| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete the square |
| Difficulty | Moderate -0.8 This is a straightforward completing-the-square question with standard follow-up parts about symmetry and tangent at the vertex. All parts are routine C1 exercises requiring only direct application of learned techniques with no problem-solving or insight needed. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(2(x^2 - 12x + 40)\) | B1 | \(a = 2\) |
| \(= 2[(x-6)^2 - 36 + 40]\) | B1 | \(b = 6\) |
| \(= 2[(x-6)^2 + 4]\) | M1 | \(80 - 2b^2\) or \(40 - b^2\) or \(80 - b^2\) or \(40 - 2b^2\) (their \(b\)) |
| \(= 2(x-6)^2 + 8\) | A1 [4] | \(c = 8\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(x = 6\) | B1 ft [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(y = 8\) | B1 ft [1+1+1=6] |
## Question 6:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $2(x^2 - 12x + 40)$ | B1 | $a = 2$ |
| $= 2[(x-6)^2 - 36 + 40]$ | B1 | $b = 6$ |
| $= 2[(x-6)^2 + 4]$ | M1 | $80 - 2b^2$ or $40 - b^2$ or $80 - b^2$ or $40 - 2b^2$ (their $b$) |
| $= 2(x-6)^2 + 8$ | A1 [4] | $c = 8$ |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $x = 6$ | B1 ft [1] | |
### Part (iii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $y = 8$ | B1 ft [1+1+1=6] | |
---6 (i) Express $2 x ^ { 2 } - 24 x + 80$ in the form $a ( x - b ) ^ { 2 } + c$.\\
(ii) State the equation of the line of symmetry of the curve $y = 2 x ^ { 2 } - 24 x + 80$.\\
(iii) State the equation of the tangent to the curve $y = 2 x ^ { 2 } - 24 x + 80$ at its minimum point.
\hfill \mbox{\textit{OCR C1 2007 Q6 [6]}}