Daily Practice - Higher Plus

A cuboid measures 8 cm by 9 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.

A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?

On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A block has mass 620 g (to the nearest 10 g) and volume 17 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 17 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.