Higher Plus

The point (10, 24) lies on the circle x² + y² = 676. Work out the gradient of the tangent to the circle at that point.The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.

A bag holds 4 red, 5 blue and 3 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 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A block has mass 640 g (to the nearest 10 g) and volume 18 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 640 g (to the nearest 10 g) and volume 18 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 (12x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.