Daily Practice - Higher Plus

On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

Expand and simplify (3 + 7)(3 - 7).Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).

Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.

A tram runs at 15 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 (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.