Daily Practice - Higher Plus

A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?

A block has mass 490 g (to the nearest 10 g) and volume 24 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 490 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

A quadratic sequence starts 1, 15, 37, 67. Work out the second difference, and the coefficient of n².A quadratic sequence starts 1, 15, 37, 67. Work out the second difference, and the coefficient of n^2.

y is directly proportional to x². When x = 6, y = 288. Work out the positive value of x when y = 72.y is directly proportional to x^2. When x = 6, y = 288. Work out the positive value of x when y = 72.

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.