Daily Practice - Higher Plus

On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?

Expand and simplify (9 + 11)(9 - 11).Expand and simplify (9 + sqrt(11))(9 - sqrt(11)).

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

A tram runs at 4 m/s for 30 s, then slows steadily to rest over 6 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.