| Exam Board | AQA |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch rational function from transformation |
| Difficulty | Moderate -0.3 This is a straightforward FP1 transformation question requiring identification of a translation vector, finding asymptotes by inspection, calculating axis intercepts (simple algebra), and sketching a transformed reciprocal function. All steps are routine applications of standard techniques with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Curve translated 7 in y direction; ... and 1 in negative x direction | B1, B1 | 2 marks |
| (b)(i) Asymptotes \(x = -1\) and \(y = 7\) | B1B1 | 2 marks |
| (b)(ii) Intersections at \((0, 8)\) ...; ... and \((-\frac{8}{7}, 0)\) | B1, M1A1 | 3 marks |
| (c) At least one branch; Complete graph; All correct including asymptotes | B1, B1, B1 | 3 marks |
**(a)** Curve translated 7 in y direction; ... and 1 in negative x direction | B1, B1 | 2 marks | or answer in vector form
**(b)(i)** Asymptotes $x = -1$ and $y = 7$ | B1B1 | 2 marks |
**(b)(ii)** Intersections at $(0, 8)$ ...; ... and $(-\frac{8}{7}, 0)$ | B1, M1A1 | 3 marks | Allow AWRT $-1.14$; NMS 1/2
**(c)** At least one branch; Complete graph; All correct including asymptotes | B1, B1, B1 | 3 marks | of correct shape; translation of $y = 1/x$; in roughly correct positions
**Total: 10 marks**7 A curve $C$ has equation
$$y = 7 + \frac { 1 } { x + 1 }$$
\begin{enumerate}[label=(\alph*)]
\item Define the translation which transforms the curve with equation $y = \frac { 1 } { x }$ onto the curve $C$.
\item \begin{enumerate}[label=(\roman*)]
\item Write down the equations of the two asymptotes of $C$.
\item Find the coordinates of the points where the curve $C$ intersects the coordinate axes.
\end{enumerate}\item Sketch the curve $C$ and its two asymptotes.
\end{enumerate}
\hfill \mbox{\textit{AQA FP1 2008 Q7 [10]}}