Moderate -0.5 This is a straightforward binomial expansion requiring identification of the term where powers of x sum to -1. Students need to apply the binomial theorem systematically and simplify one term—routine technique with minimal problem-solving, but slightly more involved than pure recall since it requires careful tracking of negative powers.
Must be 4th term – needs \((2x)^2(1/x)^3\). Includes and converts \(C_2\) or \(C_3\). Whole series given and correct term not quoted, allow 2/3
$5C_3 = 5.4/2$; $C_2 = x 2^2 \times (-1)^3$; $\rightarrow -40$ | M1, DM1, A1 [3] | Must be 4th term – needs $(2x)^2(1/x)^3$. Includes and converts $C_2$ or $C_3$. Whole series given and correct term not quoted, allow 2/3
1 Find the value of the coefficient of $\frac { 1 } { x }$ in the expansion of $\left( 2 x - \frac { 1 } { x } \right) ^ { 5 }$.
\hfill \mbox{\textit{CAIE P1 2003 Q1 [3]}}