WAEC SSCE - Further Mathematics - 2012 (Objective)

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

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. 

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

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

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

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.

Find the number of different arrangements of the word IKOTITINA.

\(g \circ h\) is

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

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.

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.

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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