MGS 2023 Sec 4 Prelim AM P2_Solutions

This question paper consists of 17 printed pages and 3 blank pages. Class Index Number Name : __________________________________________ METHODIST GIRLS’ SCHOOL Founded in 1887 PRELIMINARY EXAMINATION 2023 Secondary 4 Monday ADDITIONAL MATHEMATICS 4049/02 21 August 2023 PAPER 2 Solution 2 hours 15 minutes 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. 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. 90

Page 2 of 20 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Examination 2023 1. ALGEBRA Quadratic Equation For the quadratic equation , Binomial Expansion , where n is a positive integer and . 2. TRIGONOMETRY Identities 22cosec 1 cotAA=+ AAAAA 2222 sin211cos2sincos2cos −=−=−= 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  − − +== − 1cossin 22 =+ AA AA 22 tan1sec += BABABA sincoscossin)sin( = BABABA sinsincoscos)cos( = BA BABA tantan1 tantan)tan(  = AAA cossin22sin = A AA 2tan1 tan22tan −=

Page 3 of 20 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Examination 2023 1. (i) A prism has a volume of ( ) 23 8 1xx++ cm3 and a cross-sectional area of ( ) 2 21xx++ cm2. Write down an expression for the height of the prism, in the form ( ) ( ) 2 1 1 BCA x x ++ + + . [4] 2 22 3 8 1 2 2Height, 3 2 1 2 1 x x xh x x x x + + −= = ++ + + + ( ) ( ) 22 22 2 1 1 1 x B C x x x x − =++ + + + ( ) 1 22 4 x C C =− −= =− 0 24 2 x B B = − = − = ( ) 2 24Height, 3 1 1 h x x = + −+ + (ii) Find ( ) ( ) 2 d1 1 BCAx x x ++ + + . [3] ( ) ( ) ( ) ( ) 2 2 243 d 1 1 43 2ln 1 1 xx x x x C x +− + + = + + + + +  where C is an arbitrary constant B1 B1 B1 M1 B1 B1 B1

Page 4 of 20 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Examination