MGS 2024 Sec 4 Prelim AM P1_with Solutions

Class Index Number Name : _____________Solutions____________ This question paper consists of 21 printed pages and 3 blank pages. METHODIST GIRLS’ SCHOOL Founded in 1887 PRELIMINARY EXAMINATION 2024 Secondary 4 Monday ADDITIONAL MATHEMATICS 4049/01 12 August 2024 Paper 1 2 h 15 min Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your class, index number and name in the spaces at the top of this page. Write in dark blue or black pen You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. Give non-exact numerical answers correct to 3 significant figure, 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. 90

Page 2 of 24 Methodist Girls’ School Additional Mathematics Paper 1 Sec 4 Preliminary Examination 2024 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the quadratic equation , Binomial Expansion , where n is a positive integer and . 2. TRIGONOMETRY Identities 22sin cos 1AA+= 22sec 1 tanAA=+ 22cosec 1 cotAA=+ cos2A = cos2 A- sin2 A = 2cos2 A-1= 1- 2sin2 A Formulae for ABC sin sin sin a b c A B C== a2 = b2 + c2 − 2bc cos A  = 2 1 bc sin A 02 =++ cbxax a acbbx 2 42 −−= ( ) nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− 221 21 ( ) ! ( 1)...( 1) ! ! ! n n n n n r r r n r r  − − +== − BABABA sincoscossin)sin( = BABABA sinsincoscos)cos( = BA BABA tantan1 tantan)tan(  = AAA cossin22sin = A AA 2tan1 tan22tan −=

Page 3 of 24 Methodist Girls’ School Additional Mathematics Paper 1 Sec 4 Preliminary Examination 2024 1 (i) Express 24 24 49y x x= + + in the form 2()a x b c++ . [2] 2 2 2 2 4 24 49 4( 6 ) 49 4[( 3) 9] 49 4( 3) 13 xx xx x x ++ = + + = + − + = + + (ii) Hence, state the maximum value of 1 y and the corresponding value of x at which 1 y is maximum. [2] Maximum 11 13y = It occurs when x = –3

Page 4 of 24 Methodist Girls’ School Additional Mathematics Paper 1 Sec 4 Preliminary Examination 2024 2 By using a suitable substitution, solve the equation 22 4(1 )xxee −=− . [3] 22 2 2 2 2 2 2 4(1 ) 44 44 44 4 4 0 ( 2) 0 2 2 ln 2 2 0.347 xx x x x ee e e y y yy yy y y e x −=− =− =− =− − + = −= = = = =

Page 5 of 24 Methodist Girls’ School Additional Math