| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2011 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch modulus functions involving quadratic or other non-linear |
| Difficulty | Moderate -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. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function |
\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]}}