Daily Practice - Higher Plus

In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.

A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.

On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A block has mass 450 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 450 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 = 100 and y = x + 2 simultaneously.Solve x^2 + y^2 = 100 and y = x + 2 simultaneously.