| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2016 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Completing the square and sketching |
| Type | Complete the square |
| Difficulty | Easy -1.2 This is a straightforward algebraic manipulation question testing basic expansion and simplification skills. Part (i) requires expanding two squared brackets and collecting like terms, while part (ii) involves identifying which term products give x³ - both are routine C1 exercises with no problem-solving or conceptual depth required. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(4x^2 - 12x + 9 - 2(9 - 6x + x^2)\) | M1 | Square to get at least one 3/4 term quadratic |
| \(2x^2 - 9\) | A1 | Fully correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(-6x^3\) or \(-4x^3\) | B1 | \(-6x^3\) or \(-4x^3\) soi www in these terms; ignore other terms |
| \(-10\) | B1 | Condone \(-10x^3\); if only embedded in full expansion then award B1B0 |
## Question 1:
### Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $4x^2 - 12x + 9 - 2(9 - 6x + x^2)$ | M1 | Square to get at least one 3/4 term quadratic |
| $2x^2 - 9$ | A1 | Fully correct |
### Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $-6x^3$ or $-4x^3$ | B1 | $-6x^3$ **or** $-4x^3$ soi www in these terms; ignore other terms |
| $-10$ | B1 | Condone $-10x^3$; if only embedded in full expansion then award B1B0 |
---1 (i) Simplify $( 2 x - 3 ) ^ { 2 } - 2 ( 3 - x ) ^ { 2 }$.\\
(ii) Find the coefficient of $x ^ { 3 }$ in the expansion of $\left( 3 x ^ { 2 } - 3 x + 4 \right) \left( 5 - 2 x - x ^ { 3 } \right)$.
\hfill \mbox{\textit{OCR C1 2016 Q1 [4]}}