MATHEMATICS PAST QUESTIONS

Solve the simultaneous equations: x + y = 2 and 3x – 2y = 1

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

There are m boys and 12 girls in a class. What is the probability of selecting at random a girl from the class?

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

A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord

N140, 000 is shared between Abu, Kayode and Uche. Abu has twice as much as Kayode, and Kayode has twice as much as Uche. What is Kayode’s share?

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

A rectangular carpet 2.5m long and 2.4m wide covers 5% of a rectangle floor. Calculate the area of the floor.

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

A seller allows 20% discount for cash payment on the marked price of his goods. What is the ratio of the cash payment to the marked price?

Find the mean deviation of 6, 7, 8, 9, 10

If 30% of y is equal to x, what, in terms of x is 30% of 3y?

A house bought for N 100,000 was later auctioned for N80, 000. Find the loss percent.

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.

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

The sum of the 1^st and 2^nd terms of an AP is 4 and the 10^th term is 19. Find the sum of the 5^th and 6^th terms

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

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

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?

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)

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

Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm. calculate correct to the nearest degree, the smallest angle of the triangle

Divide 3.6721 by 4

Given that 2P – m = 6 and 2p + 4m = 1. Find the value of (4p + 3m)

The population of students in a school is 810. If this represented on a pie chart. Calculate the sectoral angle for a class of 72 students

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

From a point P, R is 5km due west and 12km due south. Find the distance between P and R.

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

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?

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

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

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

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

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

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?

A boy estimated his transport fare for a journey as N 190 instead of N200. Find the percentage error in his estimate

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

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?

Divide the sum of 8,6,7,2,0,4,7,2,3 by their mean

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

Which of the following statements describes the locus of a point R which moves in a plane such that it is a point R which moves in a plane such that it is equidistant from two intersecting lines?

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 ladder, 6cm long, leans against a vertical wall at an angel 53 degree to the horizontal. How high up the wall does the ladder reach?

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

Ladi sold a car for N84, 000 at a loss of 4%. How much did Ladi buy the car?

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

The monthly salary of a man increased from N2, 700 to N3, 200. Find the percentage increase

The curved surface area of a cylindrical tin is 704cm cube. If the radius of its base is 8cm. find the height (Take Pi = 22/7)

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

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

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

The interior angle of a regular polygon is twice the exterior angle. How many sides have the polygon?

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?

An arc of a circle of radius 14cm subtends angle 300^o at the centre. Find the perimeter of the sector formed by the arc (Take Pi=22/7)

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

A trader bought 100 tubers of yam at 5 for N350.00. She sold them in sets of 4 for N290.00. Find her gain percent

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

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