| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Discriminant for real roots condition |
| Difficulty | Moderate -0.3 This is a straightforward C1 question requiring discriminant analysis and completing the square. Part (i) is routine (discriminant = 0, one root). Part (ii) involves standard algebraic manipulation to reach the required surd form. Slightly easier than average due to the perfect square structure and clear method, but requires accurate execution across multiple steps. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown |
6.
$$f ( x ) = 4 x ^ { 2 } + 12 x + 9 .$$
(i) Determine the number of real roots that exist for the equation $\mathrm { f } ( x ) = 0$.\\
(ii) Solve the equation $\mathrm { f } ( x ) = 8$, giving your answers in the form $a + b \sqrt { 2 }$ where $a$ and $b$ are rational.\\
\hfill \mbox{\textit{OCR C1 Q6 [6]}}