| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2014 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Line tangent to curve, find k for tangency |
| Difficulty | Moderate -0.5 This is a straightforward C1 question testing standard techniques: discriminant calculation, completing the square, and finding a tangent parameter by setting discriminant to zero. All methods are routine with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown |
11. Given that
$$f ( x ) = 2 x ^ { 2 } + 8 x + 3$$
\begin{enumerate}[label=(\alph*)]
\item find the value of the discriminant of $\mathrm { f } ( x )$.
\item Express $\mathrm { f } ( x )$ in the form $p ( x + q ) ^ { 2 } + r$ where $p , q$ and $r$ are integers to be found.
The line $y = 4 x + c$, where $c$ is a constant, is a tangent to the curve with equation $y = \mathrm { f } ( x )$.
\item Calculate the value of $c$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2014 Q11 [10]}}