Further Mathematics Past Questions

Find the unit vector in the direction of (-5i + 12j).

The functions f and g are defined on the set, R, of real numbers by \(f : x \to x^{2} - x - 6\) and \(g : x \to x - 1\). Find \(f \circ g(3)\).

Given that \(q = 9i + 6j\) and \(r = 4i - 6j\), which of the following statements is true?

A particle starts from rest and moves in a straight line such that its velocity, v, at time t seconds is given by \(v = (3t^{2} - 2t) ms^{-1}\). Determine the acceleration when t = 2 secs.

A particle starts from rest and moves in a straight line such that its velocity, v, at time t seconds is given by \(v = (3t^{2} - 2t) ms^{-1}\). Calculate the distance covered in the first 2 seconds.

A body of mass 25kg changes its speed from 15m/s to 35m/s in 5 seconds by the action of an applied force F. Find the value of F.

Two forces 10N and 15N act on an object at an angle of 120° to each other. Find the magnitude of the resultant.

A force of 200N acting on a body of mass 20kg initially at rest causes it to move a distance of 320m along a straight line for t secs. Find the value of t.

A basket contains 3 red and 1 white identical balls. A ball is drawn from the basket at random. Calculate the probability that it is either white or red.

Four doctors and two nurses are to sit round a circular table. In how many ways can this be done if the nurses are to sit together?

If \(^{3x}C_{2} = 15\), find the value of x?

The table above shows the distribution of marks of students in a class. Find the upper class boundary of the modal class.

Find the standard deviation of the numbers 3,6,2,1,7 and 5.

In how many ways can 3 prefects be chosen out of 8 prefects?

The probability that Kofi and Ama hit a target in a shooting competition are \(\frac{1}{6}\) and \(\frac{1}{9}\) respectively. What is the probability that only one of them hit the target?

The mean of 2, 5, (x + 2), 7 and 9 is 6. Find the median.

Determine the coefficient of \(x^{2}\) in the expansion of \((a + 3x)^{6}\).

Find the equation of a circle with centre (-3, -8) and radius \(4\sqrt{6}\).

Evaluate \(\frac{1}{1 - \sin 60°}\), leaving your answer in surd form.