| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete square then solve equation |
| Difficulty | Moderate -0.3 This is a straightforward completing the square question with two parts: (i) requires algebraic manipulation with a parameter k to find roots in general form, (ii) applies the result by substituting k=3. Both parts are standard C1 techniques with no novel insight required, making it slightly easier than average but not trivial since it involves working with a parameter. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown |
4. (i) By completing the square, find in terms of the constant $k$ the roots of the equation
$$x ^ { 2 } + 2 k x + 4 = 0 .$$
(ii) Hence find the exact roots of the equation
$$x ^ { 2 } + 6 x + 4 = 0 .$$
\hfill \mbox{\textit{OCR C1 Q4 [6]}}