| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | November |
| Marks | 6 |
| Topic | Indices and Surds |
| Type | Solve equations with surds |
| Difficulty | Easy -1.3 Part (a) is routine index manipulation with a mixed number requiring conversion to improper fraction. Part (b) is a straightforward surd equation solved by rearranging and rationalizing the denominator - both are standard textbook exercises requiring only direct application of techniques with no problem-solving insight needed. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
\begin{enumerate}
\item (a) Evaluate $\left( 5 \frac { 4 } { 9 } \right) ^ { - \frac { 1 } { 2 } }$.\\
(b) Find the value of $x$ such that
\end{enumerate}
$$\frac { 1 + x } { x } = \sqrt { 3 }$$
giving your answer in the form $a + b \sqrt { 3 }$ where $a$ and $b$ are rational.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM 2022 Q2 [6]}}