| Exam Board | OCR MEI |
|---|---|
| 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 -0.8 Part (i) is a standard curve sketching exercise requiring identification of roots and their multiplicities from factored form. Part (ii) tests understanding of horizontal translations by requiring students to solve (x+5)²(x)=0, which is straightforward substitution. Both parts are routine applications of basic concepts with no problem-solving insight required. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Sketch of cubic the right way up, with two turning points | B1 | No section to be ruled; no curving back; condone some curving out at ends but not approaching another turning point; condone some doubling (e.g. erased curves may continue to show); ignore position of turning points for this mark |
| Their graph touching the \(x\)-axis at \(-2\) and crossing it at \(3\) and no other places | B1 | If intercepts are not labelled, they must be shown nearby. Mark intent if 'daylight' between curve and axis at \(x = -2\) |
| Intersection of \(y\)-axis at \(-12\) | B1 | If no graph but \(-12\) marked on \(y\)-axis, or in table, allow this 3rd mark |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(-5\) and \(0\) | B2 | B1 each; allow B2 for \(-5, -5, 0\); B1 for both correct with one extra value or for \((-5, 0)\) and \((0, 0)\). Or SC1 for both of \(1\) and \(6\). If their graph wrong, allow \(-5\) and \(0\) from starting again with equation, or ft their graph with two intercepts with \(x\)-axis |
| [2] |
## Question 9(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Sketch of cubic the right way up, with two turning points | B1 | No section to be ruled; no curving back; condone some curving out at ends but not approaching another turning point; condone some doubling (e.g. erased curves may continue to show); ignore position of turning points for this mark |
| Their graph touching the $x$-axis at $-2$ and crossing it at $3$ and no other places | B1 | If intercepts are not labelled, they must be shown nearby. Mark intent if 'daylight' between curve and axis at $x = -2$ |
| Intersection of $y$-axis at $-12$ | B1 | If no graph but $-12$ marked on $y$-axis, or in table, allow this 3rd mark |
| **[3]** | | |
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## Question 9(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $-5$ and $0$ | B2 | B1 each; allow B2 for $-5, -5, 0$; B1 for both correct with one extra value or for $(-5, 0)$ and $(0, 0)$. Or SC1 for both of $1$ and $6$. If their graph wrong, allow $-5$ and $0$ from starting again with equation, or ft their graph with two intercepts with $x$-axis |
| **[2]** | | |9 You are given that $\mathrm { f } ( x ) = ( x + 2 ) ^ { 2 } ( x - 3 )$.\\
(i) Sketch the graph of $y = \mathrm { f } ( x )$.\\
(ii) State the values of $x$ which satisfy $\mathrm { f } ( x + 3 ) = 0$.
\hfill \mbox{\textit{OCR MEI C1 2013 Q9 [5]}}