| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Sketch modulus functions involving quadratic or other non-linear |
| Difficulty | Standard +0.8 This is a Further Maths FP2 question requiring systematic case analysis of modulus equations and inequalities. Part (a) is routine, but parts (b) and (c) demand careful consideration of multiple cases (x² - a² positive/negative), solving resulting quadratics, and checking validity of solutions against case conditions. The algebraic manipulation is substantial and errors are easy to make, placing this moderately above average difficulty. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities |
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $y = |x^2 - a^2|$, where $a > 1$, showing the coordinates of the points where the graph meets the axes. [2]
\item Solve $|x^2 - a^2| = a^2 - x$, $a > 1$. [6]
\item Find the set of values of $x$ for which $|x^2 - a^2| > a^2 - x$, $a > 1$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q7 [12]}}