| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete square then find vertex/turning point |
| Difficulty | Moderate -0.8 This is a straightforward completing the square exercise with a follow-up question about the minimum value. It requires routine algebraic manipulation (factoring out the coefficient, completing the square) and direct reading of the vertex form. This is easier than average as it's a standard textbook procedure with no problem-solving or conceptual challenges beyond basic technique. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points |
**Question 1:**
B1 for $a = 5$
B1 for $b = \frac{3}{2}$ oe
B2 for $c = \frac{3}{4}$ oe
or M1 for $12 - 5 \times \left(\text{their } \frac{3}{2}\right)^2$ oe soi or for $2.4 - \left(\text{their } \frac{3}{2}\right)^2$ oe [eg $0.15$] soi
0 for $(1.5, 0.75)$
Condone omission of square symbol
eg $5\left[(x + 7.5)^2 - 7.5^2\right] + 12$ oe earns B1B0M1ft
Condone found independently eg by differentiation
Answer: $5(x + 1.5)^2 + 0.75$ oe www
$0.75$ oe or ft their $c$
[5]1 Express $5 x ^ { 2 } + 15 x + 12$ in the form $a ( x + b ) ^ { 2 } + c$.\\
Hence state the minimum value of $y$ on the curve $y = 5 x ^ { 2 } + 15 x + 12$.
\hfill \mbox{\textit{OCR MEI C1 Q1 [5]}}