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 model 1.2 0.015 ktVe=+ , where k is a constant. (i) Find the initial value of the apartment. [1] (ii) The value of the apartment is 1.3 million dollars after 2 years. Find the value of k. [2] (iii) Find the number of years for the value of the apartment to be twice its initial value. [2]

7 AMKSS 4E/5N PRELIM 4049/01/2022 [Turn Over 5 Jim kicks a soccer ball from the ground. The height, h metres, of the ball t seconds after it has been kicked can be modelled by the quadratic equation 24 16h t t=− + . (i) Express 24 16tt−+ in the form 2()a t p q−+ , where a, p and q are constants. [2] (ii) State the maximum height of the ball and the time at which it occurs. [2] (iii) A goalkeeper claims he can catch the ball when it is dropping towards the ground and it is at most 2.5 m above the ground. Find the range of values of t for him to be able to catch the ball. [3]

8 AMKSS 4E/5N PRELIM 4049/01/2022 6 The equation of a curve is 2 6 21 xy x += + for 0x . (i) Find the coordinates of the turning point of the curve. [5]

9 AMKSS 4E/5N PRELIM 4049/01/2022 [Turn Over (ii) Find the equation of the normal to the curve 2 6 21 xy x += + at the point where the curve intersects the y-axis. [3]

10 AMKSS 4E/5N PRELIM 4049/01/2022 7 (a) In the expression of ( ) 6 8 41 2 x mx + + − , where m is a positive integer, the coefficient of 2x is 1212. Find the value of m. [4]