CGS 2025 AMATH PRELIM P2 MS

Name: Solution Register No.: Class: CRESCENT GIRLS’ SCHOOL SECONDARY FOUR 2025 PRELIMINARY EXAMINATION ADDITIONAL MATHEMATICS 4049/02 Paper 2 3 September 2025 Candidates answer on the Question Paper. 2 hours 15 mins 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. Mathematical Formulae Question 1 2 3 4 5 6 7 8 9 10 Marks Table of Penalties Qn. No. Presentation –1 Significant Figures/ Units –1 Parent’s/Guardian’s Signature For Examiner’s Use This document consists of 16 printed pages. 9

Crescent Girls’ School 202 5 Prelim Sec 4 A Math P2 2 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 ab a b a b b r −− −  + = + + ++ ++     , where n is a positive integer and ! ( )...( 1) !( )! ! n n n nr nr r rn r r  − −+= = − 2. TRIGONOMETRY Identities 1cos sin22 = +A A AA 22 tan1sec + = 22cosec 1 cotAA= + B A B A B Asin cos cos sin)sin( ±= ± cos( ) cos cos sin sinAB A B A B±=  tan tantan( ) 1 tan tan ABAB AB ±±=  A A Acos sin2 2sin = AA A A A 2222 sin2 1 1cos2sin cos2cos − = − = − = A AA 2tan1 tan22tan −= Formulae for ∆ABC C c B b A a sin sin sin= = A bc c b acos22 2 2− + = ∆ = C absin2 1

Crescent Girls’ School 202 5 Prelim Sec 4 A Math P2 [Turn over 3 1 (a) Show that the equation 2376xxee  has only one solution and find its value correct to 2 significant figures. [4] 2376xxee  Let xue 3u 2 + 7u – 6 = 0 (3u – 2)(u + 3) = 0 u = 2 3 or u = – 3 xe = 2 3 or xe = – 3 (no solution) x = ln 2 3 = – 0.41 (to 2 s.f.) (b) Factorise (3x + 1) 3 – 8 completely. [2] (3x + 1) 3 – 23 =   22(3 1) 2 (3 1) 2(3 1) 2x xx     = (3x – 1)(9x2 + 6x + 1+ 6x + 2 + 4) = (3x – 1)(9x2 + 12x + 7)

Crescent Girls’ School 202 5 Prelim Sec 4 A Math P2 4 2 (a) Show that x – 1 is a factor of 3x 3 + 8x2 – 5x – 6. [1] Let f(x) = 3x3