NJC_8865_2022_Prelim

* © NJC 2022 [Turn over NATIONAL JUNIOR COLLEGE SENIOR HIGH 2 Preliminary Examination NAME SUBJECT CLASS 2ma1 REGISTRATION NUMBER H1 MATHEMATICS 8865/01 12 September 2022 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, class and registration number on the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, glue or correction fluid. Answer all the questions. Write your answers in the spaces provided in the Question Paper. 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 an approved 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. Up to 2 marks may be deducted for improper presentation. The number of marks is given in the brackets [ ] at the end of each question or part question. Question Number Marks Possible Marks Obtained 1 4 2 4 3 5 4 5 5 10 6 12 7 5 8 6 9 8 10 9 11 10 12 10 13(a) 6 13(b) 6 Presentation Deduction –1 / –2 TOTAL 100 This document consists of 21 printed pages and 3 blank pages.

2 © NJC 2022 Section A: Pure Mathematics [40 marks] 1 Find the exact set of values of m such that the line 3y mx=− intersects the curve ( ) 2 12y mx m x= − − − . [4] 2 By using a suitable substitution , solve the inequality 23e e 70xx+ , giving your answer in logarithmic form. [4] 3 Tammy deposits $100 000 in three different savings plans for 2 years as shown in the table below: Savings Plan Returns I Simple interest of 1.4% per annum. II One time interest of 3.5% for a 2-year period. III Quarterly payout of $50 for every $10 000 invested. Investments are made in multiples of $10 000. At the end of 2 years, she received an interest of $3 560. The amount of money she deposits in savings plan II is twice the amount she deposits in savings plan I. (i) Find the amount of money she deposits in each savings plan. [3] For the amount of money deposited in savings plan II and III, Tammy was given an option to deposit the amount in savings plan IV, which involves a variable return, as shown below. Savings Plan Returns IV Daily interest rate that fluctuates between 3.7% to 3.9% for a period of 2 years. (ii) Explain if Tammy should take up savings plan IV, justifying your answer mathematically. [2] 4 Find the exact value of 24 1 13d xx 