Mathematics Past Questions and Answers

Find the coefficient of \(x^3\) in the binomial expansion of \((3x + 4)^4\) in ascending powers of x.

A function is defined by \(h : x \to 2 - \frac{1}{2x - 3}, x \neq \frac{3}{2}\). Find \(h^{-1}(\frac{1}{2})\).

The radius of a sphere is increasing at a rate \(3cm s^{-1}\). Find the rate of increase in the surface area, when the radius is 2cm.

<table class='tbn'><tbody><tr><td> Age in years </td><td> 10 - 14 </td><td> 15 - 19 </td><td> 20 - 24 </td><td> 25 - 29 </td><td> 30 - 34 </td></tr><tr><td> Frequency </td><td> 6 </td><td> 8 </td><td> 14 </td><td> 10 </td><td> 12 </td></tr></tbody></table><br/><br/>What is the class mark of the median class?

<table class='tbn'><tbody><tr><td> Age in years </td><td> 10 - 14 </td><td> 15 - 19 </td><td> 20 - 24 </td><td> 25 - 29 </td><td> 30 - 34 </td></tr><tr><td> Frequency </td><td> 6 </td><td> 8 </td><td> 14 </td><td> 10 </td><td> 12 </td></tr></tbody></table> <br/><br/>In which group is the upper quartile?