Higher Plus

The point (5, 12) lies on the circle x² + y² = 169. Work out the gradient of the tangent to the circle at that point.The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.

A bag holds 5 red, 6 blue and 4 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 40-wide bar have the same frequency density of 2. How many more values are in the wider class?

A block has mass 510 g (to the nearest 10 g) and volume 15 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 510 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

f(x) = 3x - 9. Work out the inverse function f^-1(x).f(x) = 3x - 9. Work out the inverse function f^-1(x).