WAEC SSCE - Further Mathematics - 2012 (Objective)

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

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

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

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.

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

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.

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

\(g \circ h\) is

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

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

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.

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

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

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

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

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. 

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

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

Find the number of different arrangements of the word IKOTITINA.

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