IJC_H2_MATH_P1_(9740)

INNOVA JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION in preparation for General Certificate of Education Advanced Level Higher 2 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Additional Materials: Answer Paper Cover Page List of Formulae (MF 15) 9740/01 28 August 2017 3 hours READ THESE INSTRUCTIONS FIRST Do not open this booklet until you are told to do so. Write your name, class and index number on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. 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 a graphic calculator. Unsupported answers from a graphic calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphic 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. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 6 printed pages.      Innova Junior College  [Turn over

2    IJC/2017/JC2 9740/01/August/17   1 Prove by the method of mathematical induction that   0 !1 ! 1 n r rr n    . [5] 2 (i) Find ec o s d x n nx x , where n is a positive constant. [3] (ii) Hence find the exact value of  2 ec o s d x n nx x   . [2] 3 The vectors p and q are given by p  2i + j +ak and q  bi + j, where a and b are non-zero constants. (i) Find (2 5 ) (2 5 )pq pq in terms of a and b. [2] Given that the i- and j- components of the answer to part (i) are equal, find the value of b. [1] Use the value of b you have found to solve parts (ii) and (iii). (ii) Given that the magnitude of (2 5 ) (2 5 ) pq pq is 80, find the possible exact values of a. [2] (iii) Given instead that 25pq and 25pq are perpendicular, find the exact value of p . [3] 4 A graphic calculator is not to be used in answering this question. (a) The equation 32 30 0wp wq w   , where p and q are real constants, has a root 2iw . Find the values of p and q, showing your working. [3] (b) The equation 2 (5 2 i ) ( 2 1 i ) 0zz     has a root 3izu  , where u is real constant. Find the value of u and hence find the second root of the equation in cartesian form, iab , showing your working. [5]

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