2017_SCGS_AM_PE_P2

SINGAPORE CHINESE GIRLS’ SCHOOL PRELIMINARY EXAMINATION 2017 SECONDARY FOUR O-LEVEL PROGRAMME ADDITIONAL MATHEMATICS 4047/02 Paper 2 Friday 4 August 2017 2 hours 30 minutes Additional Materials: Answer Paper Cover Page READ THESE INSTRUCTIONS FIRST Write your class, index number and name 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, 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 electronic 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. The Question Paper consists of 6 printed pages. [Turn over

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02  cbxax , a acbbx 2 42 Binomial Theorem   nrrnnnnn bbar nbanbanaba                  221 21 , where n is a positive integer and ! )1()1( )!(! ! r rnnn rnr 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 sin211cos2sincos2 cos  A AA 2tan1 tan22tan   Formulae for ABC C c B b A a sinsinsin  Abccba cos2222  Abc sin2 1

3 [Turn over 1. (i) Express 592 97 2   xx x in partial fractions. [3] (ii) Hence find   7 6 2 d 592 97 x xx x [3] 2. Given that 22332)(f 23  xxxx is exactly divisible by ,2 2 cbxx  (i) find the value of b and of c, [4] (ii) show that 022332 23  xxx has only one real root, [3] (iii) find the remainder when )(f x is divided by )32( x . [2] 3. The roots of the quadratic equation 0432 2  xx are  and . (i) Without using a calculator, show that 32 99 22      . [5] (ii) Hence find the quadratic equation whose roots are 2  and 2  . [2] 4. The diagram below shows a quadrilateral BCDF whose vertices lie on the circumference of a circle. The tangent to the circl