Moderate -0.8 This is a straightforward binomial expansion problem requiring students to identify the correct term, apply the binomial coefficient formula, and solve a simple equation for a. While it involves multiple steps, each is routine: finding which term gives x^5, writing out that term with the binomial coefficient, and solving -280 = -35a^2. This is easier than average as it's a standard textbook exercise with no conceptual challenges beyond basic binomial theorem application.
1 In the expansion of \(\left( x ^ { 2 } - \frac { a } { x } \right) ^ { 7 }\), the coefficient of \(x ^ { 5 }\) is - 280 . Find the value of the constant \(a\).
Term in \(x^5\) is \(_{7}C_3 \times (x^2)^4 \times (-a/x)^3\)
B1
Allow on own or in an expansion
This term isolated
M1
Correct term in \(x^5\) selected
Equated to \(-280 \rightarrow a = 2\)
A1
Equated to \(-280\)
[3]
## Question 1:
| Answer/Working | Marks | Guidance |
|---|---|---|
| Term in $x^5$ is $_{7}C_3 \times (x^2)^4 \times (-a/x)^3$ | B1 | Allow on own or in an expansion |
| This term isolated | M1 | Correct term in $x^5$ selected |
| Equated to $-280 \rightarrow a = 2$ | A1 | Equated to $-280$ |
| **[3]** | | |
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1 In the expansion of $\left( x ^ { 2 } - \frac { a } { x } \right) ^ { 7 }$, the coefficient of $x ^ { 5 }$ is - 280 . Find the value of the constant $a$.
\hfill \mbox{\textit{CAIE P1 2012 Q1 [3]}}