Higher Plus

On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?

A block has mass 900 g (to the nearest 10 g) and volume 5 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 900 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Simplify (x² - 7x + 12)/(x - 4).Simplify (x^2 - 7x + 12)/(x - 4).

A tram runs at 15 m/s for 30 s, then slows steadily to rest over 4 s. Work out its average speed for the whole journey, to 2 decimal places.

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.