OCR PURE — Question 1 5 marks

Exam BoardOCR
ModulePURE
Marks5
PaperDownload PDF ↗
TopicIndices and Surds
TypeRationalize denominator simple
DifficultyEasy -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.
Spec1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators

In this question you must show detailed reasoning.
  1. Express \(3^{\frac{1}{2}}\) in the form \(a\sqrt{b}\), where \(a\) is an integer and \(b\) is a prime number. [2]
  2. 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]

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]}}