| Exam Board | Edexcel |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Functions |
| Type | Sketch exponential graphs |
| Difficulty | Easy -1.2 This is a straightforward two-part question requiring basic exponential graph sketching (showing y-intercept at (0,1) and general shape) and solving a simple exponential equation using logarithms. Both parts are routine textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Correct shape: positive exponential curve in quadrants 1 and 2 only, passing through a point on positive \(y\)-axis | B1 | Shape must level out in Q2, not clearly stop on \(x\)-axis, no clear "U" shape |
| Fully correct: curve asymptotic to \(x\)-axis, levels out at least half way below intercept; intercept marked as 1 or \((0,1)\) or \(y=1\) | B1 | Intercept may be seen away from sketch but must correspond to it; sketch takes precedence if ambiguity |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(4^x = 100 \Rightarrow x = \log_4 100\) or \(x\log 4 = \log 100 \Rightarrow x = \dfrac{\log 100}{\log 4}\) | M1 | Uses logs to solve; allow if subsequently becomes e.g. \(\log 25\) as long as \(\dfrac{\log 100}{\log 4}\) is seen |
| \(x =\) awrt \(3.32\) | A1 | Correct answer only of awrt 3.32 scores M1A1; \(x = 3.218875...\) from \(\ln 25\) scores M0A0 unless \(\dfrac{\ln 100}{\ln 4}\) seen |
## Question 2:
### Part (a)
| Answer/Working | Mark | Guidance |
|---|---|---|
| Correct shape: positive exponential curve in quadrants 1 and 2 only, passing through a point on positive $y$-axis | B1 | Shape must level out in Q2, not clearly stop on $x$-axis, no clear "U" shape |
| Fully correct: curve asymptotic to $x$-axis, levels out at least half way below intercept; intercept marked as 1 or $(0,1)$ or $y=1$ | B1 | Intercept may be seen away from sketch but must correspond to it; sketch takes precedence if ambiguity |
### Part (b)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $4^x = 100 \Rightarrow x = \log_4 100$ or $x\log 4 = \log 100 \Rightarrow x = \dfrac{\log 100}{\log 4}$ | M1 | Uses logs to solve; allow if subsequently becomes e.g. $\log 25$ as long as $\dfrac{\log 100}{\log 4}$ is seen |
| $x =$ awrt $3.32$ | A1 | Correct answer only of awrt 3.32 scores M1A1; $x = 3.218875...$ from $\ln 25$ scores M0A0 unless $\dfrac{\ln 100}{\ln 4}$ seen |
---\begin{enumerate}
\item (a) Sketch the curve with equation
\end{enumerate}
$$y = 4 ^ { x }$$
stating any points of intersection with the coordinate axes.\\
(b) Solve
$$4 ^ { x } = 100$$
giving your answer to 2 decimal places.
\hfill \mbox{\textit{Edexcel Paper 2 2022 Q2 [4]}}