| Exam Board | AQA |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Year | 2009 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch y=|f(x)| or y=f(|x|) for non-linear f(x) and solve |
| Difficulty | Standard +0.3 This is a straightforward modulus question requiring standard techniques: sketching a reflected parabola, solving by cases (50-x²=±14), reading off inequality solutions from the graph, and describing simple transformations. All steps are routine C3 material with no novel problem-solving required, making it slightly easier than average. |
| 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 function1.02w Graph transformations: simple transformations of f(x) |
4
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = \left| 50 - x ^ { 2 } \right|$, indicating the coordinates of the point where the graph crosses the $y$-axis.
\item Solve the equation $\left| 50 - x ^ { 2 } \right| = 14$.
\item Hence, or otherwise, solve the inequality $\left| 50 - x ^ { 2 } \right| > 14$.
\item Describe a sequence of two geometrical transformations that maps the graph of $y = x ^ { 2 }$ onto the graph of $y = 50 - x ^ { 2 }$.
\end{enumerate}
\hfill \mbox{\textit{AQA C3 2009 Q4 [12]}}