SPS SPS FM 2024 February — Question 2 6 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2024
SessionFebruary
Marks6
TopicModulus function
TypeInterpret or complete given sketch of two |linear| functions
DifficultyModerate -0.8 This is a straightforward modulus equation requiring students to consider cases where expressions inside the modulus are positive or negative. Part (a) is trivial coordinate finding (intercepts), and part (b) involves standard case-by-case analysis or squaring both sides—a routine technique covered early in Further Maths with no novel problem-solving required.
Spec1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function

2. The diagram below shows the graphs of \(y = | 3 x - 2 |\) and \(y = | 2 x + 1 |\).
  1. \includegraphics[max width=\textwidth, alt={}, center]{4e1bb995-ce3d-4d16-a0a2-72383489ffe1-06_318_511_187_904} Give the coordinates of the points of intersection of the graphs with the coordinate axes.
  2. Solve the equation \(| 2 x + 1 | = | 3 x - 2 |\).
    [0pt]

2.

The diagram below shows the graphs of $y = | 3 x - 2 |$ and $y = | 2 x + 1 |$.
\begin{enumerate}[label=(\alph*)]
\item \\
\includegraphics[max width=\textwidth, alt={}, center]{4e1bb995-ce3d-4d16-a0a2-72383489ffe1-06_318_511_187_904}

Give the coordinates of the points of intersection of the graphs with the coordinate axes.
\item Solve the equation $| 2 x + 1 | = | 3 x - 2 |$.\\[0pt]

\end{enumerate}

\hfill \mbox{\textit{SPS SPS FM 2024 Q2 [6]}}