| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | February |
| Marks | 6 |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Easy -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. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
\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]}}