Daily Practice - Higher Plus

On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?

A block has mass 490 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 490 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 (3x(n) + 5) with x(0) = 5. Work out x(1) to 3 decimal places.

A cyclist speeds up steadily from 8 m/s to 17 m/s over 10 seconds. Use the area under the velocity-time graph to find the distance travelled.

In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.