Daily Practice - Higher Plus

On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A car covers 510 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.

A cyclist speeds up steadily from 7 m/s to 19 m/s over 8 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.