Further Mathematics Past Questions

A particle is projected vertically upwards with a speed of 40 m/s. At what times will it be 35m above its point of projection? \(\text{Take g} = 10 ms^{-2}\)

Given that \(p = 4i + 3j\), find the unit vector in the direction of p.

X and Y are two independent event. If \(P(X) = \frac{1}{5}\) and \(P(X \cap Y) = \frac{2}{15}\), find \(P(Y)\).

Simplify \(\frac{^{n}P_{3}}{^{n}C_{2}} + ^{n}P_{0}\)

The equation of a circle is given by \(x^{2} + y^{2} - 4x - 2y - 3\). Find the radius and the coordinates of its centre.

Given that \(P = \begin{pmatrix} 4 & 9 \end{pmatrix}\) and \(Q = \begin{pmatrix} -1 & -2 \\ 3 & 2 \end{pmatrix}\). Evaluate \(|Q|P\).

Given that \(P = \begin{pmatrix} 4 & 9 \end{pmatrix}\) and \(Q = \begin{pmatrix} -1 & -2 \\ 3 & 2 \end{pmatrix}\). Which of the following operations is possible?

How many ways can 12 people be divided into three groups of 2, 7 and 3 in that order?

The table above shows the marks obtained by 100 pupils in a test. Find the probability that a student picked at random scored at least 14 marks.

The table above shows the marks obtained by 100 pupils in a test. Find the upper class boundary of the class containing the third quartile.

The polynomial \(2x^{3} + 3x^{2} + qx - 1\) has the same reminder when divided by \((x + 2)\) and \((x - 1)\). Find the value of the constant q.

Find the value of p for which \(x^{2} - x + p\) becomes a perfect square. 

The equation of a curve is given by \(y = 2x^{2} - 5x + k\). If the curve has two intercepts on the x- axis, find the value(s) of constant k.

A body is acted upon by two forces \(F_{1} = (5 N, 060°)\) and \(F_{2} = (10 N, 180°)\). Find the magnitude of the resultant force.

A bag contains 2 red and 4 green sweets of the same size and shape. Two boys pick a sweet each from the box, one after the other, without replacement. What is the probability that at least a sweet with green wrapper is picked?

If \(f(x) = mx^{2} - 6x - 3\) and \(f'(1) = 12\), find the value of the constant m.

Evaluate \(\lim \limits_{x \to 3} \frac{x^{2} - 2x - 3}{x - 3}\)

Calculate in surd form, the value of \(\tan 15°\).

Two bodies of masses 8 kg and 5 kg travelling in the same direction with speeds x m/s and 2 m/s respectively collide. If after collision, they move together with a speed of 3.85 m/s, find, correct to the nearest whole number, the value of x.