| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Polynomial intersection with algebra |
| Difficulty | Challenging +1.2 This AEA question requires sketching two curves (one involving modulus) and finding intersections algebraically by considering cases for |x|. While it demands careful case analysis and solving resulting equations, the techniques are standard A-level methods applied systematically rather than requiring novel insight. The modulus function and intersection finding are within core A-level scope, making this moderately above average but not exceptionally challenging for AEA. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02n Sketch curves: simple equations including polynomials1.02q Use intersection points: of graphs to solve equations |
\begin{enumerate}
\item (a) On the same diagram, sketch
\end{enumerate}
$$y = ( x + 1 ) ( 2 - x ) \quad \text { and } \quad y = x ^ { 2 } - 2 | x |$$
Mark clearly the coordinates of the points where these curves cross the coordinate axes.\\
(b) Find the $x$-coordinates of the points of intersection of these two curves.\\
\hfill \mbox{\textit{Edexcel AEA 2009 Q1 [8]}}