| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2023 |
| Session | June |
| Paper | Download PDF ↗ |
| Topic | Modulus function |
| Type | Solve inequality with reciprocal in modulus |
| Difficulty | Standard +0.8 This FP1 modulus inequality requires splitting into cases (x < -6 and x ≥ -6), factoring the numerator, solving quadratic inequalities in each case, and carefully combining solution sets while respecting domain restrictions. It's more demanding than standard A-level questions due to the modulus in the denominator and the multi-step case analysis, but follows a systematic approach taught in FP1. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02i Represent inequalities: graphically on coordinate plane1.02l Modulus function: notation, relations, equations and inequalities |
\begin{enumerate}
\item In this question you must show all stages of your working.
\end{enumerate}
Solutions relying entirely on calculator technology are not acceptable.
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\includegraphics[alt={},max width=\textwidth]{c0ac1e1e-16bf-4a06-9eaa-8dcf01177722-08_748_814_392_621}
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\caption{Figure 1}
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Figure 1 shows a sketch of the curve with equation $y = \frac { x ^ { 2 } - 2 x - 24 } { | x + 6 | }$\\
and the line with equation $y = 5 - 4 x$\\
Use algebra to determine the values of $x$ for which
$$\frac { x ^ { 2 } - 2 x - 24 } { | x + 6 | } < 5 - 4 x$$
\hfill \mbox{\textit{Edexcel FP1 2023 Q3}}