| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | October |
| Marks | 6 |
| Topic | Indices and Surds |
| Type | Solve equations with surds |
| Difficulty | Easy -1.2 Part (i) requires basic algebraic manipulation and simplifying surds (recognizing √18 = 3√2), which is routine GCSE/early A-level content. Part (ii) involves expressing both sides as powers of 2 and equating exponents, a standard index laws exercise. Both parts are straightforward applications of fundamental techniques with no problem-solving insight required, making this easier than average A-level questions. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.06a Exponential function: a^x and e^x graphs and properties1.06g Equations with exponentials: solve a^x = b |
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
\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 SM 2022 Q6 [6]}}