Further Mathematics Past Questions

Find the constant term in the binomial expansion \((2x^{2} + \frac{1}{x})^{9}\)

Find the angle between forces of magnitude 7N and 4N if their resultant has a magnitude of 9N.

A body of mass 28g, initially at rest is acted upon by a force, F Newtons. If it attains a velocity of \(5.4ms^{-1}\) in 18 seconds, find the value of F.

If \(\overrightarrow{OX} = \begin{pmatrix} -7 \\ 6 \end{pmatrix}\) and \(\overrightarrow{OY} = \begin{pmatrix} 16 \\ -11 \end{pmatrix}\), find \(\overrightarrow{YX}\).

What is the probability of obtaining a head and a six when a fair coin and and a die are tossed together? 

Given that \(a = i - 3j\) and \(b = -2i + 5j\) and \(c = 3i - j\), calculate \(|a - b + c|\).

The marks scored by 4 students in Mathematics and Physics are ranked as shown in the table below

Calculate the Spearmann's rank correlation coefficient.

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.

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

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

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

Find the stationary point of the curve \(y = 3x^{2} - 2x^{3}\).

The midpoint of M(4, -1) and N(x, y) is P(3, -4). Find the coordinates of N.

Given that \(y = x(x + 1)^{2}\), calculate the maximum value of y.

Find the equation to the circle \(x^{2} + y^{2} - 4x - 2y = 0\) at the point (1, 3).

Express \(\frac{13}{4}\pi\) radians in degrees.

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

In how many ways can the letters of the word 'ELECTIVE' be arranged?

Find the radius of the circle \(x^{2} + y^{2} - 8x - 2y + 1 = 0\).