| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2020 |
| Session | October |
| Marks | 6 |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Moderate -0.8 This question tests basic algebraic manipulation: (i) rationalizing a denominator with surds is a standard C1/C2 technique requiring one multiplication step, and (ii) solving an equation with fractional indices involves straightforward index law application. Both parts are routine exercises with no problem-solving insight required, making this easier than average but not trivial since students must execute the techniques correctly. |
| 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 $\frac{\sqrt{2}}{1-\sqrt{2}}$ in the form $c + d\sqrt{e}$, where $c$ and $d$ are integers and $e$ is a prime number. [3]
\item Solve the equation $(8p^6)^{\frac{1}{3}} = 8$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2020 Q4 [6]}}