Maths with David

    9231. FP1. Rational Functions. Past Exam Questions

    1. November 2025 (9231/12). Question 7
      • The curve C has equation y = \frac{x^2 + x + 1}{x+1}
        • (a) Find the equations of the asymptotes of C. [3 marks]
        • (b) Find the coordinates of any stationary points on C. [3 marks]
        • (c) Sketch C. [3 marks]
        • (d) Sketch the curve with equation \frac{ {\lvert x \rvert}^2 + \lvert x \rvert + 1 }{ \lvert x \rvert + 1} [2 marks]
        • (e) Find, in exact form, the set of values of x for which \frac{ {\lvert x \rvert}^2 + \lvert x \rvert + 1 }{ \lvert x \rvert + 1} < 3 [3 marks]