| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2025 |
| Session | October |
| Marks | 8 |
| Topic | Indices and Surds |
| Type | Simplify algebraic expressions with indices |
| Difficulty | Easy -1.8 This is a routine algebraic manipulation question testing basic index laws and surds. All parts require straightforward application of standard rules (negative/fractional indices, power of a product, multiplication of surds) with no problem-solving or conceptual insight needed. The multi-part structure and 5 total marks indicate this is an accessible starter question, significantly easier than average A-level content. |
| Spec | 1.02a Indices: laws of indices for rational exponents |
Express each of the following in the form $px^q$, where $p$ and $q$ are constants.
\begin{enumerate}[label=(\alph*)]
\item $\frac{2}{\sqrt[3]{x}}$ [1]
\item $(5x\sqrt{x})^3$ [1]
\item $\sqrt{2x^3} \times \sqrt{8x^5}$ [1]
\item $x^5(27x^6)^{\frac{1}{3}}$ [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2025 Q1 [8]}}