| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | Finding unknown constant from coefficient |
| Difficulty | Standard +0.3 This is a standard C4 binomial expansion question with straightforward algebraic manipulation. Part (i) is routine application of the formula, part (ii) requires multiplying series and solving a quadratic (standard technique), and part (iii) is verification arithmetic. Slightly above average due to the multi-step nature and algebraic manipulation required, but follows predictable patterns taught in C4. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<1 |
\begin{enumerate}
\item (i) Expand $( 1 + a x ) ^ { - 3 } , | a x | < 1$, in ascending powers of $x$ up to and including the term in $x ^ { 3 }$. Give each coefficient as simply as possible in terms of the constant $a$.
\end{enumerate}
Given that the coefficient of $x ^ { 2 }$ in the expansion of $\frac { 6 - x } { ( 1 + a x ) ^ { 3 } } , | a x | < 1$, is 3 ,\\
(ii) find the two possible values of $a$.
Given also that $a < 0$,\\
(iii) show that the coefficient of $x ^ { 3 }$ in the expansion of $\frac { 6 - x } { ( 1 + a x ) ^ { 3 } }$ is $\frac { 14 } { 9 }$.\\
\hfill \mbox{\textit{OCR C4 Q4 [9]}}