| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Two unknowns from two coefficient conditions |
| Difficulty | Standard +0.8 This question requires applying the binomial theorem with fractional exponent, then multiplying expansions and equating coefficients to solve simultaneous equations. Part (a) is routine, but part (b) requires careful algebraic manipulation of two unknowns from coefficient matching, which is more demanding than standard single-variable binomial questions. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
5
\begin{enumerate}[label=(\alph*)]
\item Find the first three terms in the expansion of $( 1 + p x ) ^ { \frac { 1 } { 3 } }$ in ascending powers of $x$.
\item The expansion of $( 1 + q x ) ( 1 + p x ) ^ { \frac { 1 } { 3 } }$ is $1 + x - \frac { 2 } { 9 } x ^ { 2 } + \ldots$.
Find the possible values of the constants $p$ and $q$.
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 Q5 [8]}}