| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2014 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch then solve related equations |
| Difficulty | Standard +0.8 This AEA question requires systematic handling of absolute value functions across multiple parts, including the non-trivial case where |x| appears in different terms. Part (a)(iii) and part (b) require careful case analysis (x≥0 vs x<0) and algebraic manipulation beyond standard A-level. While methodical, the multi-step reasoning and need to handle piecewise definitions elevates this above typical curve sketching questions. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02s Modulus graphs: sketch graph of |ax+b|1.02t Solve modulus equations: graphically with modulus function |
(a) On separate diagrams sketch the curves with the following equations. On each sketch you should mark the coordinates of the points where the curve crosses the coordinate axes.
\begin{enumerate}[label=(\roman*)]
\item $y = x^2 - 2x - 3$
\item $y = x^2 - 2|x| - 3$
\item $y = x^2 - x - |x| - 3$
\end{enumerate}
[7]
(b) Solve the equation
$$x^2 - x - |x| - 3 = x + |x|$$
[4]
\hfill \mbox{\textit{Edexcel AEA 2014 Q3 [11]}}