| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 6 |
| 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 question with standard follow-up. Part (i) requires routine algebraic manipulation (factoring out -2, then completing the square), and part (ii) is immediate reading from the completed square form. Easier than average due to being a textbook exercise with no problem-solving element. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02e Complete the square: quadratic polynomials and turning points |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(-2(x^2 - 6x - 2)\) | B1 | or \(a = -2\) |
| \(= -2[(x-3)^2 - 2 - 9]\) | B1 | \(b = -3\) |
| M1 | \(4 + 2b^2\) | |
| \(= -2(x-3)^2 + 22\) | A1 | \(c = 22\). If \(a, b, c\) found correctly then ISW slips in format. If signs of all terms changed at start, can only score SC B1 for fully correct working to obtain \(2(x-3)^2 - 22\). If done correctly and then signs changed at end, do not ISW, award B1B1M1A0 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((3, 22)\) | B1ft | Allow follow through "– their \(b\)" |
| B1ft | Allow follow through "their \(c\)". Follow through marks are for their final answer to (i) |
## Question 6:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $-2(x^2 - 6x - 2)$ | B1 | or $a = -2$ |
| $= -2[(x-3)^2 - 2 - 9]$ | B1 | $b = -3$ |
| | M1 | $4 + 2b^2$ |
| $= -2(x-3)^2 + 22$ | A1 | $c = 22$. If $a, b, c$ found correctly then ISW slips in format. **If signs of all terms changed at start, can only score SC B1** for fully correct working to obtain $2(x-3)^2 - 22$. If done correctly and then signs changed at end, do not ISW, award B1B1M1A0 |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(3, 22)$ | B1ft | Allow follow through "– their $b$" |
| | B1ft | Allow follow through "their $c$". Follow through marks are for their final answer to (i) |
---6 (i) Express $4 + 12 x - 2 x ^ { 2 }$ in the form $a ( x + b ) ^ { 2 } + c$.\\
(ii) State the coordinates of the maximum point of the curve $y = 4 + 12 x - 2 x ^ { 2 }$.
\hfill \mbox{\textit{OCR C1 2016 Q6 [6]}}