RVHS_9758_2025_Prelim_P1

1 ©RIVER VALLEY HIGH SCHOOL 9758/01/2025 RIVER VALLEY HIGH SCHOOL 2025 JC2 Preliminary Examination Higher 2 NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Additional Materials: Printed Answer Booklet List of Formulae (MF27) 9758/01 17 Sep 2025 3 hours READ THESE INSTRUCTIONS FIRST This document consists of 6 printed pages and 2 blank pages. Write your class, index number 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 on the Printed Answer Booklet. Follow the instructions on the front cover of the answer booklet. 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. 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 must show all necessary working clearly. 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.

2 ©RIVER VALLEY HIGH SCHOOL 9758/01/2025 1 The function f is defined by ( ) 32f x ax bx cx d= + + + where a, b, c and d are real numbers. Given that 4i+ and 1− are roots of ( )f0 x = , find b, c and d in terms of a. [4] 2 Without using a calculator, solve the inequality 2 95 .11 x xx +−+ [3] Hence solve 2 9 e 5 .1 e e 1 x xx +−+ [3] 3 Do not use a calculator in answering this question. Find the roots of the equation ( ) 2 1 2i 1 7i 0zz− + + + = , giving your answers in the cartesian form iab+ . [6] 4 It is given that 1 11 1( 1) 1 n r r r n= =−++ . (a) Find ( )( )1 1 12 N r rr= ++ in terms of N. [3] (b) It is given that 11 118 ( 1) ( 1) k r k r r r r r  = + = =++ . Find the value of k. [3] 5 (a) Find 4 d 16 x x x− . [2] (b) Find 2 1sin d24 xx x−   . [5]

3 ©RIVER VALLEY HIGH SCHOOL 9758/01/2025 6 For any vectors m and n, explain why ( ) 0.  =m m n [1] With respect to the origin O, the points A, B and C have position vectors a, b and c respectively. O, A, B and C are non-coplanar. T