Daily Practice - Higher Plus

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.

A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.

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 430 g (to the nearest 10 g) and volume 25 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 430 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.