NASS 2025 AMATH PRELIM P1 MS

MARK SCHEME Register no: .............................. Class: ........... NGEE ANN SECONDARY SCHOOL O PRELIMINARY EXAMINATION ADDITIONAL MATHEMATICS 4049/01 Paper 1 1 September 2025 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, register 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 staples, paper clips, glue or correction fluid. Answer all the 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. For Examiner’s Use Total /90 Checked by student: ………………………………. Date: ………………… This document consists of 24 printed pages.

2 NAS/2025/Prelim/AM-O/P1 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 = + +c bx ax, a ac b bx 2 42 − ± −= Binomial Expansion ( ) 1 22 ... ...12 n n n n nr r nnn nab a a b a b a b b r −− −  + = + + ++ ++     , where n is a positive integer and ( ) ( ) ( ) 1 ... 1 ! ! ! ! n nn nrn r r nr r − −+ = = − 2. TRIGONOMETRY Identities 22sin cos 1AA+= 22sec 1 tanAA= + 22cosec 1 cotAA= + ( ) B A B A B Asin cos cos sinsin ±= ± ( )cos cos cos sin sinAB A B A B±=  ( ) B A B AB A tan tan1 tan tantan  ±= ± A A Acos sin2 2sin = 22 2 2cos2 cos sin 2cos 1 1 2sinA AA A A= − = −=− 2 2tantan2 1 tan AA A= − Formulae for ΔABC sin sin sin abc ABC= = 222 2 cosa b c bc A=+− 1 sin2 bc A∆=

3 NAS/2025/Prelim/AM-O/P1 1 Determine with working, whether the function ( ) ( ) 7f 31x x= + , 0x> , is an increasing or decreasing function. [3] [ ] 2 2 2 2 df() f () d 7( 1)(3 1) (3) M1 21 (3 1) For 0, (3 1) 0 21 0 M1(3 1) Since f ( ) 0, for 0,f( ) is a decreasing fu nction. A1 xx x x x x x x x xx − ′ = = − + −−−−− =− + > +> − < −−−−−+ ′ < > −−−−−

4 NAS/2025/Prelim/AM-O/P1 2 The equation of a quadratic curve is given by 2 17y x px= −+ − and it has a maximum point ( )4,q where p and q are constants. (a) By expressing y in the form of ( ) 2 xa b−− + , find the value of p and of q. [4] ( ) 2 2 22 22 2 2 17 17 17 M1 for completing the square 22 1722 17 24 Since maximum point is (4, ), 4 & 2 y x px x px ppx ppx ppx q p = −+ − = −−