Further Mathematics Past Questions

The distance between P(x, 7) and Q(6, 19) is 13 units. Find the values of x.

If \(y = x^{2} - 6x + 11\) is written in the form \(y = a(x - h)^{2} + k\), find the value of \((a + h + k)\).

The initial and final velocities of an object of mass 5 kg are \(u = \begin{pmatrix} 1 \\ 3 \end{pmatrix}\) and \(v = \begin{pmatrix} 4 \\ 7 \end{pmatrix}\) respectively. Find the magnitude of its change in momentum.

Find the value of the constant k for which \(a = 4 i - k j\) and \(b = 3 i + 8 j\) are perpendicular.

If \(p = \begin{pmatrix} 2 \\ -2 \end{pmatrix} \) and \(q = \begin{pmatrix} 3 \\ 4 \end{pmatrix}\), find \(|q - \frac{1}{2}p|\).

If n items are arranged two at a time, the number obtained is 20. Find the value of n.

A body starts from rest and moves in a straight line with uniform acceleration of \(5 ms^{-2}\). How far, in metres, does it go in 10 seconds?

A test consists of 12 questions out of which candidates are to answer 10. If the first 6 are compulsory, in how many ways can each candidate select her questions?

Express \(r = (12, 210°)\) in the form \(a i + b j\).

The table above shows the distribution of marks by some candidates in a test. If a student is selected at random, what is the probability that she scored at least 6 marks?

The table above shows the distribution of marks by some candidates in a test. Find, correct to one decimal place, the mean of the distribution.

The table above shows the distribution of marks by some candidates in a test. What is the median score?

Two forces \(F_{1} = (10N, 020°)\) and \(F_{2} = (7N, 200°)\) act on a particle. Find the resultant force.

The probability of Jide, Atu and Obu solving a given problem are \(\frac{1}{12}\), \(\frac{1}{6}\) and \(\frac{1}{8}\) respectively. Calculate the probability that only one solves the problem.

Given that \(\overrightarrow{AB} = 5i + 3j\) and \(\overrightarrow{AC} = 2i + 5j\), find \(\overrightarrow{BC}\). 

If events A and B are independent and \(P(A) = \frac{7}{12}\) and \(P(A \cap B) = \frac{1}{4}\), find P(B).

If \(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 32\), find the value of x.

Express \(\frac{1}{1 - \sin 45°}\) in surd form. 

Given that \(f '(x) = 3x^{2} - 6x + 1\) and f(3) = 5, find f(x).