Daily Practice - Higher Plus

In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.

A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.

On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A block has mass 890 g (to the nearest 10 g) and volume 11 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 890 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

The point (5, 0) lies on y = f(x). Write down its image on y = f(x - 5).