| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Polynomial Division & Manipulation |
| Type | Polynomial Expansion and Simplification |
| Difficulty | Moderate -0.8 Both parts are routine algebraic manipulation requiring only systematic expansion and collection of like terms. Part (i) is straightforward triple bracket expansion, and part (ii) requires identifying which terms multiply to give x^4 without full expansion. These are standard C1 exercises testing basic polynomial skills with no problem-solving or insight required. |
| Spec | 1.02n Sketch curves: simple equations including polynomials1.02w Graph transformations: simple transformations of f(x) |
| Answer | Marks | Guidance |
|---|---|---|
| \((2x^2 - 5x - 3)(x + 4)\) | M1 | Attempt to multiply a quadratic by a linear factor or expand all 3 brackets with appropriate number of terms (including an \(x^3\) term) |
| \(= 2x^3 + 8x^2 - 5x^2 - 20x - 3x - 12\) | ||
| \(= 2x^3 + 3x^2 - 23x - 12\) | A1, A1 [3] | Expansion with no more than one incorrect term |
| Answer | Marks | Guidance |
|---|---|---|
| \(2x^4 + 7x^4\) | B1 | \(2x^4\) or \(7x^4\) seen |
| \(= 9x^4\) | B1 | |
| \(9\) | [2] | \(9x^4\) or \(9\) |
## Question 5:
### Part (i):
$(2x^2 - 5x - 3)(x + 4)$ | M1 | Attempt to multiply a quadratic by a linear factor or expand all 3 brackets with appropriate number of terms (including an $x^3$ term)
$= 2x^3 + 8x^2 - 5x^2 - 20x - 3x - 12$ | |
$= 2x^3 + 3x^2 - 23x - 12$ | A1, A1 [3] | Expansion with no more than one incorrect term
### Part (ii):
$2x^4 + 7x^4$ | B1 | $2x^4$ or $7x^4$ seen
$= 9x^4$ | B1 |
$9$ | [2] | $9x^4$ or $9$
---5 (i) Expand and simplify $( 2 x + 1 ) ( x - 3 ) ( x + 4 )$.\\
(ii) Find the coefficient of $x ^ { 4 }$ in the expansion of
$$x \left( x ^ { 2 } + 2 x + 3 \right) \left( x ^ { 2 } + 7 x - 2 \right) .$$
\hfill \mbox{\textit{OCR C1 2009 Q5 [5]}}