JJC_H2_MATHS_P1

JURONG JUNIOR COLLEGE Preliminary Examinations MATHEMATICS 9740/01 Higher 2 2 September 2014 Paper 1 3 hours Additional materials: Answer Paper Cover Page List of Formulae (MF 15) READ THESE INSTRUCTIONS FIRST Write your name and civics 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 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 a graphic calculator. Unsupported answers from a graphic calculator are allowed 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. The number of marks is given in brackets [ ] at the end of each question or part question. At the end of the examination, fasten all your work securely together, with the cover page in front. This document consists of 6 printed pages. [Turn over

2 1 In a “catch the vouchers” game, the player has to enter into a small confined room where there are many different colour vouchers flying in the air. The player has only 30 seconds to catch as many vouchers as possible. Different colour vouchers ca rry different value of money and same colour vouchers carry the same value of money. Four players play the game. The number of different colour vouchers caught and the to tal amount of money won by each pl ayer are shown in the table below. Player A Player B Player C Player D Blue 3 5 4 2 Yellow 4 2 p 8 Red 7 4 2 5 Total amount ($) $27.40 $20.80 $43.40 $45.00 Find p. [4] 2 A sequence 0u , 1u , 2u , …is defined by nn uuu 21and3 10   , where n  (i) Prove by induction that 1 18 2 ,3 n nu     for all n  0. [4] (ii) State, briefly giving a reason for your answer, whether the sequence is convergent. [1] 3 Find integers a and b such that ( r + 1) 4 + (r + 1)2 + 1  (r 2 + ar + 3)( r 2 + r + b). [2] With these values of a and b, and by considering 22 11 3rr b ra r    , find 42 0 1 (1 )(1 )1 N r r rr    in terms of N. [4] Deduce 42 2 1 N r r rr  in terms of N. [2]

3 4 The diagram shows a region R in the first quadrant bounded by the curve C with equation 2 2 3 4 y x   , the y-axis and the line y = 5. The line y = 5 and the curve intersect at the point  3,5 . (i) Calculate the area of region R. [2] (ii) Write down the equation of the curve obtained when C is translated by 5 units in