Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?

A block has mass 580 g (to the nearest 10 g) and volume 6 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 580 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

f(x) = 4x - 9 and g(x) = 2x - 4. Work out fg(5).

A tram runs at 8 m/s for 20 s, then slows steadily to rest over 4 s. Work out its average speed for the whole journey, to 2 decimal places.

The point (8, 15) lies on the circle x² + y² = 289. Work out the gradient of the tangent to the circle at that point.The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.