AMKSS EOY Exam 2025 3E Add Math Paper-Questions

[Turn Over Candidate Name Form Class Index Number ANG MO KIO SECONDARY SCHOOL END-OF-YEAR EXAMINATION 2025 SECONDARY THREE EXPRESS ADDITIONAL MATHEMATICS 4049 06 October 2025 2 hours 15 minutes Setter: Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, index number and class in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, glue or correction fluid. Answer all questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in 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 of the marks for this paper is 90. For Examiner’s Use 90 This document consists of 18 printed pages.

2 AMKSS 3E EOY Exam 4049/2025 [Turn Over Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ + = , 2 4 2 b b acx a −  −= Binomial expansion ,......21)( 221 nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− where n is a positive integer and ! )1(...)1( )!(! ! r rnnn rnr n r n +−−=−=      2. TRIGONOMETRY Identities AAec AA AA 22 22 22 cot1cos tan1sec 1cossin += += =+ BA BABA BABABA BABABA tantan1 tantan)tan( sinsincoscos)cos( sincoscossin)sin(   = = = A AA AAAAA AAA 2 2222 tan1 tan22tan sin211cos2sincos2cos cossin22sin −= −=−=−= = Formulae for ABC a2 = b2 + c2 – 2bc cos A Cabsin2 1= C c B b A a sinsinsin ==

3 AMKSS 3E EOY Exam 4049/2025 [Turn Over 1 A right-angled triangle has an area of ( )14 8 3+ cm2. Given that the base of the triangle has a length of ( )13+ cm, find without using a calculator, the height of the triangle giving your answer in the form ( )3ab+ , where a and b are integers. [4]

4 AMKSS 3E EOY Exam 4049/2025 [Turn Over 2 (a) The equation of a curve is 223 6 3 1y x mx m=− + − − where m is a constant. Show that the curve is negative for all real values of x. [4] (b) Find the values of the k for which 2 8 6 0kx x k+ + + = has equal real roots. [4]

5 AMKSS 3E EOY Exam 4049/2025 [Turn Over (c) Find the range of values of m such that the roots of 22 3 0x x m+ + = are real. [3] (d) Solve 22 1 0xx+ −  . [2]

6 AMKSS 3E EOY Exam 4049/2025 [Turn Over 3 (a) Solve the simultaneous equations 2 5,xy−= 22 3 3 6x y xy− = − . [5]

7 AMKSS 3E EOY Exam 4049/2025 [Turn Over (b) By using a suitable substitution, solve ( ) 213 26 3 9 0xx+ + − = . [4]

8 AMKSS 3E EOY Exam 4049/2025 [Turn Over 4 The value of a new EV car is $160 000. After t months, the car depreciated by an amount $P, given by 0.21000 tPe= . Find (i) the value of the car after 15 months, to the nearest hundred dollars, [3] (ii) the number of months, to the nearest month, when its depreciation exceeded $90 000. [3]

9 AMKSS 3E EOY Exam 4049/2025 [Turn Over 5 Express 2 25 ( 1) x xx − + in partial fractions. [5]

10 AMKSS 3E EOY Exam 4049/2025 [Turn Over 6 (a) (i) Find the first four terms, in ascending powers of x, of the expansion of ( ) 921 x+ . [2] (ii) Hence find the coefficient of 4x in the expansion of ( )( ) 92211 xx−+ . [2] (b) Find the term independent of x in the expansion of 12 2 1 2x x  + . [5]