| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Direct binomial expansion then integrate |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring routine application of binomial expansion for n=3 (a small positive integer), followed by term-by-term integration of polynomials. Both skills are standard C2 techniques with no problem-solving or insight required, making it easier than average but not trivial since it involves multiple steps and algebraic manipulation. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n1.08b Integrate x^n: where n != -1 and sums |
4 (i) Find the binomial expansion of $\left( x ^ { 2 } - 5 \right) ^ { 3 }$, simplifying the terms.\\
(ii) Hence find $\int \left( x ^ { 2 } - 5 \right) ^ { 3 } \mathrm {~d} x$.
\hfill \mbox{\textit{OCR C2 2009 Q4 [8]}}