| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Quadratic equation real roots |
| Difficulty | Moderate -0.3 This is a straightforward discriminant question requiring students to apply b²-4ac < 0 for no real roots, then solve a simple quadratic inequality by factorization. It's slightly easier than average as it's a standard textbook exercise with clear steps and no novel insight required. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(b^2-4ac<0\); \(b^2-4ac=q^2-4\times2q\times(-1)\) | M1 | One of \(b\) or \(a\) correct; \(<0\) not needed for M1 |
| \(q^2-4\times2q\times(-1)<0\) i.e. \(q^2+8q<0\) | A1cso | Need intermediate step; \(<0\) seen at least one line before final answer |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(q(q+8)=0\) or \((q\pm4)^2\pm16=0\) | M1 | Factorising/completing square to get 2 values |
| \(q=0\) or \(q=-8\) | A1 | Both values |
\(-8| A1ft |
Follow through CVs; must choose "inside" region; \(q<0\) and \(q>-8\) is A1 |
|
## Question 8:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $b^2-4ac<0$; $b^2-4ac=q^2-4\times2q\times(-1)$ | M1 | One of $b$ or $a$ correct; $<0$ not needed for M1 |
| $q^2-4\times2q\times(-1)<0$ i.e. $q^2+8q<0$ | A1cso | Need intermediate step; $<0$ seen at least one line before final answer |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $q(q+8)=0$ or $(q\pm4)^2\pm16=0$ | M1 | Factorising/completing square to get 2 values |
| $q=0$ or $q=-8$ | A1 | Both values |
| $-8<q<0$ | A1ft | Follow through CVs; must choose "inside" region; $q<0$ and $q>-8$ is A1 |
---Given that the equation $2 q x ^ { 2 } + q x - 1 = 0$, where $q$ is a constant, has no real roots,
\begin{enumerate}[label=(\alph*)]
\item show that $q ^ { 2 } + 8 q < 0$.
\item Hence find the set of possible values of $q$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2008 Q8 [5]}}