MATHEMATICS PAST QUESTIONS

P is a point on the same plane with a fixed point A. If P moves such that it is always equidistant from A, the locus of P is

Every staff in an office owns either a Mercedes and/or a Toyota car. 20 own Mercedes, 15 own Toyota and 5 own both. How many staff are there in the office?

A point on the ground is 5m away from the foot of a vertical wall 7m high. Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall

Given that p varies as the square of p and q varies inversely as the square root of r. how does p vary with r?

Find the average of the first four prime numbers greater than 10

A fair coin is tossed three times. Find the probability of getting two heads and one tail.

A pyramid of volume 120cm cube has a rectangular base which measures 5cm by 6cm. calculate the height of the pyramid

If x% of 240 equals 12, find x:

Tow numbers 24 and 31 are equal in value when converted to base ten. Find the equation connecting x and y.

Q is 25km from P on a bearing 042 degrees and R is 25km from P on a bearing of 132 degrees. Calculate the bearing of R from Q

A man made a loss of 15% by selling an article for N595. Find the cost price of the article

A boy walks 800m in 20 minutes. Calculate his average speed in km per hour

A cuboid of base 12.5cm by 20 cm holds exactly 1 litre of water. What is the height of the cuboid? (1 liter = 1000cm³)

The volume of a cylinder is 1200 cm cube and the area of its base is 150cm cube. Find the height of the cylinder

The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216cm², find the length of the basic.

A chord of length 6cm is drawn in a circle of radius 5 cm. Find the distance of the chord from the centre of the circle.

The probability of an event P happening is 1/5 and that of event Q is ¼. If the events are independent, what is the probability that neither of them happens?

If the 2^nd and 5^th terms of a G.P are 6 and 48 respectively, find the sum of the first four terms

The probabilities of a boy passing English and Mathematics test are x and y respectively. Find the probability of the boy failing both tests

A man is four times as old as his son. The difference between their ages is 36 years. Find the sum of their ages

If 8x – 4 = 6x – 10, find the value of 5x

Two solid spheres have volumes 250cm³ and 128cm³ respectively. Find the ratio of their radii

What is the height 10cm and diameter 7cm? (Take Pi = 22/7)

Subtract (-y+3x+5z) from (4y – x – 2z)

A sector of a circle radius 14cm subtends an angle 135 degree at the centre of the circle. What is the perimeter of the sector (take Pi = 22/7)

A student bought 3 notebooks and 1 pen for N35. After misplacing these items. She again bought 2 notebooks and 2 pens, all of the same type for N30. What is the cost of a pen?

A man bought 220 mangoes at N5x. He sold each for 3x kobo and made again of N8. Find the value of x.

Correct 0.04945 to two significant figures

A group of eleven people can speak either English or French or both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?

Water flows from a tap into a cylindrical container at the rate of 5Pi cm cube per second. If the radius of the container is 3cm, calculate the level of water in the container at the end of a seconds

Three men, Bedu, Bakre and Kofi shared N500 in the ratio 3:2:X respectively. If Bedu’s share is N150, find the value of x

A fair die is tossed once. What is the probability of obtaining neither 5 nor 2?

A boy contains 3 red and 2 white identical balls. If 2 balls are picked at random from the bag, one after the other and with replacement, find the probability that they are of different colours

A school girl spends ¼ of her pocket money on books and 1/3 on dress. What fraction remains?

Mr. John traveled from Aba to Ikorodu a distance of 720km in 8 hours. What will be his speed in m/s?

A trader makes a loss of 15% when selling an article. Find the ration, selling price: cost price

The area of a sector of a sector of a circle with diameter 12cm is 66 cm square. If the sector is folded to form a cone, calculate the radius of the base of the cone. (Take Pi = 22/7)

If the volume of a cube is 343cm cube, find the length of its side

Which of the following is not a factor of 2P² – 2?

A messenger was paid N2.50 an hour during the normal working hours and N4.00 an hour during overtime. If he received N31.00 for 10 hours work, how many hours are for overtime?

I am x years old and my brother is 3 years older. How old was my brother last year?

The lengths of the minor and major arcs of a circle are 54cm and 126cm respectively. Calculate the angle of the major sector

If two triangles are similar, which of the following is true? Their

The area of a square field is 110.25metre square field is 110.25 metre square. Find the cost of fencing it round at N75.00 per metre

A man’s eye level is 1,7m above the horizontal ground and calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes.

A chord of a circle of radius 26cm is 10cm from the centre of the circle. Calculate the length of the chord

The length of the two parallel sides of trapezium are 6cm and 10cm and the perpendicular distance between them is 5cm. Find the area of the trapezium

The angle of elevation of an aircraft from a point K on the horizontal ground is 30 degree. If the aircraft is 800m above the ground, how far is it from K?

Out of 60 members of an association, 15 are doctors and 9 are lawyers. If a member is selected at random from the association, what is the probability that the member is neither doctor nor a lawyer?

Which of the following figures have one line of symmetry only? (I) Isosceles triangle (II) Rhombus (III) Kite

The probabilities that John and James pass an examination are ¾ and 3/5 respectively. Find the probability of both boys failing the examination

Calculate. Correct to 2 significant figures, the length of arc of a circle of radius 3.5cm which subtends an angle of 75 degree at the centre of the circle (Take Pi = 22/7)

A regular polygon has 9 sides. What is the size of one of its exterior angles?

If the simple interest on a sum of money invested at 3% per annum for 2 ½ years is N123, find the principal

The wheel of a tractor has diameter 1.4m. What distance does it cover in 100 complete revolutions? (Take Pi = 22/7)

A machine valued at N20, 000 depreciates by 10% every year. What will be the value of the machine at the end of two years?

Two circles has radii 16cm and 23cm. What is the difference between their circumferences? (Take Pi=22/7)

Find the next two terms of the sequence 1, 5, 14, 30, 50…

The salary of a man was increased in the ratio 40:47. Calculate the percentage increase in the salary

The cross-section of a prism is a right-angled triangle 3cm by 4cm by 5cm. The height of the prism is 8cm. calculate its volume