Higher Plus

On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A car covers 620 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.

Simplify (x² + 13x + 42)/(x + 7).Simplify (x^2 + 13x + 42)/(x + 7).

A cyclist speeds up steadily from 9 m/s to 15 m/s over 8 seconds. Use the area under the velocity-time graph to find the distance travelled.

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.