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?

Expand and simplify (3 + √11)(3 - √11).Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).

Solve x² + y² = 225 and y = x - 3 simultaneously.Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.

A cyclist speeds up steadily from 8 m/s to 16 m/s over 10 seconds. Use the area under the velocity-time graph to find the distance travelled.

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.