2025 Fmss Prelim Paper 2 with AnsKey

NAME: ____________________________ ( ) CLASS: _______ FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2025 SECONDARY 4 EXPRESS ADDITIONAL MATHEMATICS 4049/02 Paper 2 Date: 28 August 2025 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 2025 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 2025 3 Additional Mathematics Paper 2 Answer all the questions. 1 In an experiment, a liquid is heated to reach its boiling point and then allowed to cool down. The temperature of the liquid T is given by the formula 0.225 200 tTe −=+ when the liquid is cooling for time t minutes. (a) Find the (i) boiling point of the liquid, [1] (ii) value of t for which T = 150, [2] (iii) rate at which the temperature of the liquid is decreasing at the instance when t = 10. [2] (b) Explain why the temperature of the liquid can never fall to 25  C. [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2025 4 Additional Mathematics Paper 2 2 It is given that 32f ( ) 2 4 4x hx kx x= + + + , where h and k are constants, has a factor of ( 1)x− . The remainder when the expression is divided by ( 2)x− is four times the remainder when it is divided by ( 1)x+ . (a) Find the value of h and of k. [4]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2025 5 Additional Mathematics Paper 2 (b) Using these values of h and k, solve f ( ) 0x = , leaving your answers in the form 3ab where applicable. [4]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2025 6 Additional Mathematics Paper 2 3 (a) Show that 4sec tan 3cot  += can be expressed as 24sin 4sin 3 0+ − = . [3] (b) Hence, solve 4sec2 tan 2 3cot 2x x x+= for x−   . [4]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2025 7 Additional Mathematics Paper 2 4 (a) State the values between which each of the following must lie: (i) the principal value of x1tan− , [1] (ii) the principal value of     −− 3 1tan 1 . [1] (b) If 4 3sin −= and  22 3  , find the exact value of (i) tan , [1] (ii)    + 2cos . [1]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2025 8 Additional Mathematics Paper 2 (c) The acute angles P and Q are such that tan( ) 5PQ+= and tan 2Q= . Without using a calculator, find the exact value of sin P . [5]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2025 9 Additional Mathematics Paper 2 5 (a) (i) Given that 1y x x=+ , show d 3 2 d 21 yx x x += + . [3]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express Preliminary Examination 2025 10 Additional Mathematics Paper 2 (a) (ii) Hence or otherwise, find 8 0 d 1 x x x+ . [5]