| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Easy -1.3 This is a straightforward surds manipulation question testing basic algebraic skills. Part (i) is trivial recognition that 3^(1/2) = 1√3. Part (ii) requires rationalizing the denominator by multiplying by the conjugate, which is a standard textbook exercise with no problem-solving element. The 5 total marks reflect routine working rather than difficulty. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
In this question you must show detailed reasoning.
\begin{enumerate}[label=(\roman*)]
\item Express $3^{\frac{1}{2}}$ in the form $a\sqrt{b}$, where $a$ is an integer and $b$ is a prime number. [2]
\item Express $\frac{\sqrt{2}}{1-\sqrt{2}}$ in the form $c + d\sqrt{e}$, where $c$ and $d$ are integers and $e$ is a prime number. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q1 [5]}}