Daily Practice - 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 5 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?

A block has mass 390 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 390 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.

Use the iteration x(n+1) = cube root of (5x(n) + 6) with x(0) = 4. Work out x(1) to 3 decimal places.