Daily Practice - Higher Plus

The point (7, 24) lies on the circle x² + y² = 625. Work out the gradient of the tangent to the circle at that point.The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.

A bag holds 3 red, 6 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 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?

A block has mass 760 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 760 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.

A quadratic sequence starts 12, 33, 64, 105. Work out the second difference, and the coefficient of n².A quadratic sequence starts 12, 33, 64, 105. Work out the second difference, and the coefficient of n^2.