November 2025 (9709/12). Question 1

(a) Express 9x² – 36x + 8 in the form p(x+q)² + r, where p, q and r are constants [2 marks]

(b) Hence find the set of values of the constant k for which the equation 9x² – 36x + 8 = k has no real roots [1 mark]

(c) Find the exact roots of the equation 9x² – 36x + 8 = -15. [2 marks]

9709/11/M/J/25q6 – Mark Scheme

The equation of a curve is 2x³ – kxy + 2 = 0 and the equation of a line is y = px + 3, where k and p are constants.

(a) Given that k=2 and p=11, find the coordinates of the points of intersection of the curve and the line. [4 marks]

(b) Given instead that p=4, find the set of values of k for which the curve and the line do not intersect. [5 marks]

9709/12/M/J/25q2

Find the coordinates of the points of intersection of the curve and the line with equations and [4 marks]

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