Daily Practice - Higher Plus

On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?

A car covers 700 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

f(x) = 3x - 8. Work out the inverse function f^-1(x).f(x) = 3x - 8. Work out the inverse function f^-1(x).

A cyclist speeds up steadily from 6 m/s to 24 m/s over 4 seconds. Use the area under the velocity-time graph to find the distance travelled.

The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at that point.The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.