2023_CCHM_Prelim_AMath P2 - Questions

2023 Preliminary Exam/CCHMS/Secondary 4/Additional Mathematics/4049/02 [Turn over For Examiner’s Use Question Number Marks Obtained 1 2 3 4 5 6 7 8 9 10 Total Marks Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2023 SECONDARY 4 ADDITIONAL MATHEMATICS 4049/02 Paper 2 Tuesday 29 August 2023 Candidates answer on the Question Paper. 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 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. At the end of the examination, fasten all your work securely together. 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 20 printed pages and 2 blank pages. _________________________ Parent’s Signature

2 2023 Preliminary Exam/CCHMS/Secondary 4/Additional Mathematics/4049/02 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ + = , 2 4 2 b b acx a −  −= Binomial expansion nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− ......21)( 221 , where n is a positive integer and ! ( 1) ... ( 1) !( )! ! n n n n n r 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= − Formulae for ABC sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − 1 sin2 ab C=

3 2023 Preliminary Exam/CCHMS/Secondary 4/Additional Mathematics/4049/02 [Turn over 1 (a) The line 4 3 2xy=+ intersects the curve 2 50x xy− + = at the points A and B. Find the midpoint of AB. [5]

4 2023 Preliminary Exam/CCHMS/Secondary 4/Additional Mathematics/4049/02 (b) Find the least value of the integer h for which 2 5hx x h++ is positive for all real values of x. [3] (c) Given that the line 3y x p=+ is tangent to the curve 2 5y x x q= + + , where p and q are integers, prove that p and q are consecutive numbers. [4]

5 2023 Preliminary Exam/CCHMS/Secondary 4/Additional Mathematics/4049/02