| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Solving quadratics and applications |
| Type | Curve intersection leads to quadratic |
| Difficulty | Moderate -0.3 Part (i) is a routine quadratic formula application requiring completion to exact (surd) form. Part (ii) requires setting up a discriminant condition (b²-4ac=0) for tangency, which is standard C1 material but involves slightly more problem-solving than pure recall. Overall, this is a straightforward two-part question slightly easier than the typical C1 average due to its predictable structure. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown1.07m Tangents and normals: gradient and equations |
\begin{enumerate}[label=(\roman*)]
\item Find in exact form the coordinates of the points where the curve $y = x^2 - 4x + 2$ crosses the $x$-axis. [4]
\item Find the value of the constant $k$ for which the straight line $y = 2x + k$ is a tangent to the curve $y = x^2 - 4x + 2$. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR C1 Q5 [8]}}