FFMS 2024 Sec 4 Add Math (4049) Prelim Paper 2_Final

NAME: ____________________________ ( ) CLASS: _______ FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS ADDITIONAL MATHEMATICS 4049/02 Paper 2 Date: 22 August 2024 Duration: 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. The number of marks is given in brackets [ ] at the end of each question or part question. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 90. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142. For Examiner’s Use Table of Penalties Question Number Presentation  1  2 Rounding off  1 Parent’s/Guardian’s Signature Setters: Mr Joel Li This question paper consists of 23 printed pages  90

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 2 Additional Mathematics Paper 2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0 , x = -b ± b2 - 4ac 2a Binomial expansion a + b( ) n = an + n 1 æ èç ö ø÷ an-1b + n 2 æ èç ö ø÷ an-2b2 + ...+ n r æ èç ö ø÷ an-rbr + ...+ bn , where n is a positive integer and n r æ èç ö ø÷ = n! r!(n - r)! = n(n -1)...(n - r +1) r! 2. TRIGONOMETRY Identities sin2 A+ cos2 A = 1 sec2 A = 1+ tan2 A cosec2 A = 1+ cot2 A sin( A ± B) = sin Acos B ± cos Asin B cos( ) cos cos sin sinA B A B A B= tan tantan( ) 1 tan tan ABAB AB = sin2A = 2sin Acos A cos2A = cos2 A- sin2 A = 2cos2 A-1= 1- 2sin2 A tan 2 A = 2 tan A 1- tan2 A Formulae for DABC a sin A = b sin B = c sinC a2 = b2 + c2 - 2bccos A D = 1 2 absinC

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 3 Additional Mathematics Paper 2 Answer all the questions. 1 Show that the equation 1 22( 3) xxee−= has only one solution and find this value correct to 3 significant figures. [4]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2024 4 Additional Mathematics Paper 2 2 The equation of a curve is 3y ax b=+ , where