Daily Practice - Higher Plus

A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?

A block has mass 520 g (to the nearest 10 g) and volume 12 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 520 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Solve x² + y² = 100 and y = x - 2 simultaneously.Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.

y is directly proportional to x². When x = 6, y = 216. Work out the positive value of x when y = 486.y is directly proportional to x^2. When x = 6, y = 216. Work out the positive value of x when y = 486.

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.