| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Evaluate log expression using laws |
| Difficulty | Easy -1.2 This is a straightforward application of basic logarithm laws (log_a(a)=1, power rule, addition rule) with no problem-solving required. Both parts are routine drill exercises testing recall of standard identities, making this easier than average for A-level. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06f Laws of logarithms: addition, subtraction, power rules |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| (i) \(7\) | 1 | |
| (ii) \(5.5\) o.e. | 2 | M1 for at least one of \(5\log_{10}a\) or \(\frac{1}{2}\log_{10}a\) or \(\log_{10}a^{5.5}\) o.e. |
# Question 9:
| Answer/Working | Mark | Guidance |
|---|---|---|
| (i) $7$ | 1 | |
| (ii) $5.5$ o.e. | 2 | M1 for at least one of $5\log_{10}a$ or $\frac{1}{2}\log_{10}a$ or $\log_{10}a^{5.5}$ o.e. | **[3]** |
---9 Simplify\\
(i) $10 - 3 \log _ { a } a$,\\
(ii) $\frac { \log _ { 10 } a ^ { 5 } + \log _ { 10 } \sqrt { a } } { \log _ { 10 } a }$.
Section B (36 marks)
\hfill \mbox{\textit{OCR MEI C2 2009 Q9 [3]}}