MI_8865_2022_Prelim

1 2022 End-of-Year Examination Pre-University 2 MATHEMATICS 8865/01 Paper 1 12 September 2022 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your admission number, name and class 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. Give 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 requ ired 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 questio n. The total number of marks for this paper is 100. This document consists of 26 printed pages. Qn No. Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 * Total Score Max Score 4 7 8 9 12 5 5 6 8 10 13 13 100 CANDIDATE NAME CLASS ADMISSION NUMBER

Section A: Pure Mathematics [40 marks] 1 At a salad stall, patrons can customise their salads by choosing the number of servings of beans, vegetables and nuts. Dressings are free of charge. Amy, Betty and Cathy go for lunch at the salad stall. Amy pays $9.10 for her salad which consists of two serving of beans, three servings of vegetables and one serving of nuts. Betty pays $14 for her salad which consists of three serving of beans, four servings of vegetables and two serving of nuts. Cathy, who has nut allergy, orders what Amy orders for her salad but replaces the one serving of nuts with another serving of beans. Cathy pays $8.10 for her salad. (i) How much does one serving of beans, vegetables and nuts each cost at the salad stall? [3] (ii) The salad stall offers a 20% discount for any purchase. Daisy pays $6.32 for her salad which consists of 1 serving of beans, a serving(s) of vegetables and 1 serving of nuts. Find the value of a. [1] 2 (a) One of the solutions for the following pair of simultaneous equations 2 58p x y−= , 22 9 3 30x y x xy+ + = + . is 3 and x y p== , where p is an integer. (i) Show that 1p=− . [2] (ii) Using 1p=− , find the other solution for this pair of simultaneous equations. [3] (b) Solve 2 5x  algebraically. [2] 3 A curve C has equation 3217 10 132y x x x= − + + . (i) Using a non-calculator