Daily Practice - Higher Plus

A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?

Expand and simplify (8 + √5)(8 - √5).Expand and simplify (8 + sqrt(5))(8 - sqrt(5)).

Solve x² + y² = 100 and y = x - 2 simultaneously.Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.

y is directly proportional to x². When x = 6, y = 72. Work out the positive value of x when y = 128.y is directly proportional to x^2. When x = 6, y = 72. Work out the positive value of x when y = 128.

The point (9, 40) lies on the circle x² + y² = 1681. Work out the gradient of the tangent to the circle at that point.The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.