CJC 2012 JC2 H2 Prelim Paper 1 Questions

9740/01/PRELIMS/2012 [Turn over CATHOLIC JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 JC2 Preliminary Examination MATHEMATICS 9740/01 Paper 1 22 AUGUST 2012 3 hours Additional Materials: List of Formulae (MF15) READ THESE INSTRUCTIONS FIRST Write your name and class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. 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. You are expected to use a graphic calculator. Unsupported answers from a graphic calculator are a llowed unless a question specifically states otherwise. Where unsupported answers from a graphic 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. At the end of the examination, arrange your answers in NUMERICAL ORDER. Place this cover sheet in front and fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. Name: ___________________________ Class: ______ __________ Question 1 2 3 4 5 6 7 8 9 10 11 Total Marks Total 6 9 10 11 10 7 12 8 9 10 8 100 This document consists of 6 printed pages. Catholic Junior College

2 9740/01/PRELIMS/2012 [Turn over 1 It is known that w satisfies the equation 112 +≤− ww . (i) If ∈w ℝ, find the range of values of w. [2] Hence, state the range of values of w for which . 11 12 ≥+ − w w [1] (ii) If ∈w ℂ, find a cartesian equation for the locus of w and hence sketch it on an Argand diagram. [3] 2 (a) Mr Thrift makes use of a special offer from a bank to obtain an interest-free loan of $2000. He decides to pay $50 in the first month. On the first day of each subsequent month, he pays $10 more than in the previous month. How many complete months would it take for him to fully repay the debt? [3] (b) On 1 January 2012, Mr. Spendalot uses a credit card to borrow $2000 from a bank, at an interest rate of 2% a month. He repays the ba nk $50 on the 10 th of each month. Interest is charged on the balance at the end of ea ch month. (i) Calculate the outstanding amount at 1 January 2013. (ii) How many months does he take to repay the entire lo an? [4] [2] 3 A sequence K,,, 321 uuu is such that 01 =u and ( )( )[ ] 2 2 1 21 4 ++ −++=+ nn nnuu nn , for all +∈ Zn . (i) Prove by mathematical induction that ( ) 2 1 1 + −= n nun for all positive integers n. [4] (ii) Hence, find ( )( )[ ]∑ = ++ −+N n nn nn 2 2 2 21 4