CAIE P1 2014 November — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2014
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeCoefficient relationship between terms
DifficultyModerate -0.3 This is a straightforward binomial theorem application requiring students to equate two coefficients and solve for a constant. It involves standard formula recall and basic algebraic manipulation, making it slightly easier than average but not trivial since students must correctly identify and equate the appropriate terms.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

In the expansion of \((2 + ax)^6\), the coefficient of \(x^2\) is equal to the coefficient of \(x^3\). Find the value of the non-zero constant \(a\). [4]

AnswerMarks Guidance
\(\left(15 \text{ or }^{16}C_2\right) \times 2^4 \times (ax)^2, \left(20 \text{ or }^{20}C_1\right) \times 2^3 \times (ax)^3\)B1B1, M1A1 \(240a = 160a\) is M0 [4]
$\left(15 \text{ or }^{16}C_2\right) \times 2^4 \times (ax)^2, \left(20 \text{ or }^{20}C_1\right) \times 2^3 \times (ax)^3$ | **B1B1, M1A1** | $240a = 160a$ is M0 [4]

---
In the expansion of $(2 + ax)^6$, the coefficient of $x^2$ is equal to the coefficient of $x^3$. Find the value of the non-zero constant $a$. [4]

\hfill \mbox{\textit{CAIE P1 2014 Q1 [4]}}