| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | October |
| Marks | 6 |
| Topic | Discriminant and conditions for roots |
| Type | Show discriminant inequality, then solve |
| Difficulty | Moderate -0.3 This is a standard discriminant problem requiring students to rearrange to standard form, apply b²-4ac > 0 for two distinct real roots, and solve a quadratic inequality. While it involves multiple steps (rearranging, discriminant condition, factorising/solving inequality), these are routine A-level techniques with no novel insight required. Slightly easier than average due to the straightforward application of well-practiced methods. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable1.02h Express solutions: using 'and', 'or', set and interval notation |
The equation
$$(k + 3)x^2 + 6x + k = 5$$, where $k$ is a constant,
has two distinct real solutions for $x$.
\begin{enumerate}[label=(\alph*)]
\item Show that $k$ satisfies
$$k^2 - 2k - 24 < 0$$ [4]
\item Hence find the set of possible values of $k$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM 2022 Q4 [6]}}