MJC_H2_MATH_P2_Question

Write your name and civics group 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 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 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, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. MERIDIAN JUNIOR COLLEGE JC2 Preliminary Examination Higher 2 ___________________________________________________________________ H2 Mathematics 9740/02 Paper 2 18 September 2015 3 Hours Additional Materials: Writing paper List of Formulae (MF 15) ___________________________________________________________________ READ THESE INSTRUCTIONS FIRST ___________________________________________________________________ This document consists of 9 printed pages. [Turn Over

2 MJC/2015 JC2 Preliminary Examinations/9740/02 Section A: Pure Mathematics [40 marks] 1 The sequence 1 2 3, , ,...u u u is such that 1 3 and u  1 23 , for all 1.n n un u     (i) By writing the first 3 terms of this sequence, s how that a possible conjecture for nu is 1 1 1 n n a a    , where a is a positive integer to be determined. [2] (ii) Using the value of a found in part (i), prove by induction that 1 1 1 n n n au a    for all 1n . [4] (iii) Hence determine if the limit of 1 2 3 ... nu u u u exists as n . [2] 2 Fig. 1 shows a rectangular piece of cardboard ABCD of sides 10 cm and 20 cm. A trapezium shape is cut out from each corner , to give the shape shown in Fig. 2. This shape consists of 2 isosceles triangles and 3 rectangles of different sizes. The remaining cardboard shown in Fig. 2 is folded along the dotted lines, to form a closed triangular prism shown in Fig. 3. (i) Show that the volume 3 cmV of the closed triangular prism is given by   4 3 21 10 25 2505V h h h h    . [4] (ii) Use differentiation to find the maximum value of V, proving that it is a maximum. [5] 10 20 Fig. 1 Fig. 2 Fig. 3 h y A B D C h h x

3