Tests and Challenges

The 100th term of an A.P. is 300 and the common difference is 3, calculate its first term.

The 4th term of an A. P. is 13 while the 10th term is 31. Find the 21st term.

Given the progression 7, 12, 17 and 22. What is the expression for the nth term of the progression?

Find the value of n in an arithmetic progression of 7, 12, 19, 24, ……, if 257 is the nth term.

The first term of a series is 4 1/2 and the 12th term is 23. Find the common difference.

If the second and fourth terms of a G.P. are 8 and 32 respectively, what is the sum of the first four terms?

Find the common difference in an Arithmetic progression, given that its first and 28th terms are -14 and -5 respectively.

Find the sum of the first five terms of the G.P. 2, 6,18…

The angle of depression of a tree when compared to the length of its shadow on the level ground is 28 degree and the length of its shadow is 9.78m. What is the height of the tree?

How many terms has the G.P whose second term is 1/2 and the common ratio and the last term are1/4 and 1/120 respectively.

Find the sum of the AP: 2, 5, 8, ____ to the 18th term.

How many terms has the A.P whose first term is 1.5 and the last term is 57 given that the common difference is 3?

A girl is 6 years younger than her brother. The product of their ages is 135. Find their ages.

Calculate the radius of a sphere whose surface area is 198cm^2.

A bus moves 5km due east and then 10km due south. Calculate his bearing from its original position.

Five interior angles of a hexagon are given as follows [2x + 85]°, [x + 90]°, [2x + 120]°, [2x – 65]°, and [x + 30]°, find the sixth angle.

A square tile has 40cm. How many of these tiles will be needed to cover a rectangular floor having a length of 8m and width of 5.3m?

The mathematics teacher formed a cone by bending a sector of a circle with an angle of 240°. Calculate the radius of the base of the cone formed given that the diameter of the circle is 16cm.

A woman is 3 times as old as her son. 8 years ago the product of their ages was 112. Find the son’s age.

Each interior angle of a regular polygon is 150°, find the number of sides the polygon has.

Twice the square of a certain whole number added to 3 times the number makes 90. Find the number.

Find the length of the area of a circle having diameter of 10cm and subtending an = angle of 25° at the circle center.

Find the value of x if the lengths of the sides of a right angled triangle are given as follows [4x + 1] cm, [4x – 1] cm and xcm.

The perimeter of a square picture is 64km. find the area of the picture.

A man is 37 years old and his child’s age is 8. How many years ago was the product of their ages 96?

Find the surface area of a cuboid of length 5cm, width 8cm and height 10cm.

The square of a certain number is 22 less than 13 times the original number. Find the number.

Find the total surface area of a cylinder having a height of 12cm and radius of 9cm.

if sin 3y = cos 2y and 0° ≤ y ≤ 90°, find the value of y.

Evaluate [3 + (2)] x [3 – (2)].

Obtaining a score of 6 when two dice are thrown. From the question, what is the probability of obtaining a total score of 11 or 12?

The base of a triangle is 3cm longer than its corresponding height. If the area is 44cm^2, find the length of its base.

Two numbers have a difference of 3. The sum of their squares is 89. Find the numbers.

Two tetrahedral dice with numbering 4, 5, 6, 7 are thrown, find the probability that the sum gotten will be greater than 11.

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 test score was 468.

A box has 5 black balls and 7 green balls. Two balls are drawn from the box without replacement find the probability that they are both black.

A rectangular plot measures 12m by 5m. A path of constant width runs along one side and one end. If the total area of the plot and the path is 120m^2, find the width of the path.

Ade tossed an unbiased coin and a fair die. From the information given, what is the probability of either a tail or an odd number?

A box has 5 black balls and 7 green balls. Two balls are drawn from the box without replacement, find the probability that both balls drawn are black, if drawn with replacement.

Teams P and Q are involved in a game of football. What is the probability that the game ends in a draw?

Lanre choose randomly a number between 1 and 400. Find the probability that the number chosen is divisible by 5.

For a class of 30 students, the scores in a mathematics test out of 10 marks were as follows: 4, 5, 7, 2, 3, 6, 5, 5, 8, 9, 5, 4, 2, 3, 7, 9, 8, 7, 7, 7, 3, 4, 5, 5, 2, 3, 6, 7, 7, 2.
What is the median score?

Find the principal which will yield ₦ 1,500 interest at the rate of 4% in 5 years.

How many two-digit numbers can be formed from the digits 0, 1, 2, 3, if a digit can be repeated and no number may begin with 0?

Odedeyi lives 7km from Oginigba. She walks 3km at 9km/hr and travels the rest of the way by bus at 16km/hr. What is the average speed for the whole distance?

₦ 600 yields ₦ 120 in y year’s interest at the rate of 6% p.a. find y.

Obi is 25 years older than Ada, a years ago, Obi’s age was thrice that of Ada. If Ada’s age is now b and a > b, find a – b.

Boneri lives 8km from his office. He walks 2km at 6km/hr and travels the rest of the way by car at 30km/hr. What is the average speed in km/hr?

In a promotional exam, a girl scored 75 out of a maximum score of 85. Express this score as a percentage to three significant figures.

The mean age of R men in a club is 50years. Two men, aged 55 and 63, left the club and the mean age reduced by 1year. Find the value of R.