WAEC SSCE - Further Mathematics - 2008 (Objective)

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

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?

A function f is defined on R, the set of real numbers, by: \(f : x \to \frac{x + 3}{x - 2}, x \neq 2\), find \(f^{-1}\).

In the diagram above, forces P, Q and 50N are acting on a body at M. If the system is in equilibrium, calculate, in terms of \(\theta\), the magnitude of P.

Two statements are represented by p and q as follows:

p : He is brilliant; q : He is regular in class

Which of the following symbols represent "He is regular in class but dull"?

A binary operation ,*, is defined on the set R, of real numbers by \(a * b = a^{2} + b + ab\). Find the value of x for which \(5 * x = 37\).

Express \(\frac{7\pi}{6}\) radians in degrees.

Which of the following quadratic curves will not intersect with the x- axis?

A rectangle has a perimeter of 24m. If its area is to be maximum, find its dimension.

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.

If \(P = \begin{pmatrix} 1 & -2 \\ 3 & 4 \end{pmatrix}\) and \(Q = \begin{pmatrix} -2 & 3 \\ 1 & 0 \end{pmatrix}\), find PQ.

If \(f(x) = 2x^{2} - 3x - 1\), find the value of x for which f(x) is minimum.

What is the coordinate of the centre of the circle \(5x^{2} + 5y^{2} - 15x + 25y - 3 = 0\)?

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 sum of the first n terms of a linear sequence is \(S_{n} = n^{2} + 2n\). Determine the general term of the sequence.

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

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

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?

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?

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

Evaluate \(\int_{1}^{2} (2 + 2x - 3x^{2}) \mathrm {d} x\).

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).

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

Simplify \(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}\)

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

Find the range of values of x for which \(2x^{2} + 7x - 15 > 0\).

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?

If \(2\log_{4} 2 = x + 1\), find the value of x.

The coefficient of the 5th term in the binomial expansion of \((1 + kx)^{8}\), in ascending powers of x is \(\frac{35}{8}\). Find the value of the constant k.

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

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.

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

The polynomial \(2x^{3} + x^{2} - 3x + p\) has a remainder of 20 when divided by (x - 2). Find the value of constant p.

Find the locus of points which is equidistant from P(4, 5) and Q(-6, -1).

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

The sum of the first n terms of a linear sequence is \(S_{n} = n^{2} + 2n\). Find the common difference of the sequence.

Find the derivative of \(3x^{2} + \frac{1}{x^{2}}\)