AQA C3 2011 June — Question 7 12 marks

Exam BoardAQA
ModuleC3 (Core Mathematics 3)
Year2011
SessionJune
Marks12
PaperDownload PDF ↗
TopicModulus function
TypeSketch modulus functions involving quadratic or other non-linear
DifficultyModerate -0.3 This is a standard modulus question testing routine techniques: sketching basic modulus graphs (linear and quadratic), solving modulus equations by considering cases, and interpreting solutions graphically for an inequality. While it requires multiple steps (12 marks total), each component follows textbook methods with no novel insight needed. Slightly easier than average due to the straightforward nature of the functions involved.
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

  1. On separate diagrams:
    1. sketch the curve with equation \(y = |3x + 3|\); [2]
    2. sketch the curve with equation \(y = |x^2 - 1|\). [3]
    1. Solve the equation \(|3x + 3| = |x^2 - 1|\). [5]
    2. Hence solve the inequality \(|3x + 3| < |x^2 - 1|\). [2]

\begin{enumerate}[label=(\alph*)]
\item On separate diagrams:
\begin{enumerate}[label=(\roman*)]
\item sketch the curve with equation $y = |3x + 3|$; [2]

\item sketch the curve with equation $y = |x^2 - 1|$. [3]
\end{enumerate}

\item \begin{enumerate}[label=(\roman*)]
\item Solve the equation $|3x + 3| = |x^2 - 1|$. [5]

\item Hence solve the inequality $|3x + 3| < |x^2 - 1|$. [2]
\end{enumerate}
\end{enumerate}

\hfill \mbox{\textit{AQA C3 2011 Q7 [12]}}