Daily Practice - Higher Plus

On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?

Rationalise the denominator of 88/√11, giving your answer in its simplest form.Rationalise the denominator of 88/sqrt(11), giving your answer in its simplest form.

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

A tram runs at 20 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 (8, 15) lies on the circle x² + y² = 289. Work out the gradient of the tangent to the circle at that point.The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.