In the expansion of $(2 + x^2) \left(\frac{1}{2x} - ax \right)^5$, there is no term in $x$. Give

Question

In the expansion of $(2 + x^2) \left(\frac{1}{2x} - ax \right)^5$, there is no term in $x$. Given that $a \neq 0$, find the value of the constant $a$.[5] Write down and simplify the first three terms in the expansion of $ \left(2+\frac{x^2}{2} \right)^5$ in ascending powers of $x$. Hence find the estimated value of $(2.005)^5$, showing all your workings clearly.[4]

Accepted Answer

(a) $\alpha = \frac{1}{4}$ (b)32.4

2025 SST PRELIMS P1 Q4

2025 SST PRELIMS P1 Q4