2007/2008 UNILAG Mathematics Post-UTME

If a*b = + ab,  evaluate 2*(12*27)

Find the sum of the infinity of the following sequence $1, \frac{9}{10},\left(\frac{9}{{10}^2}\right),{\left(\frac{9}{10}\right)}^3$

Find the value of k if $\left(\begin{array}{ccc}–2& 1& 1\\ 2& 1& \mathrm{k}\\ 1& 3& –1\end{array}\right)= 23$

$\mathrm{If} \mathrm{X} \left(\begin{array}{cc}1& 2\\ 0& 3\end{array}\right) \mathrm{and} \mathrm{Y} =\left(\begin{array}{cc}2& 1\\ 4& 3\end{array}\right) \mathrm{find} \mathrm{XY}$

In a triangle XYZ, ℘YXZ = 44° and ℘XYZ = 112°,  Calculate the acute angle between the internal bisectors of ℘XYZ and ℘XZY

Find the distance between two town P (45°N  30°W) if the radius of the earth is 7000km (π= 22/7)

Two perpendicular liens PQ and RQ intersect at (1, -1), if the equation of PQ is x – 2y + 4 = 0, find the equation of QR.

P is on the locus of points equidistant from two given points X and V, UV is a straight line through Y parallel to the locus, if < PYU is 40°, find ℘XPY.

The base diameter of a cylinder is 14cm while the height is 12cm. Calculate the total surface area if the cylinder has both a base and a top.

A schoolboy lying on the ground 30m away from a foot a water tank tower observes that the angle of elevation of a top of a tank is 60°. Calculate the height of the water tank.

QRS is a triangle with QS= 12m, ℘RQS=30° and ℘QRS=45°. Calculate the length of RS

The derivative of cosec x is

For what value of x is the tangent to the curve $\mathrm{y} = {\mathrm{x}}^2 – 4\mathrm{x} + 3$parallel to the x-axis?

Two variables x and y are such that dy/dx =4x – 3 and y = 5 when x = 2. Find y in terms of x .

Find the area bounded by the curve $\mathrm{y} = 3{\mathrm{x}}^2 – 2\mathrm{x} + 1$, the ordinates x = 1 and x = 3 and the x-axis.

A frequency distribution above shows the distribution in a secondary school. In a pie chart constructed to represent the data, the angle corresponding to the 15years old is

The pie chart above shows the distribution of students in a secondary school class. If 30 students offered French, how many offered C.R,K?

The mean and the range of the set of numbers 1.20, 1.00, 0.90, 1.40, 0.80, 0.80, 1.20, and 1.10 are m and r respectively. Find m + r

Find the standard deviation of the data using the table above.

The variance of the scores 1, 2, 3, 4, 5 is