[WDL] MYE Additional Math 2021 P1

EXPRESS EXPRESS EXPRESS Name: _________________________( ) Class: ________ WOODLANDS SECONDARY SCHOOL MID YEAR EXAMINATION 2021 Level: Sec 4Exp Marks: 90 Subject: Additional Mathematics Day: Friday Paper: 4049/01 Date: 7th May 2021 Duration: 2 hours 15 minutes Time: 0945 – 1200 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 4049/01 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 4049/01 1 Given that the coefficient of x and x4 in the expansion of   54( ) 2A x Bx   is – 272 and 811 respectively, find the value of A and B where both are positive integers. [5]

EXPRESS EXPRESS EXPRESS 4 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/01 2 (a) Given that the curve logayx passes through the point 1 ,327   , find the value of a. [2] (b) (i) Sketch the graph of logayx for 0 27x . [1] y x

EXPRESS EXPRESS EXPRESS 5 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/01 (b) (ii) Find the equation of a suitable straight line that can be inserted in part (b)(i) to solve the equation 27 9x x  . [3] 3 Without using a calculator, solve the equation 3 5 2 5 4xx   , giving your answer in the form 5mn . [3]

EXPRESS EXPRESS EXPRESS 6 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/01 4 (i) Solve the equation lg( ) 1 lg( 2)xx   . [2] (ii) Given that log2 p = a , log8 q = b and 2cp q  , express c in terms of a and b. [3]

EXPRESS EXPRESS EXPRESS 7 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/01 5 The equation of a curve is 2 3y x kx k    , where k is a constant. (i) Find the range of values of k for which the curve lies completely above the x-axis. [3] (ii) Find the range of values of k for which the line y + k + 1 = 0 and the curve 2 3y x kx k    have two distinct roots. [4]

EXPRESS EXPRESS EXPRESS 8 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/01 6 The value, V dollars, of Hi Watch in t months’ time from its launch is modelled by the equation 0 ktV V e  , where k is a constant and 0V is the original value of the watch. After 36 months from its launch, the value of the watch is half of its original value. (i) Find the value of k. [3] (ii) Twelve months after the launch, the price of Hi Watch is $855. Calculate the minimum number of months needed from the time of launch, for the watch value to fall below $600. [5]

EXPRESS EXPRESS EXPRESS 9 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/01 7 (i) Express 2 2 4 4 1 2 xx xx   in partial fractions. [5] (ii) Hence, find 2 2 4 4 1 d2 xx xxx   . [2] 8 It is given that 32 1y x px qx    where p and q are integers. y is a decreasing function when 2 53 x . Find the value of p and q. [4]

EXPRESS EXPRESS EXPRESS 10 Woodlands Secondary School Mid Year Examination 2021 Sec 4Exp 4049/01 9 (i) Prove that sincosec cot 1 cos AAA A  . [3] (ii) Hence, find all values of  , where 02  , which satisfy the equation 1 (cosec cot ) 1 cos2      . [4]