| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2012 |
| Session | June |
| 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 exercise with a standard follow-up question about the vertex. It requires only routine algebraic manipulation (factoring out the coefficient, completing the square) and direct recall that the vertex is at (q, r). No problem-solving or insight needed—purely procedural. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(2(x^2 - 10x) + 49\) | B1 | \(p = 2\). If \(p\), \(q\), \(r\) found correctly, then ISW slips in format. |
| \(= 2(x-5)^2 - 50 + 49\) | B1 | \((x-5)^2\). Various combinations: \(2(x-5)^2 + 1\) B1B1M0A0; \(2(x-5)-1\) B1B1M1A1 (BOD); \(2(x-5x)^2-1\) B1B0M1A0; \(2(x^2-5)^2-1\) B1B0M1A0; \(2(x+5)^2-1\) B1B0M1A1 (BOD); \(2x(x-5)^2-1\) B0B1M1A1 |
| \(= 2(x-5)^2 - 1\) | M1 | \(49 - 2q^2\) or \(\frac{49}{2} - q^2\) |
| A1 [4] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((5, -1)\) | B1 FT | ft their \(q\) (Do not allow "\(5x\)"). If restarted then B1B1 for each |
| B1 FT [2] | ft their \(r\) (Do not allow "\(-1y\)"). B0 if more than one answer given |
## Question 4(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $2(x^2 - 10x) + 49$ | B1 | $p = 2$. If $p$, $q$, $r$ found correctly, then **ISW** slips in format. |
| $= 2(x-5)^2 - 50 + 49$ | B1 | $(x-5)^2$. Various combinations: $2(x-5)^2 + 1$ **B1B1M0A0**; $2(x-5)-1$ **B1B1M1A1 (BOD)**; $2(x-5x)^2-1$ **B1B0M1A0**; $2(x^2-5)^2-1$ **B1B0M1A0**; $2(x+5)^2-1$ **B1B0M1A1 (BOD)**; $2x(x-5)^2-1$ **B0B1M1A1** |
| $= 2(x-5)^2 - 1$ | M1 | $49 - 2q^2$ or $\frac{49}{2} - q^2$ |
| | A1 [4] | |
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## Question 4(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(5, -1)$ | B1 FT | ft their $q$ (Do not allow "$5x$"). If restarted then **B1B1** for each |
| | B1 FT [2] | ft their $r$ (Do not allow "$-1y$"). **B0** if more than one answer given |
---4 (i) Express $2 x ^ { 2 } - 20 x + 49$ in the form $p ( x - q ) ^ { 2 } + r$.\\
(ii) State the coordinates of the vertex of the curve $y = 2 x ^ { 2 } - 20 x + 49$.
\hfill \mbox{\textit{OCR C1 2012 Q4 [6]}}