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 5 red, 6 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 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?

Rationalise the denominator of 84/7, giving your answer in its simplest form.Rationalise the denominator of 84/sqrt(7), giving your answer in its simplest form.

Use the iteration x(n+1) = cube root of (10x(n) + 6) with x(0) = 5. Work out x(1) to 3 decimal places.