Live Challenges

Make t the subject of the formula

Solve the equation 4/a + 1/5a =3

If dy/dx = x + cos x, find y

Find the derivative of

The midpoint of P(x,y) and Q(8,6) is (5,8). Find x and y

If tan x = 1/√3, find cos x – sin x such that

Rationalize the denominator of

Simplify

Find the distance between the points

Simplify

Evaluate

Find the sum to infinity of the following series.  3 +2 + 4/3 + 8/9 + 16/27 + …..

If log10 (x-3) + log10(x+2) = log10(2x^2 -8)  Find the value of x.

The mean age of five boy is 8, if the sum of the ages of the first three boys is 25. What is the sum of the ages of the last two boys?

How many sides does a regular polygon with interior angles 120° has?

The  term of a sequence is n^2 – n – 2. Find the sum of its second and fifth terms

A cone has a slant height of 29cm and a circular base of diameter 42cm. Calculate the vertical height of the cone.

Factorize

If y varies directly as √m and y=9 when m =9, find y when m= 1 7/9

Evaluate 202 + 1211 – 102 base three.Leaving your answer in base 3

The first term and the last terms of an A.P are 5 and 89  Find the number of terms in the A.P, if the sum of its terms is 611

The diagonal of a square of side x  is 4√2. Find the value of x

If the total surface area of a solid hemisphere is equal to its volume, find the radius.

Given that a= log 7 and b=log 2, express log 35 in terms of a and b

The mean of 2 – t, 4+t, 3-2t, 2 + t and t – 1

Solve the pair of equation for x and y respectively.

2x^-1 – 3y^-1 = 4

4x^-1 +y^-1 = 1

In a small village of 500  people, 350 speak the local language while  200 speaks pidgin English. What percentage of the population speaks both?

A circle of perimeter 24 cm is opened to form a square. What is the area of the square?

If 2q3 base 5 = 77 base 8, find q

Simplify

A man 40m  from the foot of a tower observes the angle of elevation of the tower to be 30°  Determine the height of the tower.

If the lines 3y = 4x -1 and y= qx + 3/q are parallel to each other, the value of q is

The ratio of the exterior angle to interior angle of a regular polygon is 1:5 . How many sides has the polygon?

In an isosceles right-angled triangle with the equal sides of size of 1 unit containing the right-angle. Find the value of cos 45°.

If

What is the possibility that an integer x, chosen at random is divisible by both 2 and 3?

From the diagram below, find the bearing of R from S.

The range of the data  k +2, k – 3, k + 4, k – 2, k, k – 5, k + 3, k – 1 and k + 6 is

Find the value of x from the Venn diagram

μ=80

Given that cos x = 3/5 and x is an acute angle, calculate without using tables the value of sinx .

What are the roots of the equation 3 – 4x – 4x^2 = 0

Jack is 11 years older than Joyce. In 5 years’ time, Jack will be twice as old as Joyce. Find Joyce’s present age.

Evaluate

A chord of length 30 cm is 8 cm away from the centre of the circle. What is the diameter of the circle?