| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| 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 C1 question testing basic discriminant knowledge and solving a perfect square quadratic. Part (i) requires applying b²-4ac ≥ 0 with simple arithmetic, while part (ii) is a perfect square trinomial that factors easily. Both parts are routine applications of standard techniques with no problem-solving required, making this easier than average but not trivial. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown |
| Answer | Marks |
|---|---|
| 11 | (i)k ≤ 25/4 |
| (ii)−2.5 | 3 |
| 2 | M2 for 52 − 4k ≥ 0 or B2 for 25/4 |
| Answer | Marks |
|---|---|
| quadratic formula | 5 |
Question 11:
11 | (i)k ≤ 25/4
(ii)−2.5 | 3
2 | M2 for 52 − 4k ≥ 0 or B2 for 25/4
obtained isw or M1 for b2− 4ac
soi or completing square
accept −20/8 or better, isw; M1
for attempt to express quadratic
as (2x + a)2 or for attempt at
quadratic formula | 5\begin{enumerate}[label=(\roman*)]
\item Find the range of values of $k$ for which the equation $x^2 + 5x + k = 0$ has one or more real roots. [3]
\item Solve the equation $4x^2 + 20x + 25 = 0$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q11 [5]}}