Daily Practice - Higher Plus

A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?

A block has mass 480 g (to the nearest 10 g) and volume 6 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 480 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.

y is directly proportional to x². When x = 4, y = 96. Work out the positive value of x when y = 150.y is directly proportional to x^2. When x = 4, y = 96. Work out the positive value of x when y = 150.

The point (8, 15) lies on the circle x² + y² = 289. Work out the gradient of the tangent to the circle at that point.The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.