SPS SPS FM 2024 October — Question 3 6 marks

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2024
SessionOctober
Marks6
TopicBinomial Theorem (positive integer n)
TypeBinomial times linear coefficient
DifficultyModerate -0.8 Part (a) is a routine binomial expansion requiring direct application of the formula with no complications. Part (b) requires multiplying two expansions and equating coefficients, which is standard practice but involves slightly more algebraic manipulation. Both parts are straightforward textbook exercises with no problem-solving insight required, making this easier than average.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n1.04b Binomial probabilities: link to binomial expansion

  1. Find and simplify the first three terms in the expansion of \((2-5x)^5\) in ascending powers of \(x\). [3]
  2. In the expansion of \((1+ax)^2(2-5x)^5\), the coefficient of \(x\) is 48. Find the value of \(a\). [3]

\begin{enumerate}[label=(\alph*)]
\item Find and simplify the first three terms in the expansion of $(2-5x)^5$ in ascending powers of $x$. [3]

\item In the expansion of $(1+ax)^2(2-5x)^5$, the coefficient of $x$ is 48.

Find the value of $a$. [3]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS FM 2024 Q3 [6]}}