| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2017 |
| Session | Specimen |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch y=|f(x)| or y=f(|x|) for non-linear f(x) and solve |
| Difficulty | Challenging +1.8 This question requires systematic understanding of modulus transformations and their graphical effects, followed by solving an equation involving nested modulus functions. Part (a) demands careful analysis of how |x| affects the graph structure (creating even/odd function components), while part (b) requires case-by-case algebraic reasoning to solve the nested modulus equation. The multi-step nature, need for geometric insight into modulus transformations, and algebraic manipulation of nested absolute values elevates this significantly above standard A-level fare, though it remains accessible to strong students with systematic approach. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02n Sketch curves: simple equations including polynomials1.02s Modulus graphs: sketch graph of |ax+b| |
2.(a)On separate diagrams,sketch the curves with the following equations.On each sketch you should label the exact coordinates of the points where the curve meets the coordinate axes.
\begin{enumerate}[label=(\roman*)]
\item $y = 8 + 2 x - x ^ { 2 }$
\item $y = 8 + 2 | x | - x ^ { 2 }$
\item $y = 8 + x + | x | - x ^ { 2 }$\\
(b)Find the values of $x$ for which
$$\left| 8 + x + | x | - x ^ { 2 } \right| = 8 + 2 | x | - x ^ { 2 }$$
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2017 Q2 [11]}}