Mathematics Practice (Interactive)

Solve the quadratic equation 2x squared minus 7x plus 3 equals 0 by factorisation. What are the solutions?

Evaluate log base 3 of 81. Which expression is equivalent to the answer?

The polynomial p(x) = x cubed minus 6x squared plus 11x minus 6 has a factor of (x minus 1). What are all three roots of p(x)?

Which trigonometric identity is correct and can be used to simplify the expression sine theta divided by cosine theta?

Solve the equation 2 sine squared x minus sine x minus 1 equals 0 for 0 degrees less than or equal to x less than or equal to 360 degrees.

Find the derivative of f(x) = 4x cubed minus 5x squared plus 7x minus 2. What is f prime of x?

Find the coordinates of the stationary point on the curve y = x cubed minus 3x plus 2 and determine whether it is a maximum or minimum.

Evaluate the definite integral of (6x squared plus 4x minus 5) dx from x = 1 to x = 3.

Given vectors a = (3, 4) and b = (2, -1), what is the scalar (dot) product a dot b and what does the result indicate about the angle between the vectors?

A line passes through the point A with position vector (2, -1, 3) and has direction vector d = (1, 4, -2). Which equation correctly represents this line in vector form?

For a normal distribution with mean 100 and standard deviation 15, approximately what percentage of the data falls within one standard deviation of the mean?