Mathematics Past Questions and Answers

Evaluate \(\int_{\frac{1}{2}}^{1} \frac{x^{3} - 4}{x^{3}} \mathrm {d} x\).

Calculate the standard deviation of 30, 29, 25, 28, 32 and 24.

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

Out of 70 schools, 42 of them can be attended by boys and 35 can be attended by girls. If a pupil is selected at random from these schools, find the probability that he/ she is from a mixed school.

If the determinant of the matrix \(\begin{pmatrix} 2 & x \\ 3 & 5 \end{pmatrix} = 13\), find the value of x.