Daily Practice - Higher Plus

On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?

A block has mass 780 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 780 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.

Solve x² + y² = 289 and y = x - 7 simultaneously.Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.

A cyclist speeds up steadily from 6 m/s to 24 m/s over 8 seconds. Use the area under the velocity-time graph to find the distance travelled.

The point (10, 24) lies on the circle x² + y² = 676. Work out the gradient of the tangent to the circle at that point.The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.