OCR C2 2006 June — Question 1 4 marks

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2006
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion
DifficultyModerate -0.8 This is a straightforward application of the binomial theorem with a small positive integer power (n=4). It requires only direct substitution into the binomial formula with no problem-solving or manipulation, making it easier than average but not trivial since students must carefully handle the coefficients and signs across five terms.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

1 Find the binomial expansion of \(( 3 x - 2 ) ^ { 4 }\).

AnswerMarks Guidance
\((3x - 2)^4 = 81x^4 - 216x^3 + 216x^2 - 96x + 16\)M1, A1, A1, A1 Attempt binomial expansion, including attempt at coeffs. Obtain one correct, simplified, term. Obtain a further two, simplified, terms. Obtain a completely correct expansion
$(3x - 2)^4 = 81x^4 - 216x^3 + 216x^2 - 96x + 16$ | M1, A1, A1, A1 | Attempt binomial expansion, including attempt at coeffs. Obtain one correct, simplified, term. Obtain a further two, simplified, terms. Obtain a completely correct expansion | 4 marks

---
1 Find the binomial expansion of $( 3 x - 2 ) ^ { 4 }$.

\hfill \mbox{\textit{OCR C2 2006 Q1 [4]}}