| Exam Board | AQA |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Solve f(x) > g(x) using sketch |
| Difficulty | Standard +0.3 This is a straightforward FP1 question testing standard techniques: identifying asymptotes from a rational function, evaluating a point, sketching a curve with given features, and solving a rational inequality. All parts are routine applications of A-level methods with no novel insight required. The inequality in part (c) requires careful sign analysis but follows standard procedures. Slightly above average difficulty due to the multi-step inequality and being FP1 content, but still a textbook-style question. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02n Sketch curves: simple equations including polynomials1.07a Derivative as gradient: of tangent to curve1.07n Stationary points: find maxima, minima using derivatives |
A curve $C$ has equation $y = \frac{1}{x(x + 2)}$.
\begin{enumerate}[label=(\alph*)]
\item Write down the equations of all the asymptotes of $C$. [2 marks]
\item The curve $C$ has exactly one stationary point. The $x$-coordinate of the stationary point is $-1$.
\begin{enumerate}[label=(\roman*)]
\item Find the $y$-coordinate of the stationary point. [1 mark]
\item Sketch the curve $C$. [2 marks]
\end{enumerate}
\item Solve the inequality
$$\frac{1}{x(x + 2)} \leqslant \frac{1}{8}$$
[5 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA FP1 2014 Q6 [10]}}