OCR MEI C1 2009 January — Question 5 5 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2009
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion coefficient
DifficultyEasy -1.2 Both parts are direct applications of standard techniques with minimal steps. Part (i) requires simple polynomial multiplication and collecting terms. Part (ii) is a routine binomial coefficient calculation using the formula. No problem-solving or insight required—pure mechanical recall for a C1 level question.
Spec1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.04a Binomial expansion: (a+b)^n for positive integer n

5
  1. Find the coefficient of \(x ^ { 3 }\) in the expansion of \(\left( x ^ { 2 } - 3 \right) \left( x ^ { 3 } + 7 x + 1 \right)\).
  2. Find the coefficient of \(x ^ { 2 }\) in the binomial expansion of \(( 1 + 2 x ) ^ { 7 }\).

5 (i) Find the coefficient of $x ^ { 3 }$ in the expansion of $\left( x ^ { 2 } - 3 \right) \left( x ^ { 3 } + 7 x + 1 \right)$.\\
(ii) Find the coefficient of $x ^ { 2 }$ in the binomial expansion of $( 1 + 2 x ) ^ { 7 }$.

\hfill \mbox{\textit{OCR MEI C1 2009 Q5 [5]}}