Simplify \(\frac{1 - 2\sqrt{5}}{2 + 3\sqrt{2}}\).

Solve: \(2\cos x - 1 = 0\).

Solve: \(4(2^{x^2}) = 8^{x}\)

If \(\log_{3} x = \log_{9} 3\), find the value of x.

Find the 3rd term of \((\frac{x}{2} - 1)^{8}\) in descending order of x.

Given that \(f : x \to x^{2}\) and \(g : x \to x + 3\), where \(x \in R\), find \(f o g(2)\).

Given that \(\frac{2x}{(x + 6)(x + 3)} = \frac{P}{x + 6} + \frac{Q}{x + 3}\), find P and Q.

Given that \(P = \begin{pmatrix} -2 & 1 \\ 3 & 4 \end{pmatrix}\) and \(Q = \begin{pmatrix} 5 & -3 \\ 2 & -1 \end{pmatrix}\), find PQ - QP.

Which of the following is a factor of the polynomial \(6x^{4} + 2x^{3} + 15x + 5\)?

Given that \(f : x \to \frac{2x - 1}{x + 2}, x \neq -2\), find \(f^{-1}\), the inverse of f.

If \(36, p, \frac{9}{4}, q\) are consecutive terms of an exponential sequence (G.P.). Find the sum of p and q.

Find the minimum value of \(y = x^{2} + 6x - 12\).

A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\), what is the gradient of the line?

A line passes through the origin and the point \((1\frac{1}{4}, 2\frac{1}{2})\). Find the y-coordinate of the line when x = 4.

In how many ways can a committee of 5 be selected from 8 students if 2 particular students are to be included?

If \(x = i - 3j\) and \(y = 6i + j\), calculate the angle between x and y.

The gradient of a curve at the point (-2, 0) is \(3x^{2} - 4x\). Find the equation of the curve.

If \(\alpha\) and \(\beta\) are the roots of \(x^{2} + x - 2 = 0\), find the value of \(\frac{1}{\alpha^{2}} + \frac{1}{\beta^{2}}\).

Given that \(x^{2} + 4x + k = (x + r)^{2} + 1\), find the value of k and r.

Given the statements:

p : the subject is difficult

q : I will do my best

Which of the following is equivalent to 'Although the subject is difficult, I will do my best'?

Given that \(r = 2i - j\), \(s = 3i + 5j\) and \(t = 6i - 2j\), find the magnitude of \(2r + s - t\).

Marks	0	1	2	3	4	5
Number of candidates	6	4	8	10	9	3

The table above shows the distribution of marks scored by students in a test. How many candidates scored above the median score?

Marks	0	1	2	3	4	5
Number of candidates	6	4	8	10	9	3

The table above shows the distribution of marks scored by students in a test. Find the interquartile range of the distribution.

A mass of 75kg is placed on a lift. Find the force exerted by the floor of the lift on the mass when the lift is moving up with constant velocity. \([g = 9.8ms^{-2}]\)

Each of the 90 students in a class speak at least Igbo or Hausa. If 56 students speak Igbo and 50 speak Hausa, find the probability that a student selected at random from the class speaks Igbo only.

If \(\begin{vmatrix}  1+2x & -1 \\ 6 & 3-x \end{vmatrix} = -3 \), find the values of x.

Find \(\int \frac{x^{3} + 5x + 1}{x^{3}} \mathrm {d} x\)

Find the coordinates of the point which divides the line joining P(-2, 3) and Q(4, 6) internally in the ratio 2 : 3.

A particle starts from rest and moves in a straight line such that its acceleration after t seconds is given by \(a = (3t - 2) ms^{-2}\). Find the other time when the velocity would be zero.

A particle starts from rest and moves in a straight line such that its acceleration after t secs is given by \(a = (3t - 2) ms^{-2}\). Find the distance covered after 3 secs.

Given that \(y = 4 - 9x\) and \(\Delta x = 0.1\), calculate \(\Delta y\).

Four fair coins are tossed once. Calculate the probability of having equal heads and tails.

In calculating the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers. If he obtained 20 as the mean, find the correct mean. 

Simplify: \(^{n}C_{r} ÷ ^{n}C_{r-1}\)

If \(2\sin^{2} \theta = 1 + \cos \theta, 0° \leq \theta \leq 90°\), find the value of \(\theta\).