| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Quadratic with surd roots, exact form |
| Difficulty | Moderate -0.8 This is a straightforward two-part question testing basic quadratic formula application and simple differentiation. Part (i) requires routine use of the quadratic formula with minimal algebraic manipulation to simplify surds. Part (ii) is a standard differentiation exercise requiring only the power rule and substitution. Both parts are mechanical procedures with no problem-solving or conceptual challenge, making this easier than the average A-level question. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.07i Differentiate x^n: for rational n and sums |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | Valid attempt to use quadratic formula | No marks for attempting to factorise |
| A1 | Both roots correct and simplified | Must get to \((x-3)\) and \(\pm\) stage for the M mark, constants combined correctly gets A1 |
| A1 | Rearranged to correct form (cao) | |
| [3] |
| Answer | Marks |
|---|---|
| B1 | |
| B1 | www |
| [2] |
### (i)
$6 \pm \sqrt{(-6)^2 - 4 \times 1 \times -2} / 2 \times 1 = 6 \pm \sqrt{44} / 2 = 3 \pm \sqrt{11}$
OR: $(x-3)^2 - 9 - 2 = 0$, $x - 3 = \pm\sqrt{11}$, $x = 3 \pm \sqrt{11}$
| M1 | Valid attempt to use quadratic formula | No marks for attempting to factorise |
| A1 | Both roots correct and simplified | Must get to $(x-3)$ and $\pm$ stage for the M mark, constants combined correctly gets A1 |
| A1 | Rearranged to correct form (cao) | |
| [3] | | |
### (ii)
$\frac{dy}{dx} = 2x - 6 = -16$
| B1 | | |
| B1 | www | |
| [2] | | |\begin{enumerate}[label=(\roman*)]
\item Solve the equation $x^2 - 6x - 2 = 0$, giving your answers in simplified surd form. [3]
\item Find the gradient of the curve $y = x^2 - 6x - 2$ at the point where $x = -5$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 2013 Q1 [5]}}