CAIE P1 2024 June — Question 3 5 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2024
SessionJune
Marks5
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Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeSingle coefficient given directly
DifficultyModerate -0.8 Part (a) is a straightforward application of the binomial theorem requiring students to equate the coefficient formula to 160 and solve for a. Part (b) requires multiplying two expansions and collecting terms, which is slightly more involved but still a standard textbook exercise with clear methodology. The question tests routine binomial expansion skills with minimal problem-solving demand.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n
The coefficient of \(x^3\) in the expansion of \((3 + ax)^6\) is 160.
  1. Find the value of the constant \(a\). [2]
  2. Hence find the coefficient of \(x^5\) in the expansion of \((3 + ax)^6(1 - 2x)\). [3]
Question 3:
AnswerMarks Guidance
3(a)2027a3160 M1
Allow 6C3  33 .
Accept 540a3 with no other working for M1.
2
a
AnswerMarks Guidance
3A1 Allow 0.667 AWRT.
2
SC B1 is a = with no other working.
3
2
AnswerMarks Guidance
QuestionAnswer Marks
AnswerMarks
3(b)2
 2
Coefficient of x2 is 1581  their  540
AnswerMarks Guidance
 3B1 FT May be in a list. 6C2 and 34 must be evaluated but may be
implied by later work. Condone 540 with no working.
AnswerMarks Guidance
16012their 540M1
920A1 Condone 920x3.
3
AnswerMarks Guidance
QuestionAnswer Marks 
Question 3:
--- 3(a) ---
3(a) | 2027a3160 | M1 | a3160
Allow 6C3  33 .
Accept 540a3 with no other working for M1.
2
a
3 | A1 | Allow 0.667 AWRT.
2
SC B1 is a = with no other working.
3
2
Question | Answer | Marks | Guidance
--- 3(b) ---
3(b) | 2
 2
Coefficient of x2 is 1581  their  540
 3 | B1 FT | May be in a list. 6C2 and 34 must be evaluated but may be
implied by later work. Condone 540 with no working.
16012their 540 | M1
920 | A1 | Condone 920x3.
3
Question | Answer | Marks | Guidance
The coefficient of $x^3$ in the expansion of $(3 + ax)^6$ is 160.

\begin{enumerate}[label=(\alph*)]
\item Find the value of the constant $a$. [2]

\item Hence find the coefficient of $x^5$ in the expansion of $(3 + ax)^6(1 - 2x)$. [3]
\end{enumerate}

\hfill \mbox{\textit{CAIE P1 2024 Q3 [5]}}
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