| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 9 |
| 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 with standard parts: (a) requires identifying a simple vertical stretch transformation, (b) is routine sketching with asymptote identification, and (c) involves setting up a tangency condition (discriminant = 0) which is a standard technique. The question requires multiple steps but uses well-practiced methods without requiring novel insight or complex problem-solving. |
| Spec | 1.02o Sketch reciprocal curves: y=a/x and y=a/x^21.02w Graph transformations: simple transformations of f(x)1.07m Tangents and normals: gradient and equations |
| Answer | Marks |
|---|---|
| or stretch by factor of 3 in x-direction about y-axis | B2 |
| (b) asymptotes: \(x = 0\) and \(y = 0\) | B2 |
| B1 |
| Answer | Marks |
|---|---|
| \(3x^2 - cx + 3 = 0\) | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(c^2 = 36\), \(c = \pm 6\) | M1 A1 | (9 marks) |
(a) stretch by factor of 3 in y-direction about x-axis
or stretch by factor of 3 in x-direction about y-axis | B2 |
(b) asymptotes: $x = 0$ and $y = 0$ | B2 |
| B1 |
(c) $\frac{3}{x} = c - 3x$
$3 = cx - 3x^2$
$3x^2 - cx + 3 = 0$ | M1 |
tangent $\therefore$ equal roots, $b^2 - 4ac = 0$
$(-c)^2 - (4 \times 3 \times 3) = 0$
$c^2 = 36$, $c = \pm 6$ | M1 A1 | (9 marks)\begin{enumerate}[label=(\alph*)]
\item Describe fully a single transformation that maps the graph of $y = \frac{1}{x}$ onto the graph of $y = \frac{3}{x}$. [2]
\item Sketch the graph of $y = \frac{3}{x}$ and write down the equations of any asymptotes. [3]
\item Find the values of the constant $c$ for which the straight line $y = c - 3x$ is a tangent to the curve $y = \frac{3}{x}$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q7 [9]}}