| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2025 |
| Session | November |
| Marks | 7 |
| Topic | Indices and Surds |
| Type | Express in form with given base |
| Difficulty | Easy -1.3 This question tests basic algebraic manipulation: cube roots, index laws, and rationalizing denominators. All parts are routine procedures requiring only recall and direct application of standard techniques with no problem-solving or insight needed. Part (a) is straightforward cube root extraction, (b)(i) is simple index manipulation, and (b)(ii) is standard surds rationalization—all typical of early AS-level content. |
| Spec | 1.02a Indices: laws of indices for rational exponents1.02b Surds: manipulation and rationalising denominators |
Do not use a calculator for this question
\begin{enumerate}[label=(\alph*)]
\item Find $a$, given that $a^3 = 64x^{12}y^3$. [2]
\item
\begin{enumerate}[label=(\roman*)]
\item Express $\frac{81}{\sqrt{3}}$ in the form $3^k$. [2]
\item Express $\frac{5 + \sqrt{3}}{5 - \sqrt{3}}$ in the form $\frac{a + b\sqrt{3}}{c}$, where $a$, $b$ and $c$ are integers. [3]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2025 Q1 [7]}}