| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Solve log equation with unknown inside argument (standard base) |
| Difficulty | Moderate -0.3 Part (a) is straightforward substitution and solving a simple logarithm equation (log₁₀(2-c)=1 gives c=-8). Part (b) requires setting up |f(α)-g(α)|=1.2, using log laws to get log₁₀((5-α)/(2-α))=±1.2, then solving algebraically—this involves more steps and careful manipulation but remains a standard A-level exercise without requiring novel insight. The 5 marks reflect routine multi-step work rather than conceptual difficulty. |
| Spec | 1.06c Logarithm definition: log_a(x) as inverse of a^x1.06d Natural logarithm: ln(x) function and properties |
A function $f$ is defined by $f(x) = \log_{10}(2 - x)$. Another function $g$ is defined by $g(x) = \log_{10}(5 - x)$. The diagram below shows a sketch of the graphs of $y = f(x)$ and $y = g(x)$.
\includegraphics{figure_17}
\begin{enumerate}[label=(\alph*)]
\item The point $(c, 1)$ lies on $y = f(x)$. Find the value of $c$. [2]
\item A point P lies on $y = f(x)$ and has $x$-coordinate $\alpha$. Another point Q lies on $y = g(x)$ and also has $x$-coordinate $\alpha$. The distance between P and Q is 1.2 units. Find the value of $\alpha$, giving your answer correct to three decimal places. [5]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2024 Q17 [7]}}