Daily Practice - Higher Plus

On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

Expand and simplify (2 + √11)(2 - √11).Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).

A quadratic sequence starts 10, 28, 56, 94. Work out the second difference, and the coefficient of n².A quadratic sequence starts 10, 28, 56, 94. Work out the second difference, and the coefficient of n^2.

A tram runs at 5 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 (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.