SPS SPS FM 2019 — Question 5 6 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2019
Marks6
TopicInequalities
TypeSolve absolute value inequality
DifficultyStandard +0.3 Part (a) requires squaring both sides to eliminate absolute values and solving a quadratic inequality - a standard technique. Part (b) involves rearranging a rational inequality and analyzing sign changes, which is routine for Further Maths students. Both are textbook-style exercises with clear methods, slightly above average difficulty due to the absolute value manipulation and rational inequality, but no novel insight required.
Spec1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities

Solve the following inequalities giving your answer in set notation:
  1. \(|4x + 3| < |x - 8|\) [3]
  2. \(\frac{x}{x^2+1} < \frac{1}{2}\) [3]

Solve the following inequalities giving your answer in set notation:

\begin{enumerate}[label=(\alph*)]
\item $|4x + 3| < |x - 8|$ [3]
\item $\frac{x}{x^2+1} < \frac{1}{2}$ [3]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS FM 2019 Q5 [6]}}