2025 School of Science and Technology Prelims A Math Paper 2
In the expansion of \((2+x^2)\left(\frac{1}{2x}-ax\right)^5\), there is no term in \(x\). Given that \(a \ne 0\), 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]
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