2023 JSS AMATH P2 PRELIM MS

[Turn Over] O JURONG SECONDARY SCHOOL 2023 GRADUATION EXAMINATION SECONDARY 4 EXPRESS/ SECONDARY 5 NORMAL ACADEMIC CANDIDATE NAME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS 4049/02 PAPER 2 2023 Candidates answer on the Question Paper. 2 hours 15 minutes Additional Materials : Writing Paper (1 sheet) READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB 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. The use of an approved scientific calculator is expected, where appropriate. 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. The total number of marks for this paper is 90. For Examiner’s Use This document consists of 17 printed pages including this page. 90

2 4049/2/GE/23 1. ALGEBRA Quadratic Equation For the equation Binomial expansion , where n is a positive integer, and 2. TRIGONOMETRY Identities Formulae for 02 =++ cbxax a acbbx 2 42−−= nrrnnnnn bbar nbanbanaba ++    ++     +     +=+ −−− ......21)( 221 ! )1)...(1( )!(! ! r rnnn rnr n r n +−−=−=      1cossin 22 =+ AA 22sec 1 tanAA=+ 22cosec 1 cotAA=+ ( ) BABABA sincoscossinsin = ( ) BABABA sinsincoscoscos = ( ) BA BABA tantan1 tantantan  = AAA cossin22sin = AAAAA 2222 sincossin211cos22cos −=−=−= A AA 2tan1 tan22tan − = ABC C c B b A a sinsinsin == Abccba cos2222 −+= Abcsin2 1=

3 4049/2/GE/23 [Turn Over] 1 At the beginning of a virus outbreak, the number of cases of infected people increased with time. After t days, the number of recorded cases was N. It was observed that N can be modelled by the equation 1200 ktNe= . (a) Write down the initial number of cases recorded. [1] The number of cases recorded after 6 days rose to 4800. (b) Estimate the number of cases recorded after 10 days. [4] A pandemic is declared if the number reaches 20 000 cases. (c) Assuming the trend continues, estimate after how many days will it take for a pandemic to be declared. [2] Solution Marks 1200 B1 Solution Marks 6 6 10(0.231049) 4800 1200 4800 1200 48006 ln 1200 0.231049 1200 12095.2 12100 k k e e k k Ne N = = = = = =  M1 – substitute values correctly M1 – value of k – accept rounded off v