Moderate -0.8 This is a straightforward binomial expansion question requiring only basic substitution into the binomial coefficient formula. Given one coefficient to find the constant 'a', then calculate another coefficient using the same formula—purely mechanical with no problem-solving insight needed.
## Question 2:
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(1+ax)^6$: Term in $x = 6ax$ | $B1$ | co |
| Equate with $-30 \rightarrow a = -5$ | $B1\sqrt{}$ | $\sqrt{}$ from his answer for $6ax$ |
| Term in $x^3 = \frac{6.5.4}{3!}a^3$ | $B1$ | co |
| $\rightarrow$ coefficient of $-2500$ | $B1\sqrt{}$ | For $20 \times a^3$ |
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2 In the expansion of $( 1 + a x ) ^ { 6 }$, where $a$ is a constant, the coefficient of $x$ is - 30 . Find the coefficient of $x ^ { 3 }$.
\hfill \mbox{\textit{CAIE P1 2010 Q2 [4]}}