OCR C2 — Question 3 6 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeRatio of coefficients condition
DifficultyModerate -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.
Spec1.04a 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 \(n \geq 2\),
  1. find and simplify the first three terms,
  2. find the value of \(n\) for which the coefficient of \(x\) is equal to the coefficient of \(x ^ { 2 }\).

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]}}