Daily Practice - Higher Plus

A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?

A block has mass 830 g (to the nearest 10 g) and volume 8 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 830 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

f(x) = 4x - 8. Work out the inverse function f^-1(x).f(x) = 4x - 8. Work out the inverse function f^-1(x).

y is directly proportional to x². When x = 4, y = 144. Work out the positive value of x when y = 729.y is directly proportional to x^2. When x = 4, y = 144. Work out the positive value of x when y = 729.

The point (20, 21) lies on the circle x² + y² = 841. Work out the gradient of the tangent to the circle at that point.The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.