Mathematics Past Questions

Exam Type:

Exam year:

Question Type:

Topics:

4076

If 2x\(^2\) + x - 3 divides x - 2, find the remainder.

4077

If \(\begin{vmatrix} 2 & -5 & 3 \\ x & 1 & 4 \\ 0 & 3 & 2 \end{vmatrix} = 132\), find the value of x.

4078

Given the matrix \(A = \begin{vmatrix} 3 & -2 \\ 1 & 6 \end{vmatrix}\). Find the inverse of matrix A.

A. \(\begin{vmatrix} 6 & 2 \\ 1 & 6 \end{vmatrix}\)
B. \(\begin{vmatrix} \frac{2}{11} & \frac{1}{12}\\ \frac{3}{20} & \frac{1}{10} \end{vmatrix}\)
C. \(\begin{vmatrix} -3 & 2 \\ -1 & -6 \end{vmatrix}\)
D. \(\begin{vmatrix} \frac{3}{10} & \frac{1}{10} \\ \frac{-1}{20} & \frac{3}{20}\end{vmatrix}\)

4079

If y = 8x\(^3\) - 3x\(^2\) + 7x - 1, find \(\frac{\mathrm d^2 y}{\mathrm d x^2}\).

4080

Differentiate \(\frac{2x}{\sin x}\) with respect to x.