Daily Practice - Higher Plus

On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

Rationalise the denominator of 8/√2, giving your answer in its simplest form.Rationalise the denominator of 8/sqrt(2), giving your answer in its simplest form.

Solve x² + y² = 289 and y = x - 7 simultaneously.Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.

A cyclist speeds up steadily from 8 m/s to 26 m/s over 4 seconds. Use the area under the velocity-time graph to find the distance travelled.

The point (12, 16) lies on the circle x² + y² = 400. Work out the gradient of the tangent to the circle at that point.The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.