2020_H2_Prelim_P2

ANGLO-CHINESE JUNIOR COLLEGE JC2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME TUTORIAL/ INDEX FORM CLASS NUMBER MATHEMATICS 9758/02 Paper 2 28 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 signi ficant 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 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. The total number of marks for this paper is 100. This document consists of __ printed pages. [Turn Over Question Marks 1 /9 2 /9 3 /10 4 /12 5 /5 6 /6 7 /7 8 /7 9 /9 10 /12 11 /14 /100

2 ANGLO-CHINESE JUNIOR COLLEGE 2020 H2 MATHEMATICS 9758/02 Section A: Pure Mathematics [40 marks] 1 (a) If 2=a , 3−=ab and 5 2=a.b , use the cosine rule for triangles to find b . [3] (b) It is given that r ijkabc=++ where a, b and c are constants. Give the geometrical interpretations of (i) r.k , [1] (ii) rk× . [1] (iii) Given that kr p×= and rp k×= , in either order, show that 22 1ab+= and find the value of c. [4] 2 A scientist and his student are investigating the growth of bacteria in a petri dish. At time t minutes after the bacteria is first introduced into the dish, the number of bacteria in the dish is denoted by x, in hundreds . Initially, 100 bacteria were introduced into the dish. In 10 minutes, the number of bacteria became 400. (i) The student claims that the growth rate of the bacteria in the dish is inversely proportional to the square root of the number of bacteria in the dish. Write down a differential equation for this situation and solve it to get x as a function of t. [4] (ii) The scientist claims that ( ) 2d 100d x m xxt = − , where m is a constant. Show that 1e Hmt Hx A −= + , where H is a whole number to be determined. (You need not find the values of A and m.) [4] (iii) Whose model do you think is better, the student’s or the scientist’s? Justify your answer. [1]

3 ANGLO-CHINESE JUNIOR COLLEGE 2020 H2 MATHEMATICS 9758/