| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2023 |
| Session | November |
| Marks | 6 |
| Topic | Indices and Surds |
| Type | Solve equations with surds |
| Difficulty | Moderate -0.8 Part (i) requires basic algebraic manipulation and simplifying surds (√18 = 3√2), then solving a linear equation. Part (ii) involves expressing both sides as powers of 2 and equating exponents. Both are routine procedural questions testing fundamental skills with no problem-solving insight required, making this easier than average but not trivial. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.06g Equations with exponentials: solve a^x = b |
\begin{enumerate}
\item (i) Solve the equation
\end{enumerate}
$$x \sqrt { 2 } - \sqrt { 18 } = x$$
writing the answer as a surd in simplest form.\\
(ii) Solve the equation
$$4 ^ { 3 x - 2 } = \frac { 1 } { 2 \sqrt { 2 } }$$
\hfill \mbox{\textit{SPS SPS FM Pure 2023 Q1 [6]}}