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

A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?

A block has mass 360 g (to the nearest 10 g) and volume 21 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 360 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Use the iteration x(n+1) = cube root of (9x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.