Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?

Expand and simplify (6 + √3)(6 - √3).Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).

In an algebraic proof, how would you write three consecutive integers in terms of an integer n?

A tram runs at 14 m/s for 30 s, then slows steadily to rest over 4 s. Work out its average speed for the whole journey, to 2 decimal places.

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.