Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?

Rationalise the denominator of 14/√2, giving your answer in its simplest form.Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.

Write 3/(x - 6) + 4/(x + 2) as a single fraction.

A cyclist speeds up steadily from 3 m/s to 10 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.