JSS_AMATH_P2

O JURONG SECONDARY SCHOOL 2020 GRADUATION EXAMINATION SECONDARY 4 EXPRESS CANDIDATE NAME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS 4047/02 PAPER 2 31 August 2020 Candidates answer on the Question Paper. 2 hours 30 minutes Additional Materials : Writing Paper (1 sheet) 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 on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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 100. For Examiner’s Use This document consists of 16 printed pages including this page. 100

2 4047_S4_2020GE_P2 [Turn Over 1. ALGEBRA Quadratic Equation For the equation Binomial expansion , where n is a positive integer, and 2. TRIGONOMETRY Identities Formulae for 02  cbxax a acbbx 2 42 nrrnnnnn bbar nbanbanaba                 ......21)( 221 ! )1)...(1( )!(! ! r rnnn rnr n r n       1cossin 22  AA 22sec 1 tanAA 22cosec 1 cotAA   BABABA sincoscossinsin    BABABA sinsincoscoscos    BA BABA tantan1 tantantan   AAA cossin22sin  AAAAA 2222 sincossin211cos22cos  A AA 2tan1 tan22tan   ABC C c B b A a sinsinsin  Abccba cos2222  Abcsin2 1

3 4047_S4_2020GE_P2 [Turn Over 1 (i) Differentiate ln( 1)xx  with respect to x. [2] (ii) Hence, find ln( 1) dx.x [3] 2 (i) Prove that 2 2 2(sin 2 )(cot tan ) 4cos 2 .x x x x  [4] (ii) Hence, solve the equation 2 22 23sin 2 cot tanx xx  for 0 180 .x   [3]

4 4047_S4_2020GE_P2 [Turn Over 3 (i) Prove that 1x is a factor of 32 5 3.x x x   [1] (ii) Express 2 32 2 3 11 53 xx x x x     as the sum of partial fractions. [6]

5 4047_S4_2020GE_P2 [Turn Over 4 (a) Solve the equation 5 25 52log log 16 log (9 2).xx   [3] (b) Given that 1ab and 11 293log logabba , find the value of 11 log logab abab . [5]

6 4047_S4_2020GE_P2 [Turn Over 5 A curve has the equation 2 .xy xe (i) Find the x-coordinates of the