Daily Practice - Higher Plus

A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?

A block has mass 200 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 200 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.

Write 5/(x + 4) + 7/(x - 6) as a single fraction.

y is directly proportional to x². When x = 6, y = 108. Work out the positive value of x when y = 243.y is directly proportional to x^2. When x = 6, y = 108. Work out the positive value of x when y = 243.

The point (12, 16) lies on the circle x² + y² = 400. Work out the gradient of the tangent to the circle at that point.The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.