| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Laws of Logarithms |
| Type | Two unrelated log parts: one non-log algebraic part |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic index laws and manipulation of powers. Part (a) requires recognizing that 1/√2 = 2^(-1/2) and 4√2 = 2^(5/2), which is routine for students who know index notation. Part (b) is a simple application of the law 2^(y-x) = 2^y/2^x. The question involves no problem-solving or novel insight—just direct application of standard techniques, making it easier than average but not trivial since it requires fluency with fractional and negative indices. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.06g Equations with exponentials: solve a^x = b |
Given that $2^x = \frac{1}{\sqrt{2}}$ and $2^y = 4\sqrt{2}$,
\begin{enumerate}[label=(\alph*)]
\item find the exact value of $x$ and the exact value of $y$, [3]
\item calculate the exact value of $2^{y-x}$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q9 [5]}}