SRJC_H2_MATH_P1_STUDENT_S

1 SERANGOON JUNIOR COLLEGE 2015 JC2 PRELIMINARY EXAMINATION MATHEMATICS Higher 2 9740/1 Wednesday 19 Aug 2015 Additional materials: Writing paper List of Formulae (MF15) TIME : 3 hours READ THESE INSTRUCTIONS FIRST Write your name and class on the cover page and on all the work you hand in. Write in dark 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 u sing 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. Total marks for this paper is 100 marks. This question paper consists of 6 printed pages (inclusive of this page) and 2 blank pages. [Turn Over

2 1 A landscape gardener is tasked to design a garden with a total area of 140 m2. Part of the garden will be decking, part will be flowers and the rest will be grass. Let the area of decking, the area of flowers and the area of grass, be denoted by d, f and g respectively, all measured in m2. It is required that the area of grass is 20 m 2 more than the total area of flowers and decking. Including labour, each square metre of grass, decking and flowers cost s $10, $21 and $42 respectively. The landscape gardener has been instructed to come up with a design that will cost $2900. Find the values of d, f and g that the landscape gardener should use. [4] 2 The diagram below shows the graph of f ( )yx with asymptotes 2x and 3y . The curve cuts the x-axis at x = 1 and x = 2.5 , the y-axis at y = 3 and has only one stationary point at  4,10 . Sketch on separate diagrams, the graphs of (a) f ( )yx , [3] (b) 1 f ( )y x , [3] showing clearly any equations of asymptotes, axial intercepts and coordinates of the turning points.

3 3 Find the exact value of 3 2 0 3 sec dx x x   . [5] 4 A sequence nu is given by 1 1u  and 1 1( 1) 2 n nnu u n     , for n ∊ ℤ+. Prove using mathematical induction that un = 1 14 ( 2) 2 n n    . [5] 5 The diagram below sho ws a figure made up of a pyramid and a cuboid. The pyramid has a square base OABC of side 6 units. The vertex D is 4 unit