SPS SPS FM Pure 2023 November — Question 1 6 marks

Exam BoardSPS
ModuleSPS FM Pure (SPS FM Pure)
Year2023
SessionNovember
Marks6
TopicIndices and Surds
TypeSolve equations with surds
DifficultyModerate -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.
Spec1.02b Surds: manipulation and rationalising denominators1.06g Equations with exponentials: solve a^x = b

  1. (i) Solve the equation
$$x \sqrt { 2 } - \sqrt { 18 } = x$$ writing the answer as a surd in simplest form.
(ii) Solve the equation $$4 ^ { 3 x - 2 } = \frac { 1 } { 2 \sqrt { 2 } }$$

\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]}}