| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2012 |
| Session | Specimen |
| Marks | 7 |
| Topic | Laws of Logarithms |
| Type | Combine logs into single logarithm |
| Difficulty | Easy -1.8 This question tests basic recall of logarithm laws (sum/difference rules) and index laws with no problem-solving required. Part (a)(i) is trivial application of log(x)+log(y)=log(xy), part (a)(ii) requires one additional step to simplify powers, and part (b) is straightforward index manipulation. These are textbook drill exercises significantly easier than average A-level questions. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.06f Laws of logarithms: addition, subtraction, power rules |
**(a)(i)** $\log_a 15$ [B1]
**(a)(ii)**
- Use $b \log a = \log a^b$ at least once [M1]
- Use $\log a - \log b = \log \frac{a}{b}$ [M1]
- Obtain $\log_b \frac{1}{2}$ [A1]
**(b)**
- $\frac{1}{3}$ [B1]
- $\frac{1}{3a^2}$ o.e. [B1]
**Total: 7 marks**1
\begin{enumerate}[label=(\alph*)]
\item Express each of the following as a single logarithm.
\begin{enumerate}[label=(\roman*)]
\item $\log _ { a } 5 + \log _ { a } 3$
\item $5 \log _ { b } 2 - 3 \log _ { b } 4$
\end{enumerate}\item Express $\left( 9 a ^ { 4 } \right) ^ { - \frac { 1 } { 2 } }$ as an algebraic fraction in its simplest form.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2012 Q1 [7]}}