| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2019 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Two unrelated log parts: one non-log algebraic part |
| Difficulty | Standard +0.3 Part (a) requires converting to common bases (3^(3x+2y)=3^3 and 2^(-3x-3y)=2^6) then solving linear simultaneous equations - straightforward but multi-step. Part (b) uses standard log laws to combine terms then solve the resulting equation, requiring careful algebraic manipulation and checking validity. Both parts are routine A-level techniques with no novel insight required, slightly above average due to the combined length and potential for algebraic errors. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}[label=(\alph*)]
\item Solve the following simultaneous equations.
$$3^{3x} \times 9^y = 27$$
$$2^{-3x} \times 8^{-y} = \frac{1}{64}$$ [6]
\item Find the value of $x$ satisfying the equation
$$\log_a 3 + 2\log_a x - \log_a(x - 1) = \log_a(5x + 2).$$ [7]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2019 Q10 [13]}}