OCR MEI Paper 3 2018 June — Question 6 2 marks

Exam BoardOCR MEI
ModulePaper 3 (Paper 3)
Year2018
SessionJune
Marks2
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TopicBinomial Theorem (positive integer n)
TypeSingle binomial expansion
DifficultyModerate -0.3 This is a straightforward binomial expansion question requiring students to identify which term has x^0 by setting up the general term and solving 2r - (15-r) = 0, giving r=5. Then calculate C(15,5). It's slightly easier than average because it's a single-step problem with a clear method, though it does require careful algebraic manipulation of powers.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
6 Find the constant term in the expansion of \(\left( x ^ { 2 } + \frac { 1 } { x } \right) ^ { 15 }\).
Question 6:
AnswerMarks Guidance
AnswerMarks Guidance
\({}_{15}C_5\left(x^2\right)^5\left(\frac{1}{x}\right)^{10}\)M1 AO 3.1a
\(3003\)A1 [2] AO 1.1 
## Question 6:

| Answer | Marks | Guidance |
|--------|-------|----------|
| ${}_{15}C_5\left(x^2\right)^5\left(\frac{1}{x}\right)^{10}$ | M1 | AO 3.1a | Identifying term with $\left(x^2\right)^5\left(\frac{1}{x}\right)^{10}$; Must see |
| $3003$ | A1 [2] | AO 1.1 | |
6 Find the constant term in the expansion of $\left( x ^ { 2 } + \frac { 1 } { x } \right) ^ { 15 }$.

\hfill \mbox{\textit{OCR MEI Paper 3 2018 Q6 [2]}}
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Q1 3 Q2 2 Q3 2 Q4 10 Q5 11 Q6 2 Q7 8 Q8 8 Q9 4 Q10 10 Q11 2 Q12 3 Q13 3 Q14 4 Q15 3