SPS SPS SM 2022 February — Question 1 6 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2022
SessionFebruary
Marks6
TopicIndices and Surds
TypeRationalize denominator simple
DifficultyEasy -1.3 This is a straightforward multi-part question testing basic index laws and surds manipulation. Part (i) is routine index calculation, part (ii) is simple index conversion, and part (iii) is standard rationalizing the denominator—all are textbook exercises requiring recall of techniques with minimal problem-solving, making this easier than average.
Spec1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators

  1. Evaluate \(27^{-\frac{2}{3}}\). [2]
  2. Express \(5\sqrt{5}\) in the form \(5^n\). [1]
  3. Express \(\frac{1-\sqrt{5}}{3+\sqrt{5}}\) in the form \(a + b\sqrt{5}\). [3]

\begin{enumerate}[label=(\roman*)]
\item Evaluate $27^{-\frac{2}{3}}$. [2]

\item Express $5\sqrt{5}$ in the form $5^n$. [1]

\item Express $\frac{1-\sqrt{5}}{3+\sqrt{5}}$ in the form $a + b\sqrt{5}$. [3]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS SM 2022 Q1 [6]}}