AMKSS Prelim 2019 4E5N AMath P1 Question

[Turn Over Class Index Number Name ANG MO KIO SECONDARY SCHOOL PRELIMINARY EXAMINATION 2019 SECONDARY FOUR EXPRESS / FIVE NORMAL ACADEMIC ADDITIONAL MATHEMATICS 4047/01 Paper 1 Tuesday 17 September 2019 2 hours READ THESE INSTRUCTIONS FIRST Write your name, index number and class 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 staples, 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 of the marks for this paper is 80. For Examiner’s Use 80 This document consists of 18 printed pages.

2 AMKSS 4E5N Prelim 4047/01/2019 [Turn Over Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02  cbxax , a acbbx 2 42  Binomial expansion ,......21)( 221 nrrnnnnn bbar nbanbanaba                  where n is a positive integer and ! )1(...)1( )!(! ! r rnnn rnr n r n       2. TRIGONOMETRY Identities AAec AA AA 22 22 22 cot1cos tan1sec 1cossin    BA BABA BABABA BABABA tantan1 tantan)tan( sinsincoscos)cos( sincoscossin)sin(      A AA AAAAA AAA 2 2222 tan1 tan22tan sin211cos2sincos2cos cossin22sin    Formulae for ABC a2 = b2 + c2 – 2bc cos A Cabsin2 1 C c B b A a sinsinsin 

3 AMKSS 4E5N Prelim 4047/01/2019 [Turn Over 1 The curve fyx is such that  2f8 1x px x   . Given that  f2 4  and the curve passes through the point (3, 0), find (i) the value of p, [2] (ii) an expression for  f x . [3]

4 AMKSS 4E5N Prelim 4047/01/2019 [Turn Over 2 When the graph of 2y against x is drawn, a straight line is obtained which passes through the points (10, 16) and (16, 25). Find the value of x when 2y . [4]

5 AMKSS 4E5N Prelim 4047/01/2019 [Turn Over 3 The equation 223 0xx p has roots  and  . Given that the equation 286 4 0xq x has roots 3 and 3 , find the value of p and of q. [7]

6 AMKSS 4E5N Prelim 4047/01/2019 [Turn Over 4 (i) Sketch the graph 2 32yx for 0x . [1] (ii) (a) In order to solve the equation 32 xx , a graph of a suitable straight line is drawn on the same set of axes as the graph of 2 32yx . Find the equation of this straight line. [2] (b) On the same axes as (i), sketch the graph of the straight line for 0x , indicating the coordinates of the points of intersection clearly. [3] x y

7 AMKSS 4E5N Prelim 4047/01/2019 [Turn Over 5 Without using a calculator, solve the equation 18 2 6xx , giving your answer in the form 2 7 ab  , where a and b are integers. [5]

8 AMKSS 4E5N Prelim 4047/01/2019 [Turn Over 6 It is given that  32f 2 11 12 9x xx x  . (i) Show that  21x is a factor of  f x . [1] (ii) Hence, or otherwise, factorise f x completely. [3]

9 AMKSS 4E5N Prelim 4047/01/2019 [Turn Over (iii) Hence express 32 15 17 21 11 2 9 x xxx    as a sum of 3 partial fractions. [4]

10 AMKSS 4E5N Prelim 4047/01/2019 [Turn Over 7 (i) Prove that  2 1c o scosec cot 1c o s     . [3] (ii) Hence find, for 02   , the values of  in radians for which  2 1cosec cot 4 . [3]