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 stationary point on the curve. [3] (ii) Find the value of k for which 2 2 2 (1 ).xdy ke xdx  [3] (iii) Hence, determine the nature of the stationary point. [2] 

7 4047_S4_2020GE_P2 [Turn Over 6 A ( 1,3) , B (3,3) and C (0,6) are points that lie on the circumference of circle C1. (i) Find the equation of the perpendicular bisector of BC. [2] (ii) Hence, find the equation of circle C1. [4] (iii) Given that BP is the diameter of the circle, find the coordinates of P. [2] (iv) A second circle C2 has equation 22( 2) ( 6) 19xy    . Explain why circle C1 will not intersect circle C2. [2]

8 4047_S4_2020GE_P2 [Turn Over 7 (a) (i) Solve the equation 2 6 6.xx   [3] (ii) Sketch the graph of 2 6y x x   , indicating clearly the coordinates of the intercepts & turning points. [3] (iii) Hence, state the range of values of x for which 2 6 6.xx   [1]

9 4047_S4_2020GE_P2 [Turn Over (b) The diagram shows part of the graph 2yx . A line y mx c is drawn on the same axes to determine the number of solutions to the equation 2. x mx c   (i) If 1,m state the range of values of c such that there is 1 solution to the equation. [1] (ii) If c = 0, state the range of values of m such that the equation has 2 distinct solutions. [2] y x 2 2

10 4047_S4_2020GE_P2 [Turn Over 8 The table shows experimental values of two variable, x and y, which are connected by an equation of the form pxy qx  . x 1 3 5 7 9 y 0.25 0.5 0.625 0.7 0.75 (i) Plot y against y x for the given data and draw a straight line graph. [3] (ii) Use your graph to estimate (a) the values of p and q, [3] (b) the value of y when 2x = 7y. [2] (iii) By drawing a suitable line on your graph, solve the following simultaneous equations. pxy qx y xy    [3]