| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2026 |
| Session | November |
| Marks | 6 |
| Topic | Indices and Surds |
| Type | Solve equations with surds |
| Difficulty | Easy -1.2 Both parts are routine algebraic manipulations requiring standard techniques. Part (i) involves simplifying surds and solving a linear equation (√18 = 3√2, then collect terms). Part (ii) requires expressing both sides as powers of 2 and equating exponents. These are textbook exercises testing basic skills with minimal problem-solving demand, making them easier than average A-level questions. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}[label=(\roman*)]
\item Solve the equation
$$x\sqrt{2} - \sqrt{18} = x$$
writing the answer as a surd in simplest form.
[3]
\item Solve the equation
$$4^{3x-2} = \frac{1}{2\sqrt{2}}$$
[3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2026 Q1 [6]}}