EJC_8865_2022_Prelim

2022 JC2 H1 Mathematics Preliminary Examination [Turn over (modify this one, Update Field for the next 2 pages and the last page) EUNOIA JUNIOR COLLEGE JC2 Preliminary Examination 2022 General Certificate of Education Advanced Level Higher 1 CANDIDATE NAME CIVICS GROUP INDEX NO. MATHEMATICS Paper 1 [100 marks] 8865/01 13 September 2022 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, civics group and index number on 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. DO NOT WRITE ON ANY BARCODES. Answer all questions. Write your answers in the spaces provided in the Question Paper. 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 21 printed pages and 1 blank page. Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Total

2 2022 JC2 H1 Mathematics Preliminary Examination Section A: Pure Mathematics [40 marks] 1 Find the set of values of the real constant k for which the expression ( ) 2 1 2 1kx k x k+ − + + is always negative. [4] 2 Starluck Coffee is a distributor that brings in three types of coffee beans: Arabica, Robusta and Liberica. The selling price of Arabica coffee beans, Robusta coffee beans and Liberica coffee beans is $4.00 per kilogram, $1.50 per kilogram and $3.50 per kilogram respectively. On International Coffee Day, Starluck Coffee brought in a total of 550 kilograms of coffee beans to sell at a bazaar. At the end of the day, 4 5 of the Arabica coffee beans and 4 9 of the Robusta coffee beans brought in were sold. The amount of Liberica coffee beans sold was 70 kilograms less than the amount of Arabica coffee beans sold. The amount collected from selling these coffee beans was $1315. If all the coffee beans brought in were sold at the end of International Coffee Day, Starluck Coffee would have collected $1685. (i) By writing down three linear equations, find the mass of each type of coffee beans, in kilograms, brought in by Starluck Coffee on International Coffee Day. [4] (ii) Given that the cost of one kilogram of Arabica coffee beans, Robusta coffee beans and Liberica