VJC_8865_2022_Prelim

1 [Turn over VICTORIA JUNIOR COLLEGE JC 2 PRELIMINARY EXAMINATION 2022 CANDIDATE NAME CLASS INDEX NUMBER H1 MATHEMATICS 8865/01 Paper 1 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your 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 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 calculato r 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 23 printed pages and 1 blank page.

2 Section A: Pure Mathematics [40 marks] 1 (a) Find the set of values of k for which the graphs of 22y x kx k= − + and y kx= intersect at most once. [4] 1 (b) MARS Café serves three types of coffee: Flat, Cappuccino and Macchiato. On 23 December 2021, a customer paid $17.30 for two cups of Flat, one cup of Cappuccino and three cups of Macchiato after using a $10 cash voucher. On the same day, the Café owner recorded a total sale of $1151.30 from selling 84 cups of Flat, 123 cups of Cappuccino and 65 cups of Macchiato. The total price of three cups of Macchiato is equivalent to the total price of five cups of Flat. Express this information as 3 linear equatio ns and hence find the price of one cup of Macchiato. [4] 2 The curve 1C has equation 42 xy=− . The curve 2C has equation 2 4 3xy=− . (i) Sketch 1C and 2C on the same diagram, stating the exact coordinates of any points of intersection with the axes and the equations of any asymptotes. [4] (ii) Find the x-coordinates of the points of intersection of 1C and 2C , giving your answers correct to 4 decimal places. [1] (iii) Write down as an integral an expression for the area of the region bounded by the curves C1 and C2, the line 5x=− and the y-axis. Evaluate this integral, giving your answer correct to 3 decimal places. [2] 3 (i) Differentiate ( ) 2 3ln 5 e xx − . [3] (ii) Integrate 2 1 2 x x  + . [3