Daily Practice - Higher Plus

The point (8, 15) lies on the circle x² + y² = 289. Work out the gradient of the tangent to the circle at that point.The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.

A bag holds 6 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 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A block has mass 200 g (to the nearest 10 g) and volume 10 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 200 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Solve x² + y² = 225 and y = x + 3 simultaneously.Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.