| Exam Board | AQA |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2005 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Show discriminant inequality, then solve |
| Difficulty | Standard +0.3 This is a standard discriminant question with algebraic manipulation. Part (a) is routine simplification, part (b)(i) requires setting b²-4ac≥0 and factorizing (guided by 'show that'), and part (b)(ii) involves solving a quadratic inequality—all well-practiced C1 techniques with no novel insight required. Slightly above average due to the multi-step algebra and inequality solving. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions |
| Answer | Marks |
|---|---|
| Total: 10 |
| | **Total: 10**
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# TOTAL: 757
\begin{enumerate}[label=(\alph*)]
\item Simplify $( k + 5 ) ^ { 2 } - 12 k ( k + 2 )$.
\item The quadratic equation $3 ( k + 2 ) x ^ { 2 } + ( k + 5 ) x + k = 0$ has real roots.
\begin{enumerate}[label=(\roman*)]
\item Show that $( k - 1 ) ( 11 k + 25 ) \leqslant 0$.
\item Hence find the possible values of $k$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA C1 2005 Q7 [10]}}