WAEC SSCE - Further Mathematics - 2012 (Objective)

The equation of a circle is \(3x^{2} + 3y^{2} + 24x - 12y = 15\). Find its radius.

Simplify \(\frac{x^{3n + 1}}{x^{2n + \frac{5}{2}}(x^{2n - 3})^{\frac{1}{2}}}\)

Given that \(\sqrt{6}, 3\sqrt{2}, 3\sqrt{6}, 9\sqrt{2},...\) are the first four terms of an exponential sequence (G.P), find in its simplest form the 8th term. 

If the midpoint of the line joining (1 - k, -4) and (2, k + 1) is (-k, k), find the value of k.

Two forces 10N and 6N act in the directions 060° and 330° respectively. Find the x- component of their resultant.

In computing the mean of 8 numbers, a boy mistakenly used 17 instead of 25 as one of the numbers and obtained 20 as the mean. Find the correct mean

If (x + 1) is a factor of the polynomial \(x^{3} + px^{2} + x + 6\). Find the value of p.

A binary operation, \(\Delta\), is defined on the set of real numbers by \(a \Delta b = a + b + 4\). Find the identity element.

If \(y = x^{3} - x^{2} - x + 6\), find the values of x at the turning point.

Find the constant term in the binomial expansion of \((2x - \frac{3}{x})^{8}\).

A stone is dropped from a height of 45m. Find the time it takes to hit the ground. \([g = 10 ms^{-2}]\)

QRS is a triangle such that \(\overrightarrow{QR} = (3i + 2j)\) and \(\overrightarrow{SR} = (-5i + 3j)\), find \(\overrightarrow{SQ}\).

From the diagram above, which of the following represents the vector V in component form?

The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the mean mark.

\(g \circ h\) is

A fair die is tossed twice. Find the probability of obtaining a 3 and a 5.

A straight line makes intercepts of -3 and 2 on the x- and y- axes respectively. Find the equation of the line.

The marks obtained by 10 students in a test are as follows: 3, 7, 6, 2, 8, 5, 9, 1, 4 and 10. Find the variance.

Which of the following sets is equivalent to \((P \cup Q) \cap (P \cup Q')\)?

Which of the following is nor a measure of central tendency?

Given that \(P = \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix}\) and \(Q = \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}\), Find (2P - Q).

If r denotes the correlation coefficient between two variables, which of the following is always true?

Simplify: \(\frac{\cos 2\theta - 1}{\sin 2\theta}\)

Evaluate \(\int_{-2}^{3} (3x^{2} - 2x - 12) \mathrm {d} x\)

The diagram above is a velocity- time graph of a moving object. Calculate the distance travelled when the acceleration is zero.

Given that \(^{n}P_{r} = 90\) and \(^{n}C_{r} = 15\), find the value of r.

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

The distance s in metres covered by a particle in t seconds is \(s = \frac{3}{2}t^{2} - 3t\). Find its acceleration.

The angle of a sector of a circle is 0.9 radians. If the radius of the circle is 4cm, find the length of the arc of the sector.

Find the number of different arrangements of the word IKOTITINA.

Solve the inequality \(x^{2} - 2x \geq 3\)

Find the acute angle between the lines 2x + y = 4 and -3x + y + 7 = 0.

A box contains 4 red and 3 blue identical balls. If two are picked at random, one after the other without replacement, find the probability that one is red and the other is blue.

If P(x - 3) + Q(x + 1) = 2x + 3, find the value of (P + Q).

Given that \(\sin x = \frac{-\sqrt{3}}{2}\) and \(\cos x > 0\), find x.

Differentiate \(\frac{x}{x + 1}\) with respect to x.

Evaluate \(\log_{10}(\frac{1}{3} + \frac{1}{4}) + 2\log_{10} 2 + \log_{10} (\frac{3}{7})\)

Find the values of x at the point of intersection of the curve \(y = x^{2} + 2x - 3\) and the lines \(y + x = 1\).

A polynomial is defined by \(f(x + 1) = x^{3} + px^{2} - 4x + 2\), find f(2).

From the diagram above, \(h[g(3)]\) is