Higher Plus

On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?

Rationalise the denominator of 4/2, giving your answer in its simplest form.Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.

Use the iteration x(n+1) = cube root of (6x(n) + 9) with x(0) = 5. Work out x(1) to 3 decimal places.

A tram runs at 12 m/s for 10 s, then slows steadily to rest over 4 s. Work out its average speed for the whole journey, to 2 decimal places.

The point (9, 12) lies on the circle x² + y² = 225. Work out the gradient of the tangent to the circle at that point.The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.