2017 SNGS Sec 4 AM Prelim P2

[Turn over Name: _________________________ ( ) Class: ____________ PRELIMINARY EXAMINATION GENERAL CERTIFICATE OF EDUCATION ORDINARY LEVEL ADDITIONAL MATHEMATICS 4047/02 Paper 2 Monday 21 August 2017 2 hours 30 minutes Additional Materials: Answer Paper Graph 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 on both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use paper clips, highlighters, glue, or correction fluid. Answer all the questions. Write your answers on the separate Answer Paper provided 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, staple all your work together with this cover sheet. 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 Q1 Q5 Q9 Q2 Q6 Q10 100 Q3 Q7 Q11 Q4 Q8 This document consists of 6 printed pages.

2 CHIJ SNGS Preliminary Examinations 2017 - Additional Mathematics 4047/02 [Turn over Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02  cbxax , a acbbx 2 42 Binomial Theorem   nrrnnnnn bbar nbanbanaba                  ......21 221 , where n is a positive integer and       ! 1........1 !! ! r rnnn rrn n r n       2. TRIGONOMETRY Identities 1cossin 22  AA . AA 22 tan1sec  . AA 22 cot1cosec  . BABABA sincoscossin)(sin  BABABA sinsincoscos)cos(  BA BABA tantan1 tantan)tan(   AAA cossin22sin  AAAAA 2222 sin211cos2sincos2cos  A AA 2tan1 tan22tan   Formulae for ∆ABC C c B b A a sinsinsin  Abccba cos2222  Abc sin2 1

3 CHIJ SNGS Preliminary Examinations 2017 - Additional Mathematics 4047/02 [Turn over 1 The curve  xy f is such that 542)('f 2  xxx . (i) Explain why the curve )(f xy has no stationary points. [2] (ii) Given that the curve passes through the point (–1, –6), find an expression for )(f x . [3] 2 The function f is defined by 82)(f 234  kxxxx , where k is a constant. It is given that 0)(f x has a repeated root 2. (i) Find the value of k, [2] (ii) Determine, showing all necessary working, the number of real