CJC_9758_2022_Promo_QP

9758/01/J1Promo/2022 [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 03 Oct 2022 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) 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 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 approving graphing calculator is expected, where appropriate. Unsupported answers from a graphing calculator are allowed unl ess 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 5 6 6 7 8 8 8 9 9 10 12 12 100 This document consists of 25 printed pages and 1 blank page.

2 9758/01/J1Promo/2022 1 (i) Sketch, on the same diagram, the graphs of 23yx and 22 8 3y x x   . (You are not required to label any axial intercepts and stationary points.) [2] (ii) Solve exactly the inequality 22 3 2 8 3x x x    . [3] 2 The second, fifth and tenth terms of an arithmetic series with non-zero common difference are the first three terms of a geometric series respectively. (i) Find the common ratio. [3] It is further given that the first terms of the arithmetic and geometric series are 7 and 9 respectively. (ii) Find the least value of n for which the nth term of the arithmetic series is smaller than the nth term of the geometric series by at least 1000. [3] 3 The curve C defined by 1 2 axy bx   passes through  3, 13 and has vertical asymptote 2x . (i) Find the values of a and b . [2] (ii) Describe a sequence of three transformations that transform the graph of 1y x onto the graph of C . [4] 4 It is known that the thn term of a sequence is given by  4 n nu p qn r    , where p , q and r are constants. It is given that 1 6u  , 2 0u  and 3 15 4u  . (i) Find p , q and r . [3] (ii) Show   2 1 4 n n r r u A B Cn Dn      where A , B , C and D are constants to be determined. [4]

3 9758/01/J1Promo/2022 [Turn