2019 J2 SAJC H2 Math Prelim (with ans)

[Turn Over] ST ANDREW’S JUNIOR COLLEGE PRELIMINARY EXAMINATION MATHEMATICS HIGHER 2 9758/01 Wednesday 28 August 2019 3 hrs Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) NAME:_________________________________________( _____ ) C.G.: __ ________ TUTOR’S NAME: _________________________________________ SCIENTIFIC / GRAPHIC CALCULATOR MODEL: _______________________ READ THESE INSTRUCTIONS FIRST Write your name, civics group, index number and calculator models on the cover page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Total marks : 100 Write your answers in the spaces provided in the question paper. Give non-exact numerical answers correct to 3 significant figur es, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved graphing calculator is expected, where appropriate. Unsupported answers from a graphi ng calculator are allowed unle ss a question specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a question, you are required to present the mathematical steps using mathematical notations and not calculator commands. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. Question 1 2 3 4 5 6 7 8 9 10 TOTAL Marks 6 7 1 0 9 1 01 01 21 21 21 2 1 0 0 This document consists of 27 printed pages and 1 blank page including this page. www.KiasuExamPaper.com 681

2 [Turn Over 1 The diagram below shows the graph of 2f (3 )yx . The graph passes through the origin O, and two other points A 93, 4   and B(3,0). The equations of the vertical and horizontal asymptotes are 1x  and 2y  respectively. (a) State the range of values of k such that the equation f( 3 )xk has exactly two negative roots. [1] (b) By stating a sequence of two transformations which transforms the graph of 2f (3 )yx onto f( 3 )yx , find the coordinates of the minimum point on the graph of f( 3 )yx . Also, write down the equations of the vertical asymptote(s) and horizontal asymptote(s) of f( 3 )yx . [5] 2( i) On the same axes, sketch the curves with equations 226 4yx x  and 34 ,yx indicating any intercepts with the axes and points of intersecti on. Hence solve the inequality 234 2 6 4xx x  . [4] (ii) Find the exact area bounded by the graphs of 34yx , 226 4yx x  , x = 3 and x = 1 . [3] y xO A B(3,0) www.KiasuExamPaper.com 682

3 [Turn Over 3 The functions f and g are defined as follows: 4f: 1 xx x  6 , ,1xx 2g: 2 2xx x 6 , ,1xx  (i) Show that f has an inverse. [1] (ii) Show that 1ff  and hence evaluate 101f (101) . [5] (iii) Prove that the composite function fg exists and find