Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?

A block has mass 620 g (to the nearest 10 g) and volume 12 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 620 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Solve x² + y² = 100 and y = x - 2 simultaneously.Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.

A tram runs at 15 m/s for 30 s, then slows steadily to rest over 4 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 OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.