Mathematics Past Questions and Answers

Given that \( a = \begin{pmatrix} 2 \\ 3 \end{pmatrix}\) and \(b = \begin{pmatrix} -1 \\ 4 \end{pmatrix}\), evaluate \((2a - \frac{1}{4}b)\).

If \(y = \frac{1+x}{1-x}\), find \(\frac{dy}{dx}\).

Evaluate \(\int_{-1}^{0} (x+1)(x-2) \mathrm{d}x\)

Simplify \(\frac{\sqrt{128}}{\sqrt{32} - 2\sqrt{2}}\)

There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys