Higher Plus

On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?

Rationalise the denominator of 99/11, giving your answer in its simplest form.Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.

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 (20, 21) lies on the circle x² + y² = 841. Work out the gradient of the tangent to the circle at that point.The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.