WAEC SSCE - Further Mathematics - 2012 (Objective)

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

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

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

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

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

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

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

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

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

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

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

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

Find the number of different arrangements of the word IKOTITINA.

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

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

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

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

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

\(g \circ h\) is

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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

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