Maths Practice (Interactive)

Solve the quadratic equation x^2 - 5x + 6 = 0.

Solve the simultaneous equations: 2x + y = 7 and x - y = 2.

Simplify log_2(8) + log_2(4) using the laws of logarithms.

Find dy/dx for y = 4x^3 - 2x + 7.

Evaluate the definite integral of f(x) = 2x from x = 1 to x = 4.

In a triangle with sides a = 8 cm, b = 6 cm, and angle C = 60 degrees, what is the length of side c using the cosine rule?

A circle has a tangent and a chord that meet at a point on the circumference. The angle between the tangent and the chord is 35 degrees. What is the size of the angle in the alternate segment?

A bag contains 3 red balls and 5 blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are blue?

For the data set {3, 7, 7, 8, 12, 15}, what is the standard deviation (to 2 decimal places)?