| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Binomial times quadratic coefficient |
| Difficulty | Standard +0.3 Part (i) is straightforward application of binomial theorem requiring calculation of four terms. Part (ii) requires multiplying the expansion by a quadratic and collecting x³ terms—a standard extension that tests understanding but involves routine algebraic manipulation with no novel insight required. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
3 (i) Find and simplify the first four terms in the binomial expansion of $\left( 1 + \frac { 1 } { 2 } x \right) ^ { 10 }$ in ascending powers of $x$.\\
(ii) Hence find the coefficient of $x ^ { 3 }$ in the expansion of $\left( 3 + 4 x + 2 x ^ { 2 } \right) \left( 1 + \frac { 1 } { 2 } x \right) ^ { 10 }$.
\hfill \mbox{\textit{OCR C2 2010 Q3 [7]}}