg 5$ | M1 |
$x = \frac{\lg 5}{\lg 5 - \lg 2} = 1.76$ | A1 | (8)\begin{enumerate}[label=(\alph*)]
\item Sketch the curve $y = 5^{x-1}$, showing the coordinates of any points of intersection with the coordinate axes. [2]
\item Find, to 3 significant figures, the $x$-coordinates of the points where the curve $y = 5^{x-1}$ intersects
\begin{enumerate}[label=(\roman*)]
\item the straight line $y = 10$,
\item the curve $y = 2^x$. [6]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q5 [8]}}