UNILAG Mathematics 2013/2014 Past Questions

A solid is made up of a hemisphere of radius x cm, and a cone of height x cm of the same radius as the hemisphere. What is the volume of the composite solid?

What is the difference in the local time between two places in latitude 55°N if they are located at longitudes 8°W and 18°E respectively?

A solid sphere of radius x cm is placed in a cylinder of radius 2x cm and height 2x cm. The cylinder is then filled with water to the brim and the solid gently withdrawn. Find the volume of the water in the cylinder in cm'

The earth rotates on its own axis once in 24hrs. What is the speed in km/hr of a place whose latitude is 30°S? (take 2πR to be equal to 4 x 10⁴km)

The minor sector of a circle of diameter 3.6cm sub tends angle 35° at the Centre. What is the perimeter of the sector?

A regular polygon of (2k + 1) sides has 140° as the size of each interior angle. Find k.

Solve the following simultaneous equation x + y = 10, x² + y² = 58

A man is x years old while his son is y years old. The sum of their ages is twice difference of their ages. If the product of their ages is 675, find the age of the man.

Simplify ${√8+√{50}}/{√{7}}$ as far as possible

Factorize fully px² - py² + qx² - qy²

Evaluate $$log_3 9 - log_27 3 + log_{\sqrt3} 9$$

In a class of 30 students, there are 10 who wear spectacles and 16 girls. There are 8 boys who do not wear spectacles. How many girls wear spectacles?

Solve the equation $$log_2x - log_2(x-1)$$ = 2

(x-2) is a factor of x³ - 3x² + kx + 14. The value of k is.

Factorize the polynomial x³ - 7x + 6

y is inversely proportional to the square of x. when x =3, then y=4. Find the constant of proportionality.

Solve for x , 5 - 2x > 11 - 4x

If $$\begin{vmatrix}x & 2 \\ 1 & 5 \end{vmatrix} = \begin{vmatrix}x & 3 \\ 2 & 3 \end{vmatrix}$$, find the value of x

The determinant of $$\begin{pmatrix}1 & 2&0 \\ 3 & 2&1\\4&2&1 \end{pmatrix}$$ is

In Fig. 1, O is the center of circle <AOB = 130° find <ACB

Fig.2 shows a circle of radius 4cm. the area of the shaded segment is

Fig. 3 shows a pyramid on top of a cuboid. The height of the pyramid is b cm and the square base of both shapes has side s cm. Find the volume of the shape.

If y = sin(x² + 7), then dy/dx is

The line y = kx-3 is perpendicular to the line 2y + 3x = 7. The value of k is

The midpoint of the line segment joining (-1,3) and (5,7) is

The solution of the x² + 3x - 10 < 0 is

A binary operation is defined by a * b = a + b - 3, The identity is

A binary operation is defined by x*y = xy - x + y. The value of (3*4)*5 is

Find the difference between the mean and the median of the numbers 1,2,3,4,5,6,7,8,9 and 10.

There are 8 men and 9 women in a committee in how many ways can a subcommittee of two men and three women be chosen?

Change 671 base 9 to base 8

Write $$\frac{14}{\sqrt5-\sqrt3}$$ in the form $$a\sqrt5 - b\sqrt3$$ where a and b are rational.

In the relation log_xy = z, Write x in terms of y and z

Solve the equation $$\sqrt{x+7}$$ = x - 5

Let y = $$\frac{4x+3}{2x-3}$$ write x as a function of y

The second and fifth terms of geometric progression are 6 and -48 respectively. The first term is.

Find the positive solution of the equation log(x+1) + log(x+4) = 1

N72,000 is invested at 8% simple interest. After how many years has it reached 87,840?

Suppose that p is the probability that an event occurs, and that q is the probability that the event does not occur. Which of the following is true?

Suppose x and y are positive numbers for which x > y, which of the following is not true?

The figure above shows a trapezium. The height is 8m, 0ne of the parallel sides is 10m and the area is 104m² . Find the other parallel side

Find the remainder when x³ - 3x² + 4x - 7 is divided by (x+2)

If $$\frac{dy}{dx}$$ = 6x² + 15x⁴ and y = 7 when x = 2, find y.

The long hand minute of a clock is 7cm long. What distance does it make if the tip of the minute hand move $$1 \frac14$$ hours.

The distance |AB| is:

The mid point of AB is

Find the sum to infinity of the series $$\frac12, -\frac14, \frac18, -\frac1{16}, ...$$

Find the solution set for the set (x-2)(x-1) > 0

The solution set of the inequality |2x + 6| < 10

Write the 7th term of the sequence [1+ (-1)ⁿ]