MGS 2024 Sec 4 Prelim AM P2 Solution

This question paper consists of 19 printed pages and 1 blank page. Class Index Number Name : __________________________________________ METHODIST GIRLS’ SCHOOL Founded in 1887 PRELIMINARY EXAMINATION 2024 Secondary 4 Tuesday ADDITIONAL MATHEMATICS 4049/02 13 August 2024 PAPER 2 2 hours 15 mins 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 Exam 2024 1. ALGEBRA Quadratic Equation For the quadratic equation , Binomial Expansion , where n is a positive integer and . 2. TRIGONOMETRY Identities 22cos ec 1 cotAA= + AAA A A 2222 sin2 1 1cos2sin cos2cos − = − = − = Formulae for ∆ABC sin sin sin abc ABC= = a2 = b2 + c2 − 2bc cos A ∆ = 2 1 bc sin A 02 = + +c bx ax a ac b bx 2 42 − ± −= ( ) nr r nnnnn b b ar nb anb ana b a + +     + +     +     + = + −−− 2 21 2 1 ( ) ! ( 1)...( 1) !! ! n n nn n r r rnr r  − −+= = − 1cos sin22 = +A A AA 22 tan1sec + = B A B A B Asin cos cos sin)sin( ±= ± B A B A B Asin sin cos cos)cos( = ± B A B AB A tan tan1 tan tan)tan(  ±= ± A A Acos sin2 2sin = A AA 2tan1 tan22tan −=

Page 3 of 20 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2024 1 (a) Solve the equation 21 1xx+− = . [3] 21 1xx+− = 2 11xx+=+ 2 112x xx+=+ + M1 2xx= 2 4xx= M1 ( 4) 0xx −= 0x= or 4x= A1 (b) Express ( ) 2 235 32 − − in the form 3pq + where p and q are integers. [4] ( ) 2 235 32 − − 12 20 3 25 3 2 32 32 −+ += × −+ M1 ( ) ( )37 20 3 3 2 34 −+ = − M1 ( )37 3 74 60 40 3= − +−− M1 3 3 14= − A1

Page 4 of 20 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2024 2 The diagram shows a circle passing through the vertices of a triangle ABC. The tangent to the circle at A meets BC extended at point D. The tangent at C meets AD at E.