Higher Plus

On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?

A block has mass 420 g (to the nearest 10 g) and volume 19 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 420 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Write x² - 14x - 12 in the form (x + a)² + b.Write x^2 - 14x - 12 in the form (x + a)^2 + b.

A cyclist speeds up steadily from 4 m/s to 19 m/s over 4 seconds. Use the area under the velocity-time graph to find the distance travelled.

The point (5, 12) lies on the circle x² + y² = 169. Work out the gradient of the tangent to the circle at that point.The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.