Higher Plus

On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?

A block has mass 700 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 700 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.

Make x the subject of 2x + 4 = y(x + 4).

A cyclist speeds up steadily from 9 m/s to 28 m/s over 10 seconds. Use the area under the velocity-time graph to find the distance travelled.

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.