Daily Practice - Higher Plus

The point (12, 16) lies on the circle x² + y² = 400. Work out the gradient of the tangent to the circle at that point.The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.

A bag holds 3 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

Rationalise the denominator of 54/√6, giving your answer in its simplest form.Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.

Solve 3x² - 2x - 8 = 0.Solve 3x^2 - 2x - 8 = 0.