| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2010 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Expand from factored form |
| Difficulty | Moderate -0.8 This is a straightforward C1 question requiring routine algebraic expansion and basic curve sketching from factored form. The sketch only needs identification of roots and general shape (repeated root at x=-1, simple root at x=2.5), while the expansion is mechanical algebra with no problem-solving required. Both parts are standard textbook exercises below average A-level difficulty. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Cubic correct way up and with two turning points | B1 | |
| Touching \(x\)-axis at \(-1\), and through it at \(2.5\) and no other intersections | B1 | Intersections must be shown labelled or worked out nearby |
| \(y\)-axis intersection at \(-5\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(2x^3 - x^2 - 8x - 5\) | 2 | B1 for 3 terms correct or M1 for correct expansion of product of two of the given factors |
## Question 6(i):
| Answer | Mark | Guidance |
|--------|------|----------|
| Cubic correct way up and with two turning points | B1 | |
| Touching $x$-axis at $-1$, and through it at $2.5$ and no other intersections | B1 | Intersections must be shown labelled or worked out nearby |
| $y$-axis intersection at $-5$ | B1 | |
## Question 6(ii):
| Answer | Mark | Guidance |
|--------|------|----------|
| $2x^3 - x^2 - 8x - 5$ | 2 | B1 for 3 terms correct or M1 for correct expansion of product of two of the given factors |6 You are given that $\mathrm { f } ( x ) = ( x + 1 ) ^ { 2 } ( 2 x - 5 )$.\\
(i) Sketch the graph of $y = \mathrm { f } ( x )$.\\
(ii) Express $\mathrm { f } ( x )$ in the form $a x ^ { 3 } + b x ^ { 2 } + c x + d$.
\hfill \mbox{\textit{OCR MEI C1 2010 Q6 [5]}}