Daily Practice - Higher Plus

The point (7, 24) lies on the circle x² + y² = 625. Work out the gradient of the tangent to the circle at that point.The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.

A bag holds 4 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?

Rationalise the denominator of 42/√7, giving your answer in its simplest form.Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.

Simplify (x² + x - 12)/(x + 4).Simplify (x^2 + x - 12)/(x + 4).