Daily Practice - Higher Plus

The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at that point.The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.

A bag holds 6 red, 4 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 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?

A block has mass 690 g (to the nearest 10 g) and volume 25 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 690 g (to the nearest 10 g) and volume 25 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 (4x(n) + 8) with x(0) = 3. Work out x(1) to 3 decimal places.