2019 J2 RVHS H2 Math Prelim (with ans)

1 ©RIVER VALLEY HIGH SCHOOL 9758/01/2019 RIVER VALLEY HIGH SCHOOL 2019 JC2 Preliminary Examination Higher 2 NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Candidates answer on the Question Paper Additional Materials: List of Formulae (MF26) 9758/01 19 September2019 3 hours READ THESE INSTRUCTIONS FIRST This document consists of 5 printed pages. For examiner’s use only Question number Mark 1 2 3 4 5 6 7 8 9 10 Total Calculator Model: Write your class, index number and name on all the work you hand in. 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. Write your answers in the spaces provided in the question paper. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a diff erent level of accuracy is specified in the question. The use of an approved graphing calculator is expected, where appropriate. You are required to present the mathematical steps using mathematical notations and not calculator comma nds. 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. The total numbe r of marks for this paper is 100. www.KiasuExamPaper.com 628

2 ©RIVER VALLEY HIGH SCHOOL 9758/01/2019 1 Find the range of values of x that satisfy 21 51 x xx . [4] Hence deduce the range of values of x that satisfy 2 1 051 x xx . [2] 2. A curve f( )yx passes through the point (0 , 2) and dc os d2 yx xy . (i) Obtain the Maclaurin series of y in ascending powers of x, up to and including the term in 2x . Write down the equation of the tangent to the curve f( )yx at 0x . [4] (ii) Show that 4s i nyx . [2] (iii) Using your results in part (ii), and assuming x to be sufficiently small for terms in 3x and higher powers to be ignored, obtain the binomial series of y. [3] 3. The curve C has equation 2 2 2 xay xb , where a and b are positive integers. C passes through the point 9 ,02 §· ¨¸ ©¹ and the equation of an asymptote of C is 3x . (i) Show that 9a and 18b . [2] (ii) Sketch C, stating clearly the equations of asymptotes, the x-coordinates of turning points and axial intercepts. [4] (iii) Hence, giving your reasons, deduce the range of values o f h such that the graph of

2 2 2 8 1100 x y h , where h is a positive integer, intersects C at exac tly 6 distinct points. [2] 4. A function is said to be self-inverse when f = 1f for all x in the domain of f. Given that the function f is defined by f: ax bx cx a

ax b cx a , for , axx cz , ax, czx, , where a, b and c are positive constan