Standard +0.3 This is a straightforward binomial expansion problem requiring identification of the term containing x, application of the binomial coefficient formula, and solving a simple equation for a. While it involves multiple steps, each is routine and the problem type is standard practice for this topic.
2 In the expansion of \(\left( \frac { 1 } { a x } + 2 a x ^ { 2 } \right) ^ { 5 }\), the coefficient of \(x\) is 5 . Find the value of the constant \(a\).
\(5C2\left(\frac{1}{ax}\right)^3\left(2ax^2\right)^2\) soi
B1
Seen or implied. Can be part of an expansion
\(10 \times \frac{1}{a^3} \times 4a^2 = 5\) soi
M1A1
M1 for identifying relevant term and equating to 5, all correct. Ignore extra \(x\)
\(a = 8\) cao
A1
Total: 4 marks
## Question 2:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $5C2\left(\frac{1}{ax}\right)^3\left(2ax^2\right)^2$ soi | B1 | Seen or implied. Can be part of an expansion |
| $10 \times \frac{1}{a^3} \times 4a^2 = 5$ soi | M1A1 | M1 for identifying relevant term and equating to 5, all correct. Ignore extra $x$ |
| $a = 8$ cao | A1 | |
**Total: 4 marks**
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2 In the expansion of $\left( \frac { 1 } { a x } + 2 a x ^ { 2 } \right) ^ { 5 }$, the coefficient of $x$ is 5 . Find the value of the constant $a$.\\
\hfill \mbox{\textit{CAIE P1 2017 Q2 [4]}}