Daily Practice - Higher Plus

On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?

x = 122 and y = 74, each correct to the nearest whole number. Work out the upper bound of x - y.

f(x) = 3x - 7. Work out the inverse function f^-1(x).f(x) = 3x - 7. Work out the inverse function f^-1(x).

A tram runs at 8 m/s for 20 s, then slows steadily to rest over 10 s. Work out its average speed for the whole journey, to 2 decimal places.

The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at that point.The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.