| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Find constants from coefficient conditions on terms |
| Difficulty | Standard +0.8 This question requires students to equate coefficients from the binomial expansion to form simultaneous equations, then solve for both n and p. The presence of p² in the given expansion adds algebraic complexity, and students must recognize that the negative coefficient implies p is negative, then use the relationship between consecutive binomial coefficients. This goes beyond routine binomial expansion exercises and requires systematic algebraic manipulation across multiple steps. |
| Spec | 1.04a 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]
\hfill \mbox{\textit{Edexcel C2 Q41 [7]}}