Tests and Challenges

A student travelled for x hours at 5km/hr and for y hours at 10km/hr. The journey was 35km altogether, which of the following equations represent the given information if the average speed for the journey was 7km/hr?

Solve the equation 2a^2 – 3a – 27 = 0.

The third term of a G.P is 63 while its fifth term is 567. What is the sum of its first seven terms?

m^2 – 8m + k. What value of k makes the given expression a perfect square?

In a positive number of two digits, the sum of the digits is 15. If the digits are interchanged the number is increased by 9. Find the number.

Factorize m (2a – b) – 2n (b – 2a).

Find the value of x in 0.5x + 2.6 = 5x + 0.35.

Solve the inequality x – 1 > 4(x + 2).

In a class of 50 students, 25 play chess, 17 play squash and 13 do not play any game at all. Find the number of students who play both chess and squash.

To arrive on schedule, a train is to cover a distance of 60 km at 72 km/hr. If it starts 10 minutes late, at what speed must it move to arrive on schedule?

In a class of 50 students, every student had to study Government or Economics or both. If 38 students studied Government and 28 studied Economics, how many students studied both subjects?

David cycles for x hours at 16km/hr and y hours at 12km/hr. Altogether he cycles 96km in 7 hours. Find x and y.

Given that U = [3, 4, 5, 6, 7, 8]; A = [6, 7, 8], B = [3, 5, 6] and C = [5, 6, 7]. Find A’ B’ C’.

Given the universal set U. U = [2, 4, 6, 8, 10, 12] and A = [2, 4, 6, 8], B = [6, 8, 10], C = [4, 8, 12]. Find [A n B].

If q oranges are sold for t Naira, how many oranges can be bought for p Naira?

There are 572 students in a mixed school. 5/11 of them are boys. How many girls are in the school?

Cromwell can hoe a yam plot in 3 hours and Itunuola can hoe it in 4 hours. How long will it take them to hoe the whole plot working together?

Given the universal set U. U = [2, 4, 6, 8, 10, 12] and A = [2, 4, 6, 8], B = [6, 8, 10], C = [4, 8, 12].  Find AU [ B U C ].

What fraction of 5 weeks is 5 days?

During two years in a school, 7 ̸ 8 of the students had malaria, 3̸ 4 had catarrh and 5 ̸ 6 had neither. If the number of students that had both malaria and catarrh is 280. Find the number of students in the school.

Cromwell can hoe a yam plot in 3 hours and Itunuola can hoe it in 4 hours. What fraction of the plot can each of them hoe in 1 hour?

Find A n B ?

Determine which is the greatest of 5 ̸ 6, 3 ̸ 4, 7/8, 9 ̸10.

There are 572 students in a mixed school. 5 ̸ 11 of them are boys. How many fraction of girls are there?

In an election there were four candidates, 5 ̸ 6 of the electors voted for the winner. The runner-up received 4 ̸ 7 of the remaining votes. The third candidates received twice the votes of the fourth candidates. What fraction of the electors voted for the third candidate?

The lengths, in cm, of the sides of a right-angled triangle are x, (x + 2) and (x + 1) where x > 0. Find, in cm, the length of its hypotenuse.

A rectangle has length x cm and width (x – 1) cm. If the perimeter is 16cm, find the value of x.

Find the perimeter of a sector of a circle of radius 14cm subtended by angle 120 degree, at the centre.

What is the mass in kg of a cylindrical metal bar 0.14m long and 0.06m in diameter if 1cm^3 of the metal has a mass of 70g?

Calculate the radius of a cylinder of height 2.5cm and volume 154cm^3. Leave your answer correct to 1 decimal place.

Two square boards are made of the same material and their diagonals measure 40cm and 45cm respectively. If the smaller costs ₦192 to make, what should be the other cost?

The 14th term of an A.P is 96 while the 25th term is 173. Find the 19th term.

Three types of drinks Fanta, Coke and Lemon are sold for ₦900.00, ₦1,500.00 and ₦x.00 respectively per litre. If the cost per litre of the mixture is ₦1,430.00 and ratio of their mixture is 3 : 3 : 4, find x.

Daniel’s Plc declared a dividend of 75 kobo for one unit of share held by shareholder. Find the amount of shares a shareholder who has 6,000 shares will receive if there is a withholding tax of 15%.

The following gives a geometric sequence: 2, P, Q, 250. Find the values of P and Q.

A trader bought 200 oranges at 5 for ₦1.20, 40 oranges got spoilt and the remaining were sold at 4 for ₦1.50. How much money did the trader receive for the remaining oranges?

The sum of 8 terms of an A.P is 160 while the sum of 20 terms is 880. Find the 43rd term.

Zenith bank shares are sold in bundles. If one bundle of 6 shares is sold for ₦42.00, how many shares can ₦ 180.00 buy?

The 3rd and the 9th terms of a G.P are 54 and 39,366 respectively. Find the sum of the 4th and 7th terms.

The following is an A.P, 9, x, y, z, 25, …….. Find the values of x, y and z.

Mr. Dele invested ₦ 30,000 in ₦ 10.00 ordinary shares of Zenith bank. He bought the shares at ₦ 20.00 each. How many shares did he buy?

Find the sum of the first 25 terms of the sequence 11, 15, 19, 23, 27………

A number is selected at random between 20 and 30, both numbers inclusive. Find the probability that the number is a prime.

A survey of 100 students in an institution shows that 80 speak fluent Hausa and 20 students speak Igbo, while only 9 students speak both languages. How many students speak neither Hausa nor Igbo?

Find the smallest number by which 252 can be multiplied to obtain a perfect square.

The ratio of the number of men to women in a 20-member committee is 3: 1. How many women must be added to the number so as to make the ratio of men to women 3:2?

The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number.

Express 0.00629946 to 3 significant figures.

In a class of 80 students, every student had to study economics or geography, or both economics and geography. If 65 students studied economics and 50 studied geography, how many studied both subjects?

While doing his Physics practical, Idowu recorded a reading as 1.12cm instead of 1.21cm. Calculate his percentage error.