Further Mathematics Past Questions

A particle is projected vertically upwards from a height 45 metres above the ground with a velocity of 40 m/s. How long does it take it to hit the ground? [Take g = \(10 ms^{-2}\)].

Calculate, correct to one decimal place, the angle between 5i + 12j and -2i + 3j.

A lift moving upwards with a uniform acceleration of 5\(ms^{-2}\) carries a body of mass p kg. If the reaction on the floor is 480 N, find the value of p. [Take g = \(10 ms^{-2}\)].

If \(a = \begin{pmatrix} 3 \\ 2 \end{pmatrix}\) and \(b = \begin{pmatrix} -3 \\ 5 \end{pmatrix}\), find a vector c such that \(4a + 3c = b\).

The mean and median of integers x, y, z and t are 5 and z respectively. If x < y < z < t and y = 4, find (x + t).

Find, in surd form, the value of \(\cos 165\).

The parallelogram PQRS has vertices P(-2, 3), Q(1, 4), R(2, 6) and S(-1,5). Find the coordinates of the point of intersection of the diagonals.

A and B are two independent events such that \(P(A) = \frac{2}{5}\) and \(P(A \cap B) = \frac{1}{15}\). Find \(P(B)\).

Find the coordinates of the centre of the circle \(4x^{2} + 4y^{2} - 5x + 3y - 2 = 0\).

Given that \(\begin{pmatrix} 1 & -3 \\ 1 & 4 \end{pmatrix} \begin{pmatrix} -6 \\ P \end{pmatrix} = \begin{pmatrix} 3 \\ -26 \end{pmatrix}\), find the value of P.

A force of 32 N is applied to an object of mass m kg which is at rest on a smooth horizontal surface. If the acceleration produced is 8\(ms^{-2}\), find the value of m.

Find the least value of the function \(f(x) = 3x^{2} + 18x + 32\).

Find the coordinates of the point on the curve \(y = x^{2} + 4x - 2\), where the gradient is zero.

The equation of the line of best fit for variables x and y is \(y = 19.33 + 0.42x\), where x is the independent variable. Estimate the value of y when x = 15.

In a firing contest, the probabilities that Kojo and Kwame hit the target are \(\frac{2}{5}\) and \(\frac{1}{3}\) respectively. What is the probability that none of them hit the target?

Calculate the standard deviation of the distribution.

A particle of mass 2.5 kg is moving at a speed of 12 m/s. If a force of magnitude 10 N acts against it, find how long it takes to come to rest.

The area of a sector of a circle is 3\(cm^{2}\). If the sector subtends an angle of 1.5 radians at the centre, calculate the radius of the circle.

Simplify \(8^{n} \times 2^{2n} \div 4^{3n}\)