| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Identify transformation from equations |
| Difficulty | Standard +0.3 This is a straightforward C1 question testing basic transformation knowledge, sketching a simple rational function, and solving a quadratic equation. Part (i) is pure recall, part (ii) is routine sketching, and part (iii) involves standard algebraic manipulation leading to a quadratic with surds—all well-practiced techniques at this level with no novel problem-solving required. |
| Spec | 1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02q Use intersection points: of graphs to solve equations1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks |
|---|---|
| Translation by 1 unit in the positive \(x\)-direction | B2 |
| Answer | Marks |
|---|---|
| [Graph showing curve with vertical asymptote at \(x=1\), horizontal asymptote at \(y=0\), and point at \((0,-1)\)] | B3 |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{1}{x-1} = 2 + \frac{1}{x}\) | M1 | |
| \(x = 2x(x-1) + (x-1)\) | A1 | |
| \(2x^2 - 2x - 1 = 0\) | M1 | |
| \(x = \frac{2 \pm \sqrt{4+8}}{4}\) | M1 | |
| \(x = \frac{2 \pm 2\sqrt{3}}{4}\) | M1 | |
| \(x = \frac{1}{2} \pm \frac{1}{2}\sqrt{3}\) | A1 | (10) |
## (i)
Translation by 1 unit in the positive $x$-direction | B2 |
## (ii)
[Graph showing curve with vertical asymptote at $x=1$, horizontal asymptote at $y=0$, and point at $(0,-1)$] | B3 |
## (iii)
$\frac{1}{x-1} = 2 + \frac{1}{x}$ | M1 |
$x = 2x(x-1) + (x-1)$ | A1 |
$2x^2 - 2x - 1 = 0$ | M1 |
$x = \frac{2 \pm \sqrt{4+8}}{4}$ | M1 |
$x = \frac{2 \pm 2\sqrt{3}}{4}$ | M1 |
$x = \frac{1}{2} \pm \frac{1}{2}\sqrt{3}$ | A1 | (10) |
---\begin{enumerate}[label=(\roman*)]
\item Describe fully the single transformation that maps the graph of $y = f(x)$ onto the graph of $y = f(x - 1)$. [2]
\item Showing the coordinates of any points of intersection with the coordinate axes and the equations of any asymptotes, sketch the graph of $y = \frac{1}{x-1}$. [3]
\item Find the $x$-coordinates of any points where the graph of $y = \frac{1}{x-1}$ intersects the graph of $y = 2 + \frac{1}{x}$. Give your answers in the form $a + b\sqrt{3}$, where $a$ and $b$ are rational. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 Q7 [10]}}