Higher Plus

On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?

A car covers 490 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

f(x) = 8x - 7. Work out the inverse function f^-1(x).f(x) = 8x - 7. Work out the inverse function f^-1(x).

A tram runs at 13 m/s for 10 s, then slows steadily to rest over 6 s. Work out its average speed for the whole journey, to 2 decimal places.

The point (9, 40) lies on the circle x² + y² = 1681. Work out the gradient of the tangent to the circle at that point.The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.