AQA C4 2014 June — Question 2 4 marks

Exam BoardAQA
ModuleC4 (Core Mathematics 4)
Year2014
SessionJune
Marks4
TopicStandard Integrals and Reverse Chain Rule

2
  1. Given that \(\frac { 4 x ^ { 3 } - 2 x ^ { 2 } + 16 x - 3 } { 2 x ^ { 2 } - x + 2 }\) can be expressed as \(A x + \frac { B ( 4 x - 1 ) } { 2 x ^ { 2 } - x + 2 }\), find the values of the constants \(A\) and \(B\).
  2. The gradient of a curve is given by $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 4 x ^ { 3 } - 2 x ^ { 2 } + 16 x - 3 } { 2 x ^ { 2 } - x + 2 }$$ The point \(( - 1,2 )\) lies on the curve. Find the equation of the curve.
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