2021 ASRJC H3 Math Questions

1 ASRJC 2021 MATHEMATICS 9820/01 Paper 1 22 September 2021 3 hours Additional Materials: Answer Booklet List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST An answer booklet will be provided with this question paper. You should follow the instructions on the front cover of the booklet. If you need additional answer paper ask the invigilator for a continuation booklet. 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. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 6 printed pages ANDERSON SERANGOON JUNIOR COLLEGE JC2 Preliminary Examinations 2021 Higher 3

2 ASRJC 2021 Answer all the questions. 1 Find the set of integer values of x that satisfy   43 1 0 mod5x x x    Express 43 1x x x   as a product (modulo 5) of four linear factors with integer coefficients. [6] 2 It is given that g is a function with domain  1, . Using the substitution tx  or otherwise , show that 00 g(sin )d g(sin )d2x x x x x   . Hence find the exact values of the following definite integrals, simplifying your answers. (a) › 2 0 sin d 8 sin xx x x     (b) › 0 1 sin dx x x   [9] 3 There are n identical balls to be distributed into k distinct boxes such that every box must be filled. (i) Find the number of ways if there are no restrictions. [1] (ii) It is given that n and k are both even and 2nk . (a) Find the number of ways if every box contains an even number of balls. [2] (b) Find the number of ways if every box contains an odd number of balls. [2] (iii) Use principle of inclusion and exclusion to find the number of ways to distribute the n objects if no box can have more th