Moderate -0.8 This is a straightforward binomial expansion question requiring students to identify the constant term by finding when powers of x cancel. It involves routine application of the binomial theorem with a simple expression (x + 3/x)^4 and only requires finding one specific term rather than the full expansion or multiple terms. The calculation is mechanical with no problem-solving insight needed.
\(r = 4r\) \(r = -2\) Term is \(_4C_2 \times (3)^2 = 54\)
B1, B1, B1
Guessing or attempt at \(r = -2\); For correct \(_4C_2 \times (3)^*\) for his \(r\); Correct only – isolated from expansion
$r = 4r$ $r = -2$ Term is $_4C_2 \times (3)^2 = 54$ | B1, B1, B1 | Guessing or attempt at $r = -2$; For correct $_4C_2 \times (3)^*$ for his $r$; Correct only – isolated from expansion
1 Find the value of the term which is independent of $x$ in the expansion of $\left( x + \frac { 3 } { x } \right) ^ { 4 }$.
\hfill \mbox{\textit{CAIE P1 2002 Q1 [3]}}