2024 CCHY A Math P1

* [Turn_over 2024 Preliminary Examination Secondary Four Express / Five Normal Academic CANDIDATE NAME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS 4049/01 Paper 1 22 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and index number on the work you hand in. 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 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 of clear presentation in your answers. Up to 2 marks may be deducted for improper presentation. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 16 printed pages. For Examiner’s Use Presentation Deduction – 1 / – 2 TOTAL 90 CHUNG CHENG HIGH SCHOOL (YISHUN)

2 [Turn_over Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0bx cax + + = , 2 4 2 b b acx a −  −= Binomial Expansion ( ) 1 2 2 12 n nn n n n r rn n na b a a b a b a b b r − − −     + = + + + + + +           , where n is a positive integer and ( ) ( ) ( )11! ! ! ! n n n n rn r r n r r − − + == − 2. TRIGNOMETRY Identities 22 1cs osin A A+ = 22sec 1 tanA A= + 22 coc sec 1 to AA += ( ) os sin sin c cos sinB A B A BA = ( ) oc sos c si sco ins nB A B A BA = ( ) atant tn taan n tan1 BB B AA A  = 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 cos Aa c bcb += −  1 sin2 bc A=

3 [Turn_over 1 (i) Given that the line 2y x k=− meets the curve 2 214 ky x kx= − + , find the range of values of k. [4] (ii) A student claimed that when 1 2k =− , the curve does not intersect the line. By showing your workings clearly, explain whether the statement is valid. [2]

4 [Turn_over 2 A triangle has a base of 1 32 16 m22 48  −+ and a height of h m. Given that the area of the triangle is ( ) 22 2 3 m− , find, without using calculator, the value of h in the form 6 5 ab + where a and b are integers. [5]

5 [Turn_over 3 (i) Show that 23 5 21xx−+ is always positive for all real values of x. [3] (ii) The curve ny ax= , where a and n are constants, passes through ( )2, 48 , ( )3,108 and ( ),192k . Find the values of a, n and k where 0k  . [3]

6 [Turn_over 4 (a) Given that ( ) 23f 43 xx x += − , find ( )f x .