Daily Practice - 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 3 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 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A block has mass 590 g (to the nearest 10 g) and volume 20 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 590 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Solve 8x² - 2x - 3 = 0.Solve 8x^2 - 2x - 3 = 0.