2019 J2 ACJC H2 Math Prelim (with ans)

ANGLO-CHINESE JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME TUTORIAL/ INDEX FORM CLASS NUMBER MATHEMATICS 9758/01 Paper 1 29 August 2019 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your index number, class 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 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 u nless 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. __________________________________________________________________________________ This document consists of __ printed pages. [Turn Over www.KiasuExamPaper.com 3

2 ANGLO-CHINESE JUNIOR COLLEGE 2019 H2 MATHEMATICS 9758/01 1 The points A(2, 3) and B(3,1) are on a curve with equation f( )yx . The corresponding points on the curve y  f a(x  b)  are A (7, 3) and B (1,1). Find the values of a and b. [3] 2 Use differentiation to find the area of the largest rectangle w ith sides parallel to the coordinate axes, lying above the x-axis and below the curve with equation 244 4yx x . [5] 3 Solve the equation 2 3 231 xx xx   exactly. [4] Hence, by sketching appropriate graphs, solve the inequality 2 3 231 xx xx   exactly. [2] 4 A kite 50 m above ground is being blown away from the per son holding its string in a direction parallel to the ground at a rate 5 m per second. Assuming that the string is taut, at the instan t when the leng th of th e string already let out is 100 m, find, leaving your answers in exact form, (i) the rate of change of the angle between the string and the ground, [3] (ii) the rate at which the string of the kite should be let out, [4] 5 Given that   3tan 1 e xy  , show that  32d e1d xy kyx  , where k is a constant to be determined. By further differentiation of this result, or otherwise, find the first three non- zero terms in the Maclaurin series for   3tan 1 e x . [5] The first two terms in the Maclaurin series for   3tan 1 e x are equal to the first two non- zero terms in the series expansion of x ab x . Find