Daily Practice - Higher Plus

The point (9, 12) lies on the circle x² + y² = 225. Work out the gradient of the tangent to the circle at that point.The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.

A bag holds 5 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 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?

Rationalise the denominator of 6/√3, giving your answer in its simplest form.Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.

Use the iteration x(n+1) = cube root of (8x(n) + 5) with x(0) = 3. Work out x(1) to 3 decimal places.