| Exam Board | AQA |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2005 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conic sections |
| Type | Parametric point verification |
| Difficulty | Standard +0.3 This is a straightforward hyperbola question requiring identification of an x-intercept (trivial substitution y=0) and finding a point on the curve given a gradient constraint. Part (b) involves simultaneous equations with a linear equation and the hyperbola equation, which is standard FP1 technique with no novel insight required. Slightly easier than average due to the direct nature of both parts. |
| Spec | 1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks | Guidance |
|---|---|---|
| \(P\) is \((2, 0)\) | B1 | 1 mark |
| Answer | Marks | Guidance |
|---|---|---|
| \(PQ\) is \(y = 2(x-2)\); Elimination of \(y\) (or of \(x\)); \((x-2)(5x-22) = 0\); \(Q\) is \((4.4, 4.8)\) | M1A1F, m1A1F, A1A1 | 7 marks |
**Part (a)**
| $P$ is $(2, 0)$ | B1 | 1 mark | — |
**Part (b)**
| $PQ$ is $y = 2(x-2)$; Elimination of $y$ (or of $x$); $(x-2)(5x-22) = 0$; $Q$ is $(4.4, 4.8)$ | M1A1F, m1A1F, A1A1 | 7 marks | ft wrong value for $x_P$; ft numerical error |
**Total: 8 marks**
---8 The diagram shows a part of the curve
$$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 6 } = 1$$
and a chord $P Q$ of the curve, where $P$ lies on the $x$-axis.\\
\includegraphics[max width=\textwidth, alt={}, center]{5bfb4d19-8772-43d7-b667-bd124d2504a8-05_751_1072_680_459}
\begin{enumerate}[label=(\alph*)]
\item Write down the coordinates of $P$.
\item The gradient of the chord $P Q$ is 2 . Find the coordinates of $Q$.
\end{enumerate}
\hfill \mbox{\textit{AQA FP1 2005 Q8 [8]}}