2019 J2 TMJC H2 Math Prelim (with ans)

Tampines Meridian Junior College 2019 JC2 Prelim H2 Math CANDIDATE NAME CIVICS GROUP __________________________________________________________________________________ H2 MATHEMATICS 9758/01 Paper 1 18 September 2019 3 hours Candidates answer on the question paper. Additional material: List of Formulae (MF26) ________________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your name and civics group 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 different level of accuracy is specified in the question. The use of an approved graphing calculator is expected, where appropriate. Unsupported answers from a graphing calculator are allowed unless 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. The total number of marks for this paper is 100. _________________________________________________________________________________ TAMPINES MERIDIAN JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION For Examiners’ Use 1 2 3 4 5 6 7 8 9 10 11 Total [Turn Over www.KiasuExamPaper.com 806

2 1 Using an algebraic method, solve the inequality    2 1 1.4 21 1 x x x x   [4] Hence or otherwise, solve the inequality    2ee 1 1 e 4 21 e 1 xx xx     , leaving your answers in exact form. [2] 2 Referred to the origin O, A is a fixed point with position vector a, and d is a non-zero vector. Given that a general point R has position vector r such that rd ad ,s h o w that ,ra d where  is a real constant. Hence give a geometrical interpretation of r . [3] Let 12 2 and 1 35           ad . By writing r as x y z      , use rd ad to form three equations which represent cartesian equations of three planes. State the relationship between these three planes. [3] 3( i) The sum of the first n terms of a sequence is denoted by nS . It is known that 5 30S  , 14 168S  and 18 10 9.SS  Given that nS is a quadratic polynomial in n, find nS in terms of n.[ 4] (ii) The nth term of the sequence is denoted by nT . Find an expression for nT in terms of n. Hence find the set of values of n for which 12nT  .[ 4] 4( i) Given that f is a strictly inc reasing continuous function, explain, with the aid of a sketch, why  1 0 10 1 1f f ... f f d n xxnn n n  ½     ¾  