| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Discriminant and conditions for roots |
| Type | Find k for equal roots |
| Difficulty | Moderate -0.8 This is a straightforward discriminant question requiring recall of b²-4ac and setting it equal to zero for equal roots. The algebra is simple (16-4k²=0 gives k=±2), making it easier than average but not trivial since it requires knowing the equal roots condition and solving a basic quadratic equation. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions |
| Answer | Marks | Guidance |
|---|---|---|
| \((-4)^2 - 4 \times k \times k\) | M1 | Uses \(b^2 - 4ac\) (involving \(k\)) |
| \(= 16 - 4k^2\) | A1 (2) |
| Answer | Marks | Guidance |
|---|---|---|
| \(16 - 4k^2 = 0\) | M1 | Attempts \(b^2 - 4ac = 0\) (involving \(k\)) or attempts to complete square (involving \(k\)) |
| \(k^2 = 4\), \(k = 2\) or \(k = -2\) | B1, B1 (3) |
# Question 4:
**(i)**
$(-4)^2 - 4 \times k \times k$ | M1 | Uses $b^2 - 4ac$ (involving $k$)
$= 16 - 4k^2$ | A1 (2) |
**(ii)**
$16 - 4k^2 = 0$ | M1 | Attempts $b^2 - 4ac = 0$ (involving $k$) or attempts to complete square (involving $k$)
$k^2 = 4$, $k = 2$ or $k = -2$ | B1, B1 (3) |
---4 (i) Find the discriminant of $k x ^ { 2 } - 4 x + k$ in terms of $k$.\\
(ii) The quadratic equation $k x ^ { 2 } - 4 x + k = 0$ has equal roots. Find the possible values of $k$
\hfill \mbox{\textit{OCR C1 2007 Q4 [5]}}