Higher Plus

The point (9, 40) lies on the circle x² + y² = 1681. Work out the gradient of the tangent to the circle at that point.The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.

A bag holds 5 red, 3 blue and 4 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 3. How many more values are in the wider class?

A block has mass 400 g (to the nearest 10 g) and volume 17 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 400 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

A quadratic sequence starts 4, 6, 12, 22. Work out the second difference, and the coefficient of n².A quadratic sequence starts 4, 6, 12, 22. Work out the second difference, and the coefficient of n^2.