OCR MEI C1 2010 June — Question 7 4 marks

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
Year2010
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeStandard binomial expansion
DifficultyEasy -1.2 This is a straightforward application of the binomial theorem with a small positive integer power (n=4) and simple coefficients. It requires only direct recall of the binomial expansion formula and basic arithmetic to simplify coefficients like C(4,2)×(1/2)². No problem-solving or conceptual understanding beyond the formula itself is needed, making it easier than average but not trivial since it requires careful calculation of four terms.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

Expand \((1 + \frac{1}{2}x)^4\), simplifying the coefficients. [4]

AnswerMarks Guidance
\(1 + 2x + \frac{3}{2}x^2 + \frac{1}{4}x^3 + \frac{1}{16}x^4\) o.e. (must be simplified) isw4 B3 for 4 terms correct, or B2 for 3 terms correct or for all correct but unsimplified (may be at an earlier stage, but factorial or "C" notation must be expanded/worked out) or B1 for \(1, 4, 6, 4, 1\) soi or for \(1 + ... + \frac{1}{16}x^4\) [must have at least one other term]
$1 + 2x + \frac{3}{2}x^2 + \frac{1}{4}x^3 + \frac{1}{16}x^4$ o.e. (must be simplified) isw | 4 | B3 for 4 terms correct, or B2 for 3 terms correct or for all correct but unsimplified (may be at an earlier stage, but factorial or "C" notation must be expanded/worked out) or B1 for $1, 4, 6, 4, 1$ soi or for $1 + ... + \frac{1}{16}x^4$ [must have at least one other term]
Expand $(1 + \frac{1}{2}x)^4$, simplifying the coefficients. [4]

\hfill \mbox{\textit{OCR MEI C1 2010 Q7 [4]}}