Daily Practice - Higher Plus

On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?

A block has mass 380 g (to the nearest 10 g) and volume 19 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 380 g (to the nearest 10 g) and volume 19 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 (11x(n) + 5) with x(0) = 5. Work out x(1) to 3 decimal places.

A tram runs at 5 m/s for 10 s, then slows steadily to rest over 4 s. Work out its average speed for the whole journey, to 2 decimal places.

A cuboid measures 11 cm by 12 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.