Edexcel P1 2022 October — Question 6

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2022
SessionOctober
TopicCurve Sketching
TypePolynomial with rational/modulus curves

  1. (a) Given that \(k\) is a positive constant such that \(0 < k < 4\) sketch, on separate axes, the graphs of
    1. \(y = ( 2 x - k ) ( x + 4 ) ^ { 2 }\)
    2. \(y = \frac { k } { x ^ { 2 } }\)
      showing the coordinates of any points where the graphs cross or meet the coordinate axes, leaving coordinates in terms of \(k\), where appropriate.
      (b) State, with a reason, the number of roots of the equation
    $$( 2 x - k ) ( x + 4 ) ^ { 2 } = \frac { k } { x ^ { 2 } }$$