Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?

A block has mass 830 g (to the nearest 10 g) and volume 6 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 830 g (to the nearest 10 g) and volume 6 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 (12x(n) + 7) with x(0) = 4. Work out x(1) to 3 decimal places.

A tram runs at 5 m/s for 10 s, then slows steadily to rest over 6 s. Work out its average speed for the whole journey, to 2 decimal places.

In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.