2012/2013 UNILAG Mathematics Post-UTME

$\mathrm{Calculate} {3310}_5 – {1442}_5$

Covert 3.1415926 to 5 decimal place

The length of a notebook 15cm was measured as 16.8cm. Calculate the percentage error to 2 significant figures.

A worker’s present salary is N24.000 per annum. His annual increment is 10% of his basic salary. What would be his annual salary at the beginning of the third year?

Express the product of 0.0014 and 0.011 in standard form.

$\mathrm{Evaluate} {\left(81\right)}^{\frac{3}{4}} – {\left(27\right)}^{\frac{1}{3 }}÷ 3 \times 2^3$

Find the value of

${\left(16\right)}^{\frac{3}{2}} + {\log }_{10 } 0.0001 + {\log }_{2}32$

$\mathrm{Simplify} \frac{\sqrt{12 } – \sqrt{3}}{\sqrt{12 } + \sqrt{3}}$

Four members of a social-first eleven cricket term are also members of the first fourteen rugby team. How many boys play for at least one of the two teams?

How many ways are there to assign 3 people to 5 desks, with no more than one person to a desk?

If  x+1 and x-1 are both factors of the equator ${\mathrm{x}}^3 + {\mathrm{px}}^2 + \mathrm{qx} + 6 = 0$, evaluate p and q

Find a positive value of p in the expression $2{\mathrm{x}}^2 – \mathrm{px} + \mathrm{p}$ leaves a remainder 6 when divided x -p.

Find T in term of K, Q and S if S = 2r√(QT+K)

The graph of $\mathrm{f}\left(\mathrm{x}\right) 2={\mathrm{x}}^2 – 5\mathrm{x} + 6 \mathrm{crosses} \mathrm{the} \mathrm{x}– \mathrm{axis}$

Factorize completely the expression

${\mathrm{abx}}^{2 } + 6\mathrm{y} = 3\mathrm{ax} – 2\mathrm{byx}$

Solve the following inequality (x – 3) (x – 4) ≤  0

The 4th term of an A.P is 13 while the 10th term 31. Find the 21st term.

$\mathrm{Simplify} \frac{{\mathrm{x}}^2 – 1}{{\mathrm{x}}^2 –2{\mathrm{x}}^2 – \mathrm{x} – 2}$

Express 5x – 12 ÷ (x -2)(x -3) in partial fractions

Which of the following binary operations is commutative on the set of integers?

If a * b = ± √ ab evaluate 2 * (12 *27)

Find the sum to infinity of the following sequence

$1, 9 / 10, {(9/10)}^2, {(9/10)}^3$

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

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

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

Find the distance between two town P (45°N 30°W) and Q (15°S, 3°W) if the radius of the earth is 7000km. (π22/7)

Two perpendicular lines PQ and QR intersect at (1, -1), if the equation of PQ is x – 2y + 40. Find the equation of QR.

P is on the locus of points equidistant from two given points X and Y, UV is straight line through Y parallel to the locus. If ∠PYU is 40°. Find ∠XYR

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 the foot of a water tank tower observes that the angle elevator of a top of the 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 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.

The frequency distribution below showºs the ages of students in secondary school. In a pie chart constructed to represent the data, the angle corresponding to the 15 year old is

The pie chart below shows the distribution of students in 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 respectively, Find m + r.

Find the standard deviation of the data using the table below

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