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 260 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

Use the iteration x(n+1) = cube root of (7x(n) + 2) with x(0) = 5. Work out x(1) to 3 decimal places.

A tram runs at 12 m/s for 30 s, then slows steadily to rest over 6 s. Work out its average speed for the whole journey, to 2 decimal places.

The point (10, 24) lies on the circle x² + y² = 676. Work out the gradient of the tangent to the circle at that point.The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.