Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?

A block has mass 490 g (to the nearest 10 g) and volume 16 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 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

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

A cyclist speeds up steadily from 4 m/s to 18 m/s over 10 seconds. Use the area under the velocity-time graph to find the distance travelled.

The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at that point.The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.