8/2/2019 _STPM Trials 2009 Math T Paper 1 (KL)

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8/2/2019 _STPM Trials 2009 Math T Paper 1 (KL)

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" CONFIDENTIAL< 21 Find the equation of the normal to the curve y + f + 3 In y "" 2 at the point (1,1). [4 marks]2 Find the set of values ofx so that the series f.d x ) '( is c2,nvergent. . Determ ine the value. - o ~ 3 + x \ofx i f he sum is 9. .... .J. !:y [5 marks]

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8/2/2019 _STPM Trials 2009 Math T Paper 1 (KL)

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CONFIDENTIAL-

10 The functions f and g a . r ~ e f i n e by :f : x f - 7 2 + ~ l g : x f - 7 l + x ' . r E ~

(a) Give the range of f. .

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(b) Detennine the inverse function r-I 3nd state its domain.(e) Show that the ran ge of g is a subset of the domain of f.[I mark][3 marks]

Hence determine the composite function fog. giv ing its domain and the co rrespondingrange. " 4' maries](d) Sketch, on the same diagram, the graphs off and r-1, ..! qrks]L11 Find the equation of the t . a n g e n t ~ o the hyperbola x y ~ c':.a{ the point {cp , ;).

The perpendicular lin