Daily Practice - Higher Plus

A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?

Expand and simplify (7 + √7)(7 - √7).Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).

Use the iteration x(n+1) = cube root of (11x(n) + 1) with x(0) = 1. Work out x(1) to 3 decimal places.

y is directly proportional to x². When x = 3, y = 72. Work out the positive value of x when y = 72.y is directly proportional to x^2. When x = 3, y = 72. Work out the positive value of x when y = 72.

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.