Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?

A block has mass 610 g (to the nearest 10 g) and volume 21 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 610 g (to the nearest 10 g) and volume 21 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 (9x(n) + 8) with x(0) = 1. Work out x(1) to 3 decimal places.

A tram runs at 16 m/s for 20 s, then slows steadily to rest over 10 s. Work out its average speed for the whole journey, to 2 decimal places.

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.