Daily Practice - Higher Plus

A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?

Rationalise the denominator of 6/3, giving your answer in its simplest form.Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.

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 = 6, y = 324. Work out the positive value of x when y = 225.y is directly proportional to x^2. When x = 6, y = 324. Work out the positive value of x when y = 225.

The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at that point.The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.