Higher Plus

On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?

A car covers 310 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.

A tram runs at 17 m/s for 20 s, then slows steadily to rest over 10 s. Work out its average speed for the whole journey, to 2 decimal places.

The point (12, 16) lies on the circle x² + y² = 400. Work out the gradient of the tangent to the circle at that point.The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.