| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Exponential Equations & Modelling |
| Type | Logarithmic equation solving |
| Difficulty | Moderate -0.8 Part (i) is a straightforward application of logarithms to solve an exponential equation (take log of both sides). Part (ii) is routine manipulation using basic logarithm laws (power rule and log of reciprocal). Both parts require only direct recall and application of standard techniques with no problem-solving or insight needed, 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 |
|---|---|---|
| (i) \(2.5, 2.50, 2.500, 2.499..\) | B2 | M1 for \(\log_{10} 316\) or \(\ln 316/\ln 10\) |
| (ii) \(6\) www | B3 | B2 for \(6 \log_a a\) or \(\log_a(a^6)\). Or B1 for \(2\log_a(a)\) or \(-\log_a a^{-1}\). SC1 Using \(a=10 \Rightarrow 6\). SC2 Using numerical a, not \(10 \Rightarrow 6\) |
| 5 marks | ||
| [20] |
(i) $2.5, 2.50, 2.500, 2.499..$ | B2 | M1 for $\log_{10} 316$ or $\ln 316/\ln 10$
(ii) $6$ www | B3 | B2 for $6 \log_a a$ or $\log_a(a^6)$. Or B1 for $2\log_a(a)$ or $-\log_a a^{-1}$. SC1 Using $a=10 \Rightarrow 6$. SC2 Using numerical a, not $10 \Rightarrow 6$
| | 5 marks |
| | [20] |8 (i) Solve the equation $10 ^ { x } = 316$.\\
(ii) Simplify $\log _ { a } \left( a ^ { 2 } \right) - 4 \log _ { a } \left( \frac { 1 } { a } \right)$.
\hfill \mbox{\textit{OCR MEI C2 2005 Q8 [5]}}