2022 AMKSS AMath Prelims P1

[Turn Over Class Index Number Name ANG MO KIO SECONDARY SCHOOL PRELIMINARY EXAMINATION 2022 SECONDARY FOUR EXPRESS / FIVE NORMAL ADDITIONAL MATHEMATICS 4049/01 Paper 1 Monday 12 September 2022 2 hour 15 minutes Answer on the question paper. No additional materials are required. READ THESE INSTRUCTIONS FIRST Write your name, index number and class in the spaces at the top of this page. 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 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 90. For Examiner’s Use 90 This document consists of 22 printed pages.

2 AMKSS 4E/5N PRELIM 4049/01/2022 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 22 22 22 sin cos 1 sec 1 tan cosec 1 cot AA AA AA += =+ =+ 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 4E/5N PRELIM 4049/01/2022 [Turn Over 1 Given that cos Ap= where 3 2A   , express the following in terms of p. (i) sin A , [2] (ii) tan( )A − . [2]

4 AMKSS 4E/5N PRELIM 4049/01/2022 2 Find the range of values of h given that the graph of 2 ( 6) 3y x h x=− + − − lies entirely below the line 2y=− for all values of x. [4]

5 AMKSS 4E/5N PRELIM 4049/01/2022 [Turn Over 3 A particle moves along the curve 2 48y x=+ such that the y-coordinate of the particle is decreasing at a constant rate of 0.05 units per second. Find the rate of change of the x-coordinate when x = 2. [4]

6 AMKSS 4E/5N PRELIM 4049/01/2022 4 The value $V, in millions, of an apartment in a certain district after t years can be represented by the