CAIE P1 2012 June — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2012
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeBinomial with negative or fractional powers of x
DifficultyStandard +0.3 This is a straightforward binomial expansion problem requiring students to identify which term contains x^6 by setting up the general term (2x^3)^r(-1/x^2)^(7-r) and solving for r, then calculating the coefficient. It's slightly above average difficulty due to the negative power and the need to track powers carefully, but it's a standard textbook exercise with a clear method.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
2 Find the coefficient of \(x ^ { 6 }\) in the expansion of \(\left( 2 x ^ { 3 } - \frac { 1 } { x ^ { 2 } } \right) ^ { 7 }\).
Question 2:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\([7C3] \times [(2x^3)^4] \times [(-1/x^2)^3]\) seenB1B1 2 elements correct, 3rd element correct
\(35 \times 2^4 \times (-1)^3\) leading to their answerB1 2 elements correct. Identifying required term
\(-560(x^6)\) as answerB1 [4] SC B3 for \([560(x)^6]\) as answer 
## Question 2:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $[7C3] \times [(2x^3)^4] \times [(-1/x^2)^3]$ seen | B1B1 | 2 elements correct, 3rd element correct |
| $35 \times 2^4 \times (-1)^3$ leading to their answer | B1 | 2 elements correct. Identifying required term |
| $-560(x^6)$ as answer | B1 [4] | SC B3 for $[560(x)^6]$ as answer |

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2 Find the coefficient of $x ^ { 6 }$ in the expansion of $\left( 2 x ^ { 3 } - \frac { 1 } { x ^ { 2 } } \right) ^ { 7 }$.

\hfill \mbox{\textit{CAIE P1 2012 Q2 [4]}}
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