OCR MEI C4 2005 June — Question 2 6 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2005
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicGeneralised Binomial Theorem
TypeFactoring out constants first
DifficultyModerate -0.5 This is a straightforward application of the binomial expansion requiring factoring out the constant (4) first, then expanding (1 + x/2)^(1/2). While it requires understanding of the generalised binomial theorem and validity conditions, it's a standard textbook exercise with no novel problem-solving required, making it slightly easier than average.
Spec1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions
2 Find the first 4 terms in the binomial expansion of \(\sqrt { 4 + 2 x }\). State the range of values of \(x\) for which the expansion is valid.
AnswerMarks
Converting from base 5:
\(3.03232 = 3 + \frac{0}{5} + \frac{3}{5^2} + \frac{2}{5^3} + \frac{3}{5^4} + \frac{2}{5^5}\)M1
\(= 3.14144\)A1 [2] 
Converting from base 5: | |
$3.03232 = 3 + \frac{0}{5} + \frac{3}{5^2} + \frac{2}{5^3} + \frac{3}{5^4} + \frac{2}{5^5}$ | M1 |
$= 3.14144$ | A1 [2] |
2 Find the first 4 terms in the binomial expansion of $\sqrt { 4 + 2 x }$. State the range of values of $x$ for which the expansion is valid.

\hfill \mbox{\textit{OCR MEI C4 2005 Q2 [6]}}
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Q2 6 Q3 4 Q4 5 Q5 7 Q6 8 Q7 18