Daily Practice - Higher Plus

On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

Rationalise the denominator of 4/√2, giving your answer in its simplest form.Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.

The curve y = sin x° is drawn for 0 ≤ x ≤ 360. Write down the value of y when x = 270.The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.

A tram runs at 14 m/s for 30 s, then slows steadily to rest over 10 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.