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A-Level MathematicsYear 2021Q16

42 16. The curve C has equation y = f(x) where f(x) = ax 3 + 15x 2 – 39x + b and a and b are constants. Given • the point (2, 10) lies on C • the gradient of the curve at (2, 10) is –3 (a) (i) show that the value of a is –2 (ii) find the value of b. (4) (b) Hence show that C has no stationary points. (3) (c) Write f(x) in the form (x – 4)Q(x) where Q(x) is a quadratic expression to be found. (2) (d) Hence deduce the coordinates of the points of intersection of the curve with equation y = f(0.2x) and the coordinate axes. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________

Paper Source:8MA0_01_que_20211007.pdf

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Exam Specification Info

This question is part of the UK A-Level Mathematics syllabus. In the actual exam, structured questions typically require linking specific keywords to gain full marks. Applaa helps you drill these topics.

Syllabus levelAdvanced Level (A-Level)
SubjectMathematics
Official MarksVariable (2–6 marks)