Higher Plus

The point (3, 4) lies on the circle x² + y² = 25. Work out the gradient of the tangent to the circle at that point.The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.

A bag holds 3 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?

A block has mass 810 g (to the nearest 10 g) and volume 5 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 810 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Write 4/(x + 4) + 7/(x + 3) as a single fraction.