Daily Practice - Higher Plus

On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?

A block has mass 430 g (to the nearest 10 g) and volume 18 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 430 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

The point (3, -6) lies on y = f(x). Write down its image on y = f(x + 3).

A cyclist speeds up steadily from 4 m/s to 17 m/s over 8 seconds. Use the area under the velocity-time graph to find the distance travelled.

The point (9, 12) lies on the circle x² + y² = 225. Work out the gradient of the tangent to the circle at that point.The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.