UNILAG Mathematics 2017/2018 Past Questions

The median of the scores 5. 6. 8. 9 to two decimal places is

A ship leaves a port P and sails 30km due South. It then sails due West until it reaches a location which is 60km from the port. What is the bearing of H from P?

Solve the inequality 7x-9≤-4x -13

To what value does the sum 20+ 12+ 36/5+ ... tend as to infinity

A rectangular picture 7cm by 9cm is enclosed by a frame 1/2 cm wide. Calculate, the perimeter of the picture.

The lengths of the sides of a right-angled triangle are (3x+ 1) cm, (3x -1) cm and x cm. Find x

Which of the formulae below represents the general term of the following set of numbers: - 1, 2/3, -1/2, 2/5,...

If the sequences S_n = an² + bn and T₁ = -1, T₅ = 15. Find the values of the constants a and b.

A solid sphere of radius 3cm, a solid right cone of radius 3cm and height 12cm and a solid right circular cylinder of radius 3cm and height 4cm. Which of the following statements is true?

Convert 1232₄ to a number in base six

Solve the following equation $$\frac{p-2}{p-1} = \frac1{p+3}$$

The square base of a pyramid of side 3cm has height 8cm. If the pyramid is cut into two parts by a plane parallel to the base midway between the base and the vertex the volumes of the two parts are

Simplify $$\frac{5^x\times25^{x-1}}{125^{x-1}}$$

If log₂ x+2 = 2log₂ y express x in terms of y

Find x if (x base 4)² = 100100_{base 2}

The variance of the scores 1, 4, 5, 6 to two decimal places is

The graph of y = sinx, 0°≤x≤360° cuts the x-axis at which of the following points?

If pq + 1 = q² and t = $$\frac1{p-1}$$ express t in terms of q

(1.28 x 10⁴) ÷ (6.4 x 10²) equals

The weights of 30 new born babies are given as follows: 6, 9, 5, 7,6, 7,5, 8, 9, 5, 7,5,8,7,8, 7, 5, 7, 5,6,6,9,9, 7, 8, 8, 7, 8, 9, 8. The mode of the weights is

Simplify 3-2 ÷ $$\frac45 + \frac12$$

The mode of the positive integers 3,5,8,10,11,x,y is 8 and their mean is y. find the values of x and y.

If a figure PQRS is a cyclic quadrilateral then the angles SPQ and QRS are

Add 1101₂, 101111₂, and 111₂

If Paul can paint a fence in 2 hours and Fred can paint the same fence in 3 hours, Paul and Fred working together can paint the fence in

If two angles of a triangle are acute angles, the third angle

A cylinder of base radius 4 cm is open at one end. If the ratio of the area of its base to that of its curved surface is 1: 4, calculate the height of the cylinder.

The area of a parallelogram is 513cm² and the height is 19cm. Calculate the base

If one angle of a triangle is three times the second angle and the third angle is 20 degrees more than the second angle, the second angle is

In a family of 21 people, the average age is 14 years. If the age of the grandfather is not counted, the average age drops to 12 years. What is the age of the grandfather?

A bank manager received 8 times as much salary as one of the messengers. If the sum of their salaries is N135, 000, the manager's salary is

Given a regular hexagon, calculate each interior angle of the hexagon

The lengths of the sides of a right-angled triangle at (3x+1) cm, (3x -1) cm and x cm Find the value x.

Thirty boys and x girls sat for a test. The mean of the boys' scores and that of the girls were respectively 6 and 8. Find x if the total score was 468.

Ade and Uche can do a piece of work in 18 days. Ade can do it alone in x days, whilst Uche takes 15 days longer to do it alone. Which of the following equations describes x²

What is the probability that a number chosen at random from the integers between 1 and 10 inclusive is either a prime or a multiple of 3?

A bag contains 4 white balls and 6 red balls. Two red balls are taken from the bag without replacement. What is the probability that they are both red?

If y = $$\frac x{(x -3)} + {\frac x{(x +4)}}$$ find y when x = -2

A man invests a sum of money at 4% per annum simple interest. After 3 years, the principal amounts to N 7,000.00. Find the sum invested