ACJC 2020_H2_Prelim_P1

ANGLO-CHINESE JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME TUTORIAL/ INDEX FORM CLASS NUMBER MATHEMATICS 9758/01 Paper 1 25 August 2020 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 calculat or 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. This document consists of __ printed pages. [Turn Over Question Marks 1 /6 2 /6 3 /7 4 /8 5 /8 6 /9 7 /10 8 /10 9 /12 10 /12 11 /12 /100

2 ANGLO-CHINESE JUNIOR COLLEGE 2020 H2 MATHEMATICS 9758/01 1 (i) Use the substitution u = 2x – 1 to find 2 d 1 (2 1) x x x−−∫ . [4] (ii) Hence find 1sin (2 1) dxx− −∫ . [2] 2 The diagram above shows the graph of f( )yx= . The curve has turning points ( )1, 2−− and ( )2, 0.5− . It cuts the x-axis at 1x = and 2.5x = . The curve has asymptotes with equations 0x = , 3y = and 3yx= + . Sketch, on separate diagrams, the graphs of (i) ( )f'yx= , [3] (ii) ( ) 1 fy x= , [3] including the coordinates of the points where the graphs cross the axes, the turning points , and the equations of any asymptotes if possible. x y O

3 ANGLO-CHINESE JUNIOR COLLEGE 2020 H2 MATHEMATICS 9758/01 3 It is given that ( )fyx= , where ( ) 3f e sec 2 xxx = . (i) Show that ( ) ( )f ' 3 2 tan 2xy x= + . [1] (ii) Find the Maclaurin series for ( )f x , up to and including the term in 2x . [3] (iii) Hence find the first two non- zero terms in the Maclaurin series for ( )( )3e sec 2 3 2 tan 2x xx + . [1] (iv) Using the standard series from the List of Formulae (MF26), verify the result found in part (ii). [2] 4 (i) Given that 0<a and 1<−b , find the roots of the equation b xa xa b−= − , where a and b are constants. [2] (ii) If 0ab