2024 ZHSS AMATH P2 PRELIM QP

[Turn over ZHONGHUA SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS/ 5 NORMAL (ACADEMIC) Candidate’s Name Class Register Number ADDITIONAL MATHEMATICS 4049/02 PAPER 2 9 September 2024 Candidates answer on the Question Paper. No Additional Materials are required. 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces at the top of this page. 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 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. 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. Setter: Mr Francis Tan Vetter: Mr Lionel Ang ___________________________________________________________________ This question paper consists of 22 printed pages (including this cover page) For Examiner’s Use 90

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 =++ cbxax a acbbx 2 42 −−= Binomial expansion nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− 221 21)( , where n is a positive integer and ! )1()1( )!(! ! r rnnn rnr n r n +−−=−=       2. TRIGONOMETRY Identities 1cossin 22 =+ AA AA 22 tan1sec += 22cosec 1 cotAA=+ BABABA sincoscossin)sin( = BABABA sinsincoscos)cos( = BA BABA tantan1 tantan)tan(  = AAA cossin22sin = AAAAA 2222 sin211cos2sincos2cos −=−=−= A AA 2tan1 tan22tan −= Formulae for ABC C c B b A a sinsinsin == Abccba cos2222 −+= Abcsin2 1=

3 1 In Singapore, car owners need to secure a Certificate of Entitlement (COE) before they can register their vehicle and use it for 10 years. David bought a Toyota Prius for $170 000 in January 2022. The value of the car, C , can be modelled by the equation 150000 ntC k e=+ , where k and n are constants, t is the number of years after 2022 and 0 10t . (a) Show that 20000k = . [2] It is given that the value of the car is worth $140 000 in 2023. (b) Find the value of n . [3] (c) David intends to sell the car before it depreciates below $70 000. Which is the latest year that David has to sell the car? [4]

4 2 (a) By considering the general term in the binomial expansion of 7 2px x  + , where p is a constant, explain why every term is dependent on x . [3]

5 (b) In the ex