CGS 2025 AMATH PRELIM P1 QP

Name: Register No.: Class: ADDITIONAL MATHEMATICS 4049/01 Paper 1 29 August 2025 Candidates answer on the Question Paper. 2 hours 15 minutes 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. This document consists of 23 printed pages and 1 blank page. Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Marks Table of Penalties Qn. No. Presentation –1 Significant Figures / Units –1 Parent’s/ Guardian’s Signature For Examiner’s Use CRESCENT GIRLS’ SCHOOL SECONDARY FOUR 2025 PRELIMINARY EXAMINATION 90

2 Crescent Girls’ School 2025 Prelim Sec 4 A Math 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 ab a b a b b r −− −  + = + + ++ ++     , where n is a positive integer and ! ( 1)...( 1) !( )! ! n n nn n r 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 ±±=  sin 2 2sin cosA AA= AA A A A 2222 sin2 1 1cos2sin cos2cos − = − = − = 2 2tantan2 1 tan AA A= − Formulae for ∆ABC C c B b A a sin sin sin= = A bc c b acos22 2 2− + = ∆ = 1 sin2 bc A

3 Crescent Girls’ School 2025 Prelim Sec 4 A Math P1 1 The curve 22 6 90x xy y+ − += and line 1yx= + intersect at the points R and S. Find the x-coordinate of the midpoint of RS. [3] 2 Integrate 2 43 sin 515 xxx π−+−− with respect to x. [5] [Turn over

4 Crescent Girls’ School 2025 Prelim Sec 4 A Math P1 3 A cuboid has base area ( )4 25+ cm2 and a volume of ( )9 55+ cm3. Find, without using a calculator, the height of the cuboid, in cm, giving your answer in the form ( ) 1 52 ab+ , where a and b are integers. [3]

5 Crescent Girls’ School 2025 Prelim Sec 4 A Math P1 4 (a) Express 24 12 2xx−++ in the form 2()ax b c++ and state the coordinates of the turning point of the curve 24 12 2yx x= −++ . [3] (b) Hence explain why the turning point is a maximum point. [1] [Turn over

6 Crescent Girls’ School 2025 Prelim Sec 4 A Math P1 5 Express 2 2 3 52 ( 1)( 4) xx xx +− ++ in partial fractions. [5]

7 Crescent Girls’ School 2025 Prelim Sec 4 A Math P1 6 It is given that 21 2 xy x −= + for .xq> (a) State the value of q. [1] (b) Find d d y x . [3] (c) State whether 21 2 xy x −= + is an increasing or decreasing function. Explain your answer clearly. [2] [Turn over

8 Crescent Girls’ School 2025 Prelim Sec 4 A Math P1 7 The diagram shows the curve cosy a bx c= + for 30 2x π≤≤ radians. A minimum point ,22 π − and a maximum point 5 ,44 π  are indicated on the diagram. (a) Explain why 4b= . [2] 0 x y |

9 Crescent Girls’ School 2025 Prelim Sec 4 A Math P1 (b) Explain why c = 1. [2] (c) Hence find the equation of the curve. [2] [Turn over

10 Crescent Girls’ School 2025 Prelim Sec 4 A Math P1 8 (a) Prove the identity sin tan1 cos 2 θθ θ =+ . [3]