| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Horizontal translation of factored polynomial |
| Difficulty | Moderate -0.3 Part (i) is a standard C1 curve sketching exercise requiring finding roots and y-intercept, then sketching a cubic with negative leading coefficient—routine but requires careful execution. Part (ii) asks for a transformation between two cubics, which requires recognizing the pattern f(x) → f(-x) (reflection in y-axis), slightly elevating this above a completely routine question but still well within typical C1 scope. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| B1 | -ve cubic with 3 distinct roots | Must not stop at x-axis. Condone errors in curvature at the extremes unless extra turning point(s)/root(s) clearly implied. Must have a curve for 2nd and 3rd marks |
| B1 | (0, 6) labelled or indicated on y-axis – seen elsewhere not enough | |
| B1 | (-3, 0), (-1, 0) and (2, 0) labelled or indicated on x-axis and no other x-intercepts | Do not allow final B1 if shown as repeated root(s) |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| B1 | Not mirrored/flipped etc. | Alt Stretch (scale) factor –1 B1 parallel to the x axis for B1 |
| B1 | or \(x = 0\) | Must be a single transformation for any marks |
| [2] |
### (i)
Cubic graph with 3 distinct roots, (0, 6) labelled or indicated on y-axis, (-3, 0), (-1, 0) and (2, 0) labelled or indicated on x-axis and no other x-intercepts
| B1 | -ve cubic with 3 distinct roots | Must not stop at x-axis. Condone errors in curvature at the extremes unless extra turning point(s)/root(s) clearly implied. Must have a curve for 2nd and 3rd marks |
| B1 | (0, 6) labelled or indicated on y-axis – seen elsewhere not enough | |
| B1 | (-3, 0), (-1, 0) and (2, 0) labelled or indicated on x-axis and no other x-intercepts | Do not allow final B1 if shown as repeated root(s) |
| [3] | | |
### (ii)
Reflection in the y-axis or $x = 0$. No/through/along etc. Must be "in". Cannot get 2nd B1 without some indication of a reflection e.g. flip etc. Do not ISW if contradictory statement seen
| B1 | Not mirrored/flipped etc. | Alt Stretch (scale) factor –1 B1 parallel to the x axis for B1 |
| B1 | or $x = 0$ | Must be a single transformation for any marks |
| [2] | | |\begin{enumerate}[label=(\roman*)]
\item Sketch the curve $y = (1 + x)(2 - x)(3 + x)$, giving the coordinates of all points of intersection with the axes. [3]
\item Describe the transformation that transforms the curve $y = (1 + x)(2 - x)(3 + x)$ to the curve $y = (1 - x)(2 + x)(3 - x)$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2013 Q3 [5]}}