Daily Practice - Higher Plus

A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?

Expand and simplify (2 + √7)(2 - √7).Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).

Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.

y is directly proportional to x². When x = 3, y = 81. Work out the positive value of x when y = 81.y is directly proportional to x^2. When x = 3, y = 81. Work out the positive value of x when y = 81.

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.