| Exam Board | AQA |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2006 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conic sections |
| Type | Conic translation and transformation |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question on conic transformations. Part (a) requires recognizing a simple stretch (factor 1/2 in y-direction). Part (b) involves completing the square to identify a translation, both standard FP1 techniques requiring minimal problem-solving beyond applying learned procedures. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| Stretch parallel to \(y\) axis... | B1 | |
| ...scale-factor \(\frac{1}{2}\) parallel to \(y\) axis | B1 (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Marks | Guidance |
| \((x-2)^2 - y^2 = 1\) | M1A1 | |
| Translation in \(x\) direction... | A1 | |
| ...2 units in positive \(x\) direction | A1 (4) |
## Question 7:
### Part (a)
| Working | Marks | Guidance |
|---------|-------|----------|
| Stretch parallel to $y$ axis... | B1 | |
| ...scale-factor $\frac{1}{2}$ parallel to $y$ axis | B1 (2) | |
### Part (b)
| Working | Marks | Guidance |
|---------|-------|----------|
| $(x-2)^2 - y^2 = 1$ | M1A1 | |
| Translation in $x$ direction... | A1 | |
| ...2 units in positive $x$ direction | A1 (4) | |
---7
\begin{enumerate}[label=(\alph*)]
\item Describe a geometrical transformation by which the hyperbola
$$x ^ { 2 } - 4 y ^ { 2 } = 1$$
can be obtained from the hyperbola $x ^ { 2 } - y ^ { 2 } = 1$.
\item The diagram shows the hyperbola $H$ with equation
$$x ^ { 2 } - y ^ { 2 } - 4 x + 3 = 0$$
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{e44987a7-2cdf-442a-aecb-abd3e889ecd4-4_951_1216_824_402}
\end{center}
By completing the square, describe a geometrical transformation by which the hyperbola $H$ can be obtained from the hyperbola $x ^ { 2 } - y ^ { 2 } = 1$.
\end{enumerate}
\hfill \mbox{\textit{AQA FP1 2006 Q7 [6]}}