Daily Practice - Higher Plus

The point (20, 21) lies on the circle x² + y² = 841. Work out the gradient of the tangent to the circle at that point.The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.

A bag holds 5 red, 7 blue and 5 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 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A block has mass 670 g (to the nearest 10 g) and volume 15 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 670 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.