AQA FP1 2010 January — Question 7

Exam BoardAQA
ModuleFP1 (Further Pure Mathematics 1)
Year2010
SessionJanuary
TopicCurve Sketching
TypeSketch rational with linear numerator

7 A curve \(C\) has equation \(y = \frac { 1 } { ( x - 2 ) ^ { 2 } }\).
    1. Write down the equations of the asymptotes of the curve \(C\).
    2. Sketch the curve \(C\).
  1. The line \(y = x - 3\) intersects the curve \(C\) at a point which has \(x\)-coordinate \(\alpha\).
    1. Show that \(\alpha\) lies within the interval \(3 < x < 4\).
    2. Starting from the interval \(3 < x < 4\), use interval bisection twice to obtain an interval of width 0.25 within which \(\alpha\) must lie.