CAIE P1 2016 November — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2016
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeFind constant from coefficient condition
DifficultyModerate -0.3 This is a straightforward binomial coefficient problem requiring students to expand two binomial expressions, identify the x³ terms, set their sum equal to 100, and solve for a. It's slightly easier than average because it's a direct application of the binomial theorem with no conceptual tricks, though it does require careful arithmetic with the negative coefficient in the first term.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

The coefficient of \(x^3\) in the expansion of \((1 - 3x)^6 + (1 + ax)^5\) is 100. Find the value of the constant \(a\). [4]

Question 2:
AnswerMarks
2(+/−)20×33( x3) 0a3( x3)
, 1 soi
−540+10a3 =100 oe
AnswerMarks
a=4B1B1
M1
AnswerMarks Guidance
A1[4] Each term can include x3
Must have 3 terms and include
a3 and 100
Question 2:
2 | (+/−)20×33( x3) 0a3( x3)
, 1 soi
−540+10a3 =100 oe
a=4 | B1B1
M1
A1 | [4] | Each term can include x3
Must have 3 terms and include
a3 and 100
The coefficient of $x^3$ in the expansion of $(1 - 3x)^6 + (1 + ax)^5$ is 100. Find the value of the constant $a$. [4]

\hfill \mbox{\textit{CAIE P1 2016 Q2 [4]}}