Higher Plus

On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. 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.

A quadratic sequence starts 10, 28, 56, 94. Work out the second difference, and the coefficient of n².A quadratic sequence starts 10, 28, 56, 94. Work out the second difference, and the coefficient of n^2.

A tram runs at 7 m/s for 30 s, then slows steadily to rest over 6 s. Work out its average speed for the whole journey, to 2 decimal places.

The point (10, 24) lies on the circle x² + y² = 676. Work out the gradient of the tangent to the circle at that point.The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.