SRJC_H2_MATHS_P1_Qn

1     SERANGOON JUNIOR COLLEGE 2014 JC2 PRELIMINARY EXAMINATION MATHEMATICS Higher 2 9740/1 Wednesday 20 Aug 2014 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 calcu lator are not allowed in a question, you are required to present the mathematical steps usin g 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.

2   Answer all questions [100 marks] 1 A cubic polynomial has turning points at A(–1, 13) and B(2, –14). (i) Find the equation of this polynomial. [3] (ii) Hence find the coordinates of the point C on the graph of this polynomial such that AC is parallel to the x-axis. [2] 2 SRBank introduces the UniSave Bank Account to encourage young parents to save up for their child’s university education. This account consists of two independent components – Ordinary A ccount and Birthday Account. The bank will provide an interest rate of 1% of th e total amount in the Ordinary Account at the end of every year. As a bonus, the bank will deposit an amount equivalent to ten times the age of the child into the Birthday Account on the child’s birthday each year, with the last deposit on the 18 th birthday. Mr and Mrs Hon intend to save up for their child’s university education by depositing a fixed amount of $3000 into the UniSave’s Ordinary Account at the start of every year from the year their child turns one year old. (i) Show that the total amount in the UniSave Bank Account at the end of the year when their child is n years old, where 19,n is given by $ 303000 1.01 301290n  . [3] (ii) Given that 19,n find the least n such that the total amount in the UniSave Bank account will exceed $70000. [2] 3 A sequence of real numbers 123,,,uuu … satisfies the recurrence relation 1 3 n n n uu u    , n  . Given that 1 1u  , and by considering 2