Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?

A block has mass 450 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 450 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.

Work out the coordinates of the turning point of y = x² + 10x - 11.Work out the coordinates of the turning point of y = x^2 + 10x - 11.

A tram runs at 20 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 (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.