Daily Practice - Higher Plus

A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?

Rationalise the denominator of 12/√2, giving your answer in its simplest form.Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.

The curve y = cos x° is drawn for 0 ≤ x ≤ 360. Write down the value of y when x = 180.The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.

y is directly proportional to x². When x = 3, y = 81. Work out the positive value of x when y = 576.y is directly proportional to x^2. When x = 3, y = 81. Work out the positive value of x when y = 576.

The point (7, 24) lies on the circle x² + y² = 625. Work out the gradient of the tangent to the circle at that point.The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.