Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?

A block has mass 660 g (to the nearest 10 g) and volume 12 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 660 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

Work out the nth term of the quadratic sequence 9, 26, 51, 84, ...

A tram runs at 4 m/s for 10 s, then slows steadily to rest over 6 s. Work out its average speed for the whole journey, to 2 decimal places.

The point (12, 16) lies on the circle x² + y² = 400. Work out the gradient of the tangent to the circle at that point.The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.