CAIE Further Paper 1 2024 November — Question 6

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2024
SessionNovember
TopicCurve Sketching
TypeSolve |f(x)| > k using sketch

6 The curve \(C\) has equation \(y = \frac { 4 x ^ { 2 } + x + 1 } { 2 x ^ { 2 } - 7 x + 3 }\).
  1. Find the equations of the asymptotes of \(C\).
  2. Find the coordinates of any stationary points on \(C\).
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  3. Sketch \(C\), stating the coordinates of any intersections with the axes.
  4. Sketch the curve with equation \(y = \left| \frac { 4 x ^ { 2 } + x + 1 } { 2 x ^ { 2 } - 7 x + 3 } \right|\) and state the set of values of \(k\) for which \(\left| \frac { 4 x ^ { 2 } + x + 1 } { 2 x ^ { 2 } - 7 x + 3 } \right| = k\) has 4 distinct real solutions.