Daily Practice - Higher Plus

On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?

Rationalise the denominator of 20/√2, giving your answer in its simplest form.Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.

Use the iteration x(n+1) = cube root of (6x(n) + 1) with x(0) = 4. Work out x(1) to 3 decimal places.

A cyclist speeds up steadily from 8 m/s to 26 m/s over 6 seconds. Use the area under the velocity-time graph to find the distance travelled.

The point (20, 21) lies on the circle x² + y² = 841. Work out the gradient of the tangent to the circle at that point.The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.