| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Standard product of two binomials |
| Difficulty | Easy -1.2 This is a straightforward binomial expansion question requiring only direct application of the binomial theorem formula for small powers and basic algebraic manipulation. Part (i) involves routine calculation of binomial coefficients for n=6, and part (ii) is a simple 'hence' question that requires multiplying two polynomials and collecting terms—all standard textbook exercises with no problem-solving insight required. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
\begin{enumerate}[label=(\roman*)]
\item Find the first three terms, in ascending powers of $x$, in the expansion of
\begin{enumerate}[label=(\alph*)]
\item $(1 - x)^6$, [2]
\item $(1 + 2x)^6$. [2]
\end{enumerate}
\item Hence find the coefficient of $x^2$ in the expansion of $[(1 - x)(1 + 2x)]^6$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2015 Q3 [7]}}