| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Ratio of coefficients condition |
| Difficulty | Moderate -0.3 This is a straightforward binomial expansion question requiring standard application of the formula. Part (i) involves routine substitution into C(n,r)(1/4)^r for r=0,1,2, and part (ii) requires equating two coefficients and solving a simple linear equation in n. While it tests understanding of the binomial theorem, it's slightly easier than average as it involves no complex algebraic manipulation or problem-solving insight. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
3. For the binomial expansion in ascending powers of $x$ of $\left( 1 + \frac { 1 } { 4 } x \right) ^ { n }$, where $n$ is an integer and $n \geq 2$,\\
(i) find and simplify the first three terms,\\
(ii) find the value of $n$ for which the coefficient of $x$ is equal to the coefficient of $x ^ { 2 }$.\\
\hfill \mbox{\textit{OCR C2 Q3 [6]}}