| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Session | Specimen |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Two unrelated log/algebra parts - linked parts (hence) |
| Difficulty | Moderate -0.8 This is a straightforward application of basic logarithm laws (power rule and addition rule) followed by simple rearrangement. Part (a) requires combining logs using standard rules, and part (b) involves converting to exponential form and solving—both are routine procedures with no problem-solving insight required, making this easier than average. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(\log_3 x^2a\) | B1 (1.1) | |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(x^2a = 3^2\) | M1 (1.1) | |
| \(x = [\pm]\frac{3}{\sqrt{a}}\) oe | A1 (1.1) | |
| Disregard \(x = -\frac{3}{\sqrt{a}}\) as \(x\) cannot be negative | A1 (2.1) | Must be clear that the negative root has been considered and disregarded |
| [3] |
## Question 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $\log_3 x^2a$ | B1 (1.1) | |
| **[1]** | | |
---
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $x^2a = 3^2$ | M1 (1.1) | |
| $x = [\pm]\frac{3}{\sqrt{a}}$ oe | A1 (1.1) | |
| Disregard $x = -\frac{3}{\sqrt{a}}$ as $x$ cannot be negative | A1 (2.1) | Must be clear that the negative root has been considered and disregarded |
| **[3]** | | |
---2
\begin{enumerate}[label=(\alph*)]
\item Express $2 \log _ { 3 } x + \log _ { 3 } a$ as a single logarithm.
\item Given that $2 \log _ { 3 } x + \log _ { 3 } a = 2$, express $x$ in terms of $a$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 Q2 [4]}}