Higher Plus

On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

A car covers 830 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

Solve x² + y² = 225 and y = x + 3 simultaneously.Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.

A tram runs at 8 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 (7, 24) lies on the circle x² + y² = 625. Work out the gradient of the tangent to the circle at that point.The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.