Dunman Sec_2025 Prelims 4EXP Add Math Paper 1 QP

This document consists of 18 printed pages. DUNMAN SECONDARY SCHOOL CANDIDATE NAME CLASS INDEX NUMBER PRELIMINARY EXAMINATION 2025 SECONDARY 4 EXPRESS ADDITIONAL MATHEMATICS 4049/01 Paper 1 20 August 2025 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, 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 marks for this paper is 90. Calculator Model Total Marks

2 4049/01/PRELIM/4EXP/2025 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ + = , 2 4 2 b b acx a −  −= Binomial expansion ( ) 1 2 2 ... ...12 n n n n n r r nn n na b a a b a b a b b r − − −     + = + + + + + +           , where n is a positive integer and ( ) ( ) ( )1 ... 1! ! ! ! n n n n rn r r n r r − − + == − 2. TRIGONOMETRY Identities 22sin cos 1AA+= 22sec 1 tanAA=+ 22cosec 1 cotAA=+ ( )sin sin cos cos sinA B A B A B =  ( )cos cos cos sin sinA B A B A B= ( ) tan tantan 1 tan tan ABAB AB = sin 2 2sin cosA A A= 2 2 2 2cos 2 cos sin 2cos 1 1 2sinA A A A A= − = − = − 2 2 tantan 2 1 tan AA A= − Formula for  ABC sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + −  = 1 sin2 bc A

3 4049/01/PRELIM/4EXP/2025 [Turn over 1 The line 4yx=− and the curve 2 3y x= − intersect at the points A and B. Find the length of AB. [6]

4 4049/01/PRELIM/4EXP/2025 2 (a) State the range of 1tan p− . [1] (b) Given that 1cos kx− = , where 0 2x  , find the principal value of ( ) 1cos k− − . [1] 3 Explain why 23 15 20xx++ cannot be smaller than 1. [3]

5 4049/01/PRELIM/4EXP/2025 [Turn over 4 (a) Express 2 2 32 (2 1) xx xx ++ + in partial fractions. [5] (b) Hence integrate 2 2 32 (2 1) xx xx ++ + with respect to x. [3]

6 4049/01/PRELIM/4EXP/2025 5 Solve the equation 53log log 5 2 yy−= . [4]

7 4049/01/PRELIM/4EXP/2025 [Turn over 6 (a) Show that 62sin 105 4 += . [3] (b) The diagram below shows triangle ABC, such that AB = 4 cm, angle ABC = 105° and the area of triangle ABC is 10 2 3+ cm2. Find BC in the form ( )23ab + , where a and b are integers. [3] A B C 4 cm 105