| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Sketch then expand or factorise |
| Difficulty | Easy -1.3 This is a straightforward algebraic manipulation question from C1 requiring only expansion of brackets and collecting like terms in part (i), and basic coefficient comparison in part (ii). Both parts are routine exercises with no problem-solving or conceptual depth required, making this easier than average for A-level. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | Attempt to expand both pairs of brackets | ISW if they then put expression equal to zero and go on to "solve" |
| A1 | \(5x^2 + 17x - 12\) and \(x^2 - 4x + 4\) soi ; may be unsimplified, no more than one incorrect term, no "extra" terms at all. No "invisible brackets" | |
| A1 | \(2x^2 + 29x - 24\) | |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | Correct method to multiply out 3 brackets or correctly identify all \(x^2\) terms | No more than 8 terms, but ignore sign errors/accuracy of non-\(x\) terms |
| A1 | All \(x^2\) terms correct, no extras | |
| A1 | ||
| [3] |
### (i)
$5x^2 + 17x - 12 - 3(x^2 - 4x + 4) = 2x^2 + 29x - 24$
| M1 | Attempt to expand both pairs of brackets | ISW if they then put expression equal to zero and go on to "solve" |
| A1 | $5x^2 + 17x - 12$ and $x^2 - 4x + 4$ soi ; may be unsimplified, no more than one incorrect term, no "extra" terms at all. No "invisible brackets" | |
| A1 | $2x^2 + 29x - 24$ | |
| [3] | | |
### (ii)
$-5x^2 + 2kx^2 + 6x^2$, $k = -2$
| M1 | Correct method to multiply out 3 brackets or correctly identify all $x^2$ terms | No more than 8 terms, but ignore sign errors/accuracy of non-$x$ terms |
| A1 | All $x^2$ terms correct, no extras | |
| A1 | | |
| [3] | | |\begin{enumerate}[label=(\roman*)]
\item Simplify $(x + 4)(5x - 3) - 3(x - 2)^2$. [3]
\item The coefficient of $x^2$ in the expansion of
$$(x + 3)(x + k)(2x - 5)$$
is $-3$. Find the value of the constant $k$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2013 Q5 [6]}}