| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Find range for no real roots |
| Difficulty | Moderate -0.8 This is a straightforward discriminant question requiring recall of b²-4ac and solving a simple quadratic inequality. The structure is highly standard with explicit prompting through parts (i) and (ii), making it easier than average but not trivial since it requires understanding the connection between discriminant sign and root existence. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Discriminant is \(k^2 - 4k\) | M1 A1 | For attempted use of the discriminant; For correct expression (in any form) |
| 2 | ||
| (ii) For no real roots, \(k^2 - 4k < 0\). Hence \(k(k-4) < 0\). So \(0 < k < 4\) | M1 M1 A1 A1 | For stating their \(\Delta < 0\); For factorising attempt (or other soln method); For both correct critical values 0 and 4 seen; For correct pair of inequalities |
| 4 |
(i) Discriminant is $k^2 - 4k$ | M1 A1 | For attempted use of the discriminant; For correct expression (in any form)
| | 2 |
(ii) For no real roots, $k^2 - 4k < 0$. Hence $k(k-4) < 0$. So $0 < k < 4$ | M1 M1 A1 A1 | For stating their $\Delta < 0$; For factorising attempt (or other soln method); For both correct critical values 0 and 4 seen; For correct pair of inequalities
| | 4 |
---3 The quadratic equation $x ^ { 2 } + k x + k = 0$ has no real roots for $x$.\\
(i) Write down the discriminant of $x ^ { 2 } + k x + k$ in terms of $k$.\\
(ii) Hence find the set of values that $k$ can take.
\hfill \mbox{\textit{OCR C1 Q3 [6]}}