Elective Mathematics — 2012

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

Find the number of different arrangements of the word IKOTITINA.

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.

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.

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

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

\(g \circ h\) is

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

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