SPS SPS SM Pure 2024 February — Question 2 4 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2024
SessionFebruary
Marks4
TopicBinomial Theorem (positive integer n)
TypeSingle coefficient given directly
DifficultyModerate -0.3 This is a straightforward application of the binomial theorem requiring students to set up the general term, identify the correct term for x^8, equate the coefficient to the given value, and solve for k. While it involves some algebraic manipulation and potentially large numbers, it's a standard textbook exercise with a clear method and no conceptual challenges beyond basic binomial expansion.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

2. The coefficient of \(x ^ { 8 }\) in the expansion of \(( 2 x + k ) ^ { 12 }\), where \(k\) is a positive integer, is 79200000.
Determine the value of \(k\).

2.

The coefficient of $x ^ { 8 }$ in the expansion of $( 2 x + k ) ^ { 12 }$, where $k$ is a positive integer, is 79200000.\\
Determine the value of $k$.\\

\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q2 [4]}}