Daily Practice - Higher Plus

On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A block has mass 740 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 740 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.

Solve x² + y² = 676 and y = x + 14 simultaneously.Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.

A cyclist speeds up steadily from 7 m/s to 17 m/s over 8 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 tangent meets a radius at the point of contact. State the reason being quoted.