[WDL] MYE Additional Math 2021 P2

EXPRESS EXPRESS EXPRESS Name: _________________________( ) Class: ________ WOODLANDS SECONDARY SCHOOL MID YEAR EXAMINATION 2021 Level: Sec 4Exp Marks: 90 Subject: Additional Mathematics Day: Monday Paper: 4049/02 Date: 10th May 2021 Duration: 2 hr 15 min Time: 1030 – 1245 READ THESE INSTRUCTIONS FIRST Answer on the Question Paper. Write in dark blue or black pen. 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. 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 90. DO NOT TURN THE PAGE UNTIL YOU ARE TOLD TO DO SO. This document consists of 15 printed pages and 1 blank page.

EXPRESS EXPRESS EXPRESS 2 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/02 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02  cbxax , a acbbx 2 42  Binomial expansion   nrrnnnnn bbar nbanbanaba                  ......21 221 , 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 sincoscossinsin    BABABA sinsincoscoscos    BA BABA tantan1 tantantan   AAA cossin22sin  AAAAA 2222 sin211cos2sincos2cos  A AA 2tan1 tan22tan   Formulae for ABC sin sin sin a b c A B C 2 2 2 2 cosa b c bc A   Cabsin2 1

EXPRESS EXPRESS EXPRESS 3 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/02 1 The equation of a curve is 2y x x kx k    , where k is a constant. (i) Show that the equation y = 0 has real roots for all values of k. [2] (ii) Find the values of k for which the line y = 2x + 1 is a tangent to the curve. [3]

EXPRESS EXPRESS EXPRESS 4 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/02 2 (a) Given 442log 3 3log ( 1)yx   , express y in terms of x. [3] (b) (i) Given 3xy , express 29 18 3xx  as a quadratic equation in terms of y. [2] (ii) Hence, or otherwise, find the values of x. [4]

EXPRESS EXPRESS EXPRESS 5 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/02 3 The equation of a curve is 72ln xy x  . (i) Show that d d (7 2) yk x x x  , where k is a constant to be determined. [3] (ii) Find the equation of the normal to the curve at x = 2. [3] (iii) A point (x, y) is moving on the curve. Find the value(s) of x for which the rate of increase of y is twice the rate of increase of x. [3]

EXPRESS EXPRESS EXPRESS 6 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/02 4 The curve 2()y a x h k   , where a, h and k are constants, intersects the y-axis at (0, –1) and the x-axis at (1, 0) and 1 ,02   . (i) Find the values of a, h and k. [4] (ii) State the coordinates of the turning point. [1] (iii) Express 22 4 3xx in the form 2()p x q r , where p, q and r are constants. [2] (iv) Explain why the two curves 2()y a x h k   and 22 4 3y x x   will not intersect. [1]

EXPRESS EXPRESS EXPRESS 7 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/02 5 The variable x and y are related by the equation ( 1)x y a bx . By plotting a graph of y against 1 x , a straight line graph passing through the points (2, 3) and (14, 27) is obtained. Find the values of a and b. [4]

EXPRESS EXPRESS EXPRESS 8 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/02 6 (a) In the binomial expansion of 12 2 kx x   , where k is a constant, the term independent of x is 126720. Find the possible values of k. [4] (b) The expansion of ( )(1 5 ) na x x in ascending powers of x is 22 720px x + …, where a, n and p are constants and n is a positive integer. Find the values of a, n and p. [6]

EXPRESS EXPRESS EXPRESS 9 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/02 7 (i) Express   2d ln 3 2d xx   in the form 32 a x , where a is a constant to be found. [2] (ii) Hence evaluate 2 0 42 d32 xx    . [4]

EXPRESS EXPRESS EXPRESS 10 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/02 8 (a) It is given that f ’(x) = 1cos sin 22 xx and f (π) = 1. Express 2f (x) + 8 f ’’(x) = q – p cos 2x, where p and q are constants to be determined. [6] (b) The equation of a curve is given by 21 53 xy x   for x > 0. Determine whether the curve is an increasing or decreasing function for x > 0. Show your working clearly. [3]