Edexcel C1 2011 June — Question 6

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2011
SessionJune
TopicIndices and Surds

6. Given that \(\frac { 6 x + 3 x ^ { \frac { 5 } { 2 } } } { \sqrt { } x }\) can be written in the form \(6 x ^ { p } + 3 x ^ { q }\),
  1. write down the value of \(p\) and the value of \(q\). Given that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 x + 3 x ^ { \frac { 5 } { 2 } } } { \sqrt { } x }\), and that \(y = 90\) when \(x = 4\),
  2. find \(y\) in terms of \(x\), simplifying the coefficient of each term.