| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Horizontal stretch y = f(ax) |
| Difficulty | Moderate -0.8 This is a straightforward C1 question testing basic quadratic skills: factorising/solving, sketching with intercepts, function transformations (horizontal stretch and translation). All parts use routine techniques with no problem-solving insight required, making it easier than average but not trivial due to the multi-part structure and 10 total marks. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks |
|---|---|
| (a) \((2x - 1)(x + 2) = 0\) | M1 |
| \(x = -2, \frac{1}{2}\) | A1 |
| (b) [Sketch of parabola opening upward with x-intercepts at \((-2, 0)\) and \((\frac{1}{2}, 0)\), y-intercept at \((0, -2)\)] | B2 |
| (c) \((0, -2)\), \((-4, 0), (1, 0)\) | B1 |
| [or equivalent description of intercepts] | M1 A1 |
| (d) \(f(x - 1) = 2(x - 1)^2 + 3(x - 1) - 2\) | M1 A1 |
| \(= 2x^2 - x - 3\) | |
| \(\therefore a = 2, b = -1, c = -3\) | A1 |
**(a)** $(2x - 1)(x + 2) = 0$ | M1 |
$x = -2, \frac{1}{2}$ | A1 |
**(b)** [Sketch of parabola opening upward with x-intercepts at $(-2, 0)$ and $(\frac{1}{2}, 0)$, y-intercept at $(0, -2)$] | B2 |
**(c)** $(0, -2)$, $(-4, 0), (1, 0)$ | B1 |
[or equivalent description of intercepts] | M1 A1 |
**(d)** $f(x - 1) = 2(x - 1)^2 + 3(x - 1) - 2$ | M1 A1 |
$= 2x^2 - x - 3$ |
$\therefore a = 2, b = -1, c = -3$ | A1 |
**Total: 10 marks**
---$$f(x) = 2x^2 + 3x - 2.$$
\begin{enumerate}[label=(\alph*)]
\item Solve the equation $f(x) = 0$. [2]
\item Sketch the curve with equation $y = f(x)$, showing the coordinates of any points of intersection with the coordinate axes. [2]
\item Find the coordinates of the points where the curve with equation $y = f(\frac{1}{2}x)$ crosses the coordinate axes. [3]
\end{enumerate}
When the graph of $y = f(x)$ is translated by 1 unit in the positive $x$-direction it maps onto the graph with equation $y = ax^2 + bx + c$, where $a$, $b$ and $c$ are constants.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Find the values of $a$, $b$ and $c$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q8 [10]}}