CJC_9758_2024_Promo_Qns

9758/01/J1PROMO/2024 [Turn Over CATHOLIC JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 JC1 Promotional Examination CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 9758/01 Paper 1 7 Oct 2024 3 hours Candidates answer on the Question Paper. Additional Materials: Li st of Formulae (MF27) READ THESE INSTRUCTIONS FIRST Write your class, index number and name on the work you hand in. Write in dark blue or black pen. You may use a 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 signifi cant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. You are expected to use an approved graphing calculator. 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. Question 1 2 3 4 5 6 7 8 9 10 11 12 Total Marks Total 4 5 5 6 6 7 7 10 12 12 13 13 100 This document consists of 28 printed pages, including this cover page.

2 9758/01/J1PROMO/2024 1 A curve C has equation  lnyp x q x r x  , where p , q and r are constants. Given that C crosses the x -axis at the points where 1x , 2x and 5x , find the values of p , q and r , giving your answers correct to 3 decimal places. [4] 2 By expressing   37 132 x xx   as a single simplified fraction, solve exactly the inequality   37 132 x xx   . [3] Hence, solve exactly the inequality   3e 7 1 e3 e2 x xx    . [2] 3 It is given that 1 11 111 n r rr n  . (a) Find  1 5 1 1 n r rr    . [3] (b) Give a reason why the series in part (a) is convergent and state the value of 5 1 1r rr    . [2] 4 A curve C has equation 2 44 1 xxy x   . (a) Sketch C , stating clearly the equations of any asym ptotes, coordinates of turning points and points of intersection with the axes. [3] (b) By drawing a suitable graph on the same diagram in part (a), find the range of values of b , where 0b , such that the equation  22 2 2 14 421 4 1 xxx bx      has no real roots. [3] 5 Differentiate each of the following expressions with respect to x . (a) 31tan 2 x  [3] (b) ln 1 x x    [3]

3 9758/01/J1PROMO/2024 [Turn Over 6 It is given that  sin e 1xy . (a) Show that 2 2 2 dd edd xyy yxx  . [3] (b) Hence, find the Maclaurin series of y, up