| Exam Board | AQA |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2018 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Find range for two distinct roots |
| Difficulty | Standard +0.3 This question requires understanding that a quadratic with two distinct positive roots must have: discriminant > 0, positive sum of roots (automatically satisfied), and positive product of roots. Students must apply b²-4ac > 0 giving k < 9, and αβ = k > 0. While it involves multiple conditions, these are standard A-level techniques with straightforward algebra, making it slightly easier than average. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable1.02n Sketch curves: simple equations including polynomials |
A curve, C, has equation $y = x^2 - 6x + k$, where $k$ is a constant.
The equation $x^2 - 6x + k = 0$ has two distinct positive roots.
\begin{enumerate}[label=(\alph*)]
\item Sketch C on the axes below.
[2 marks]
\item Find the range of possible values for $k$.
Fully justify your answer.
[4 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 2 2018 Q4 [6]}}