| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Solve exponential equations |
| Difficulty | Easy -1.3 This is a straightforward C1 question testing basic index laws and equation solving. Part (a) requires recognizing that 1/8 = 2^(-3), and part (b) involves simple manipulation of negative/fractional indices. Both are routine recall exercises with minimal problem-solving, making this easier than average. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.06g Equations with exponentials: solve a^x = b |
| Answer | Marks |
|---|---|
| \(2^x = \frac{1}{8} = 2^{-3} \Rightarrow x = -3\) | B1 |
| Answer | Marks |
|---|---|
| \(x^{-\frac{1}{2}} = \frac{1}{4} \Rightarrow x^2 = 4 \Rightarrow x = 4^2 = 16\) | M1, A1 |
**Part (i)**
$2^x = \frac{1}{8} = 2^{-3} \Rightarrow x = -3$ | B1 |
**Part (ii)**
$x^{-\frac{1}{2}} = \frac{1}{4} \Rightarrow x^2 = 4 \Rightarrow x = 4^2 = 16$ | M1, A1 |5 Solve the following equations.
\begin{enumerate}[label=(\alph*)]
\item $\quad 2 ^ { x } = \frac { 1 } { 8 }$.
\item $\quad x ^ { - \frac { 1 } { 2 } } = \frac { 1 } { 4 }$
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q5 [3]}}