Daily Practice - Higher Plus

On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. 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.

Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.

A cyclist speeds up steadily from 6 m/s to 20 m/s over 8 seconds. Use the area under the velocity-time graph to find the distance travelled.

The point (7, 24) lies on the circle x² + y² = 625. Work out the gradient of the tangent to the circle at that point.The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.