Edexcel FP2 — Question 43 12 marks

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Marks12
PaperDownload PDF ↗
TopicModulus function
TypeSketch modulus functions involving quadratic or other non-linear
DifficultyStandard +0.3 This is a standard Further Maths modulus question requiring sketching of modulus graphs, solving equations by considering cases, and interpreting graphically. While it involves multiple steps and careful case analysis, the techniques are routine for FP2 students with no novel insight required. The algebraic manipulation is straightforward once cases are identified, making it slightly above average difficulty overall.
Spec1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function

  1. On the same diagram, sketch the graphs of \(y = |x^2 - 4|\) and \(y = |2x - 1|\), showing the coordinates of the points where the graphs meet the axes. [4]
  2. Solve \(|x^2 - 4| = |2x - 1|\), giving your answers in surd form where appropriate. [5]
  3. Hence, or otherwise, find the set of values of \(x\) for which of \(|x^2 - 4| > |2x - 1|\). [3]

\begin{enumerate}[label=(\alph*)]
\item On the same diagram, sketch the graphs of $y = |x^2 - 4|$ and $y = |2x - 1|$, showing the coordinates of the points where the graphs meet the axes. [4]

\item Solve $|x^2 - 4| = |2x - 1|$, giving your answers in surd form where appropriate. [5]

\item Hence, or otherwise, find the set of values of $x$ for which of $|x^2 - 4| > |2x - 1|$. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel FP2  Q43 [12]}}