2025 JVSS Sec 4 AM Prelim P2 MS

JURONGVILLE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2025 Secondary 4 Express STUDENT NAME MARK SCHEME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS 4049/02 Paper 2 20 AUGUST 2025 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. This document consists of 19 printed pages. 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 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. 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. DO NOT OPEN THE BOOKLET UNTIL YOU ARE TOLD TO DO SO O For Examiner’s Use 90

2 Jurongville Secondary School 4049/02/2025 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ + = , 2 4 2 b b acx a −  −= Binomial expansion 1 2 2( ) ... ... 12 n n n n n r r n n n na b a a b a b a b b r − − −     + = + + + + + +           , where n is a positive integer and ! ( 1)...( 1) !( )! ! n n n n n r r r n r r  − − +== − 2. TRIGONOMETRY Identities 22sin cos 1AA+= 22sec 1 tanAA=+ 22cos ec 1 cotAA=+ sin( ) sin cos cos sinA B A B A B =  cos( ) cos cos sin sinA B A B A B=  tan tantan( ) 1 tan tan ABAB AB =  sin 2 2sin cosA A A= 2 2 2 2cos 2 cos sin 2cos 1 1 2sinA A A A A= − = − = − 2 2 tantan 2 1 tan AA A= − Formulae for ABC sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + −  = 1 sin2 bc A

3 Jurongville Secondary School 4049/02/2025 [Turn Over 1 (a) Find the first 3 terms in the expansion of 8(1 3 )x+ in ascending powers of x. [2] 82 2 8(1 3 ) 1 8(3 ) (3 ) ... 2 1 24 252 ... x x x xx + = + + +  = + + + (b) Hence determine the first 3 terms in the expansion of 28(2 6 3 )xx++ . [3] ( ) ( ) 8 2 8 8 2 8 2 2 22 22 2 2 (2 6 3 ) 2 1 3 1256 1 3 11256 1 24 252 ... 256 1 24 12 252 ... 256 1 24 264 ... 256 6144 6758 3 2 2 22 4 ... xx x x x xx x x x xx xx x xx + + = + +   = + +       = + + + + +         = + + + + = + + + = + + + (c) Explain why there is no constant term in the expansion of 2 82 1 133 () xx  − + . [3] 22 82 2 2 11 1 3 1 24 252 ) 2 ( ) 2 ( ...) 44( 33 1 .1 24 2523 ..9 x x xxx xxxx− + + + +    − = − +       =+ ++