| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2022 |
| Session | October |
| Marks | 6 |
| Topic | Indices and Surds |
| Type | Rationalize denominator simple |
| Difficulty | Moderate -0.8 Part (a) is a standard rationalizing denominator exercise requiring multiplication by the conjugate—routine A-level technique. Part (b) involves expressing both sides as powers of 2 and equating exponents, which is straightforward index law application. Both parts are textbook exercises with no problem-solving insight required, making this easier than average. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}
\item a) Rationalise the denominator for $\frac { \sqrt { 8 } + 2 } { 5 - \sqrt { 2 } }$\\
b) Solve
\end{enumerate}
$$( \sqrt { 2 } ) ^ { x + 1 } = \frac { 1 } { 4 ^ { 4 - 3 x } }$$
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\hfill \mbox{\textit{SPS SPS FM 2022 Q1 [6]}}