Daily Practice - Higher Plus

On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?

A block has mass 850 g (to the nearest 10 g) and volume 7 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 850 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

f(x) = 6x - 3. Work out the inverse function f^-1(x).f(x) = 6x - 3. Work out the inverse function f^-1(x).

A cyclist speeds up steadily from 5 m/s to 23 m/s over 12 seconds. Use the area under the velocity-time graph to find the distance travelled.

The point (10, 24) lies on the circle x² + y² = 676. Work out the gradient of the tangent to the circle at that point.The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.