| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Quadratic with equal roots |
| Difficulty | Moderate -0.8 Part (a) is a direct application of the discriminant condition (b²-4ac=0) requiring minimal calculation. Part (b) involves factorising a quadratic and determining the solution set of an inequality - both standard C1 procedures. This is routine bookwork with no problem-solving insight required, making it easier than average but not trivial since it tests multiple basic techniques. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks |
|---|---|
| (a) equal roots \(\therefore b^2 - 4ac = 0\) | M1 |
| \((-6)^2 - (4 \times 1 \times k) = 0\) | |
| \(36 - 4k = 0\) | |
| \(k = 9\) | A1 |
| (b) \((2x - 1)(x - 4) < 0\) | M1 |
| critical values: \(\frac{1}{2}, 4\) | A1 |
| [sketch of parabola opening upward with roots at \(\frac{1}{2}\) and \(4\)] | M1 |
| \(\frac{1}{2} < x < 4\) | A1 |
**(a)** equal roots $\therefore b^2 - 4ac = 0$ | M1 |
$(-6)^2 - (4 \times 1 \times k) = 0$ |
$36 - 4k = 0$ |
$k = 9$ | A1 |
**(b)** $(2x - 1)(x - 4) < 0$ | M1 |
critical values: $\frac{1}{2}, 4$ | A1 |
[sketch of parabola opening upward with roots at $\frac{1}{2}$ and $4$] | M1 |
$\frac{1}{2} < x < 4$ | A1 |
**Total: 6 marks**
---\begin{enumerate}[label=(\alph*)]
\item Find the value of the constant $k$ such that the equation
$$x^2 - 6x + k = 0$$
has equal roots. [2]
\item Solve the inequality
$$2x^2 - 9x + 4 < 0.$$ [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q4 [6]}}