Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?

A block has mass 210 g (to the nearest 10 g) and volume 10 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 210 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Simplify (x² + 6x - 7)/(x + 7).Simplify (x^2 + 6x - 7)/(x + 7).

A tram runs at 13 m/s for 10 s, then slows steadily to rest over 10 s. Work out its average speed for the whole journey, to 2 decimal places.

The point (20, 21) lies on the circle x² + y² = 841. Work out the gradient of the tangent to the circle at that point.The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.