2024 ZHSS AMATH P2 PRELIM MS

[Turn over ZHONGHUA SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS/ 5 NORMAL (ACADEMIC) Candidate’s Name Class Register Number STUDENT SOLUTIONS ADDITIONAL MATHEMATICS 4049/02 PAPER 2 9 September 2024 Candidates answer on the Question Paper. No Additional Materials are required. 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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 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. 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. Setter: Mr Francis Tan Vetter: Mr Lionel Ang ___________________________________________________________________ For Examiner’s Use 90

3 1 (a) When 0t = , 0170000 150000ke=+ 170000 150000k=+ 20000k = (b) 140000 20000 150000 ne=+ 120000 150000 ne= 4 5 ne= 4ln 5 n= 0.223144n=− 0.223n=− (c) 0.22370000 20000 150000 te−+ 0.22350000 150000 te− 0.2231 3 te− 1ln 0.2233 t− 4.92t 4t = David must sell the car in 2026

4 2 (a) General term 7 2px x  + = ( ) 77 2 r r pxr x −    Consider the power of x = 7 rr−− = 72 r− If there is an independent term, 7 2 0r−= 7 2r = Since r is not a whole number, there is no term independent of x and as such, every term is dependent on x (b) ( ) 7 2 52px x x  +− Since there is no independent term in 7 2px x  + , the only term to form the independent term is the 1 x in the expansion of ( ) 7 2 52px x x  +− . Find the 1 x term Power of x : 7 2 1r− =− 4r= 1 x term = ( ) 4 37 2 4 px x     = 335 16p x  = 3560p x

5 Thus, the term independent of x 3560 2p xx − = 241920− 3 216p = 6p= 3 (a) Consider ABD ADC = (by tangent chord theorem) ADC BAD = (alternate angles) Thus, ABD BAD = . Since there are 2 equal angles in triangle ABD , triangle ABD is isosceles. (b) Let ABD x= , Since triangle ABD is isosceles (part(a)), 180 2BDA x = − (angle sum of triangle) by tangent chord theorem, ABD ADC x = = Or 180 [ 180 2 ]ADC x x = − + − x= (interior angles) Since tangents from an external point are equal, triangle CDA is also isosceles. Thus, ADC CAD x = = And 180 2DCA x BDA = − = (shown)