A-Level MathematicsYear 2020Q5
16 5. (a) y = tan−1 x Assuming the derivative of tan x , prove that d d y x x = + 1 1 2 (3) f ( x ) = x tan−1 4x (b) Show that f d ( ) tan tan x x Ax x Bx C x k ∫ = + + + − − 2 1 1 4 4 where k is an arbitrary constant and A, B and C are constants to be determined. (5) (c) Hence find, in exact form, the mean value of f( x ) over the interval 0 3 4 , (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________
Paper Source:9FM0_02_que_20201009.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)