CAIE P1 2017 June — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2017
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeRatio of coefficients condition
DifficultyModerate -0.8 This is a straightforward application of the binomial theorem requiring identification of two specific coefficients and computing their ratio. The calculation involves standard binomial coefficient formulas with no conceptual difficulty or problem-solving insight needed—purely mechanical execution of a familiar technique.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
1 The coefficients of \(x ^ { 2 }\) and \(x ^ { 3 }\) in the expansion of \(( 3 - 2 x ) ^ { 6 }\) are \(a\) and \(b\) respectively. Find the value of \(\frac { a } { b }\).
Question 1: \((3-2x)^6\)
AnswerMarks Guidance
AnswerMarks Guidance
Coeff of \(x^2 = 3^4 \times (-2)^2 \times {}_6C_2 = a\)B3,2,1 Mark unsimplified forms. −1 each independent error but powers must be correct. Ignore any '\(x\)' present.
Coeff of \(x^3 = 3^3 \times (-2)^3 \times {}_6C_3 = b\)
\(\frac{a}{b} = -\frac{9}{8}\)B1 OE. Negative sign must appear before or in the numerator
Total: 4 
## Question 1: $(3-2x)^6$

| Answer | Marks | Guidance |
|--------|-------|----------|
| Coeff of $x^2 = 3^4 \times (-2)^2 \times {}_6C_2 = a$ | **B3,2,1** | Mark unsimplified forms. −1 each independent error but powers must be correct. Ignore any '$x$' present. |
| Coeff of $x^3 = 3^3 \times (-2)^3 \times {}_6C_3 = b$ | | |
| $\frac{a}{b} = -\frac{9}{8}$ | **B1** | OE. Negative sign must appear before or in the numerator |
| **Total: 4** | | |

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1 The coefficients of $x ^ { 2 }$ and $x ^ { 3 }$ in the expansion of $( 3 - 2 x ) ^ { 6 }$ are $a$ and $b$ respectively. Find the value of $\frac { a } { b }$.\\

\hfill \mbox{\textit{CAIE P1 2017 Q1 [4]}}
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