JPJC_8865_2022_Prelim

[Turn over Name:____________________________________ Class:_____________ JURONG PIONEER JUNIOR COLLEGE JC2 Preliminary Examination 2022 MATHEMATICS 8865/01 Higher 1 16 September 2022 Paper 1 3 hours Candidates answer on the Question Paper. Additional materials: List of Formulae (MF 26) This document consists of 6 printed pages. Qn Marks 1 /4 2 /6 3 /6 4 /9 5 /15 6 /6 7 /6 8 /7 9 /7 10 /10 11 /10 12 /14 Accuracy Total /100 READ THESE INSTRUCTIONS FIRST Write your name and civics class 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. Answer all the 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 require d 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.

2 [Turn over Section A: Pure Mathematics [40 marks] 1 Without using a calculator, find the set of values of the real constant k for which the expression 22 41kx x x k+ − + − is always positive for all real values of x. [4] 2 (i) Find 2 d 3 1 4 x x− . [3] (ii) Differentiate 2 2 2 53e e x x  − with respect to x, giving your answer in the form 44eexxpq −+ , where p and q are constants to be determined. [3] 3 A restaurant sells three set meals A, B and C. Set Meal A is the cheapest while Set Meal C is the most expensive. Recently, the restaurant offers a sales promotion. For every two set meals sold, the set meal which is cheaper or of equivalent price is sold at half price. • The original price of one Set Meal C is $11.00 cheaper than the total original prices of one Set Meal A and one Set Meal B. • The original prices of one Set Meal A, one Set Meal B and one Set Meal C adds up to be $51.80. • A group of five friends intends to order one Set Meal A, two Set Meals B and two Set Meals C at the restaurant. If they use this sales promotion to pay for their order in a single receipt, the restaurant will charge them a total of $73.40. (i) Write this information as three linear equations, and hence find the original prices o