XJC H2 Math - Set 1 - P1 (QP)

X Junior College [Turn over This document consists of 5 printed pages and 3 blank pages. X JUNIOR COLLEGE YEAR 6 PRELIMINARY EXAMINATION Mock Arrangement in preparation for Candidates’ Examination Higher 2 MATHEMATICS Paper 1 Additional Materials: Answer Paper Graph paper List of Formulae and Results (MF27) 9758/01 Set I 3 hours READ THESE INSTRUCTIONS FIRST Write your name on the work you hand in. Write in dark blue or black pen on both sides of the paper. 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. 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 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. ABOUT THIS PAPER X Junior College (XJC) is an unofficial initiative aimed at preparing pre-university and/or junior college students in Singapore for school-level and/or national-level H2 Mathematics examinations through self-prepared mock papers. It has no affiliation with any existing institution in Singapore or worldwide. This mock paper follows closely the 9758 H2 Mathematics GCE Advanced Level syllabus, most suitable for preparation towards preliminary examinations and A–Levels. The paper intends to explore the unconventional ways and/or applications in which topics within the syllabus can be tested, which may affect the difficulty of this paper to varying degrees. While it is ideal to attempt this paper under examination constraints, prospective candidates are reminded not to use this potentially non-conforming paper as a definitive gauge for actual performance. (For enquiries, mail to: xjuniorcollege@gmail.com)

© XJC 9758/01/I 2 1 When the complex polynomial P(𝑧) is divided by (𝑧+i), (𝑧−i) and (𝑧2+1), the remainders are 1+i, 1−i and 𝐴𝑧+𝐵 respectively. Find 𝐴 and 𝐵. [3] 2 An arithmetic sequence with first term 𝑎 and common difference 𝑑 is such that the sum of its first 𝑛 terms is 𝑚, and the sum its first 𝑚 terms is 𝑛. (a) Find 𝑎 and 𝑑 in terms of 𝑚 and 𝑛. [4] (b) Hence, show that the sum of the first (𝑚+𝑛) terms of the sequence is −(𝑚+𝑛). [2] 3 A complex number 𝑧=𝑥+i𝑦, where 𝑥 and 𝑦 are real, satisfies |𝑧+3|=2Re(𝑧). (a) Show that 𝑥 and 𝑦 are related by the equation of a hyperbola. State the equations of its asymptotes. [3] (b) Sketch the part of