Edexcel C2 — Question 3 7 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicBinomial Theorem (positive integer n)
TypeFind constants from coefficient conditions on terms
DifficultyStandard +0.8 This question requires students to apply binomial expansion coefficients, set up and solve a system of two equations involving both n and p, and handle the algebraic manipulation of p² in the third term. While the binomial theorem is standard C2 content, the simultaneous solving with the parameter p appearing squared adds non-routine algebraic complexity beyond typical textbook exercises.
Spec1.04a Binomial expansion: (a+b)^n for positive integer n

The first three terms in the expansion, in ascending powers of \(x\), of \((1 + px)^n\), are \(1 - 18x + 36p^2x^2\). Given that \(n\) is a positive integer, find the value of \(n\) and the value of \(p\). [7]

The first three terms in the expansion, in ascending powers of $x$, of $(1 + px)^n$, are $1 - 18x + 36p^2x^2$. Given that $n$ is a positive integer, find the value of $n$ and the value of $p$. [7]

\hfill \mbox{\textit{Edexcel C2  Q3 [7]}}