Further Mathematics Past Questions

A force of 30 N acts at an angle of 60° on a body of mass 6 kg initially at rest on a smooth horizontal plane. Find the distance covered in 10 seconds.

A group of 5 boys and 4 girls is to be chosen from a class of 8 boys and 6 girls. In how many ways can this be done?

Calculate, correct to one decimal place, the standard deviation of the numbers: -1, 5, 0, 2 and 9.

Given that \(R = (4, 180°)\) and \(S = (3, 300°)\), find the dot product.

Three students are working independently on a Mathematics problem. Their respective probabilities of solving the problem are 0.6, 0.7 and 0.8. What is the probability that at least one of them solves the problem?

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.