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?

Rationalise the denominator of 66/11, giving your answer in its simplest form.Rationalise the denominator of 66/sqrt(11), giving your answer in its simplest form.

Write x² - 16x - 15 in the form (x + a)² + b.Write x^2 - 16x - 15 in the form (x + a)^2 + b.

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 (9, 12) lies on the circle x² + y² = 225. Work out the gradient of the tangent to the circle at that point.The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.