CAIE P1 2018 November — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2018
SessionNovember
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 question requiring identification of the correct term using the general term formula, then arithmetic calculation. It's slightly above average difficulty due to the negative power and fractional coefficients requiring careful algebraic manipulation, but follows a standard method taught explicitly in P1.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
Find the coefficient of \(\frac{1}{x^2}\) in the expansion of \(\left(3x + \frac{2}{3x^2}\right)^7\). [4]
Question 1:
AnswerMarks
11
For a correctly selected term in : (3x)4 or 34
AnswerMarks Guidance
x2B1 Components of coefficient added together 0/4
B1 expect 81
 2 
×  ³ or (2/3)3
AnswerMarks Guidance
3x2 B1 B1 expect 8/27
× C or C
AnswerMarks Guidance
7 3 7 4B1 B1 expect 35
840
→ 840 or
AnswerMarks Guidance
x2B1 All of the first three marks can be scored if the correct term is
seen in an expansion and it is selected but then wrongly
simplified.
SC: A completely correct unsimplified term seen in an
expansion but not correctly selected can be awarded B2.
4
AnswerMarks Guidance
QuestionAnswer Marks 
Question 1:
1 | 1
For a correctly selected term in : (3x)4 or 34
x2 | B1 | Components of coefficient added together 0/4
B1 expect 81
 2 
×  ³ or (2/3)3
3x2  | B1 | B1 expect 8/27
× C or C
7 3 7 4 | B1 | B1 expect 35
840
→ 840 or
x2 | B1 | All of the first three marks can be scored if the correct term is
seen in an expansion and it is selected but then wrongly
simplified.
SC: A completely correct unsimplified term seen in an
expansion but not correctly selected can be awarded B2.
4
Question | Answer | Marks | Guidance
Find the coefficient of $\frac{1}{x^2}$ in the expansion of $\left(3x + \frac{2}{3x^2}\right)^7$. [4]

\hfill \mbox{\textit{CAIE P1 2018 Q1 [4]}}
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