Higher Plus

On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?

A block has mass 520 g (to the nearest 10 g) and volume 15 cm³ (to the nearest cm³). Work out the upper bound of its density, to 2 decimal places.A block has mass 520 g (to the nearest 10 g) and volume 15 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 12, 19, 28, 39, ...

A tram runs at 19 m/s for 20 s, then slows steadily to rest over 6 s. Work out its average speed for the whole journey, to 2 decimal places.

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.