AMKSS Prelim 2024 AMath P1 QP

[Turn Over Candidate Name Form Class Index Number ANG MO KIO SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY FOUR EXPRESS / FIVE NORMAL ACADEMIC ADDITIONAL MATHEMATICS 4049/01 Paper 1 26 August 2024 2 hours 15 minutes Candidates 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. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, glue or correction fluid. Answer all questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in 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 23 printed pages and 1 blank page.

2 AMKSS 4E5N AM PRELIM 4049/01/2024 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 =++ cbxax , a acbbx 2 42 −−= Binomial Expansion ( ) nrn -rn-n-nn bbar nbanbanaba ++     ++     +     +=+ ... .......... 2 1 221 where n is a positive integer and ( ) ( ) ( ) ! 1.............. 1 ! ! ! r rnnn rnr n r n +−−=−=      2. TRIGONOMETRY Identities AAec AA AA 22 22 22 co t1co s tan1sec 1co ssin += += =+ BA BABA BABABA BABABA tantan1 tantan)tan ( sinsinco sco s)co s( sinco sco ssin)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 4E5N AM PRELIM 4049/01/2024 [Turn Over 1 The curve 5 12 7xy y x xy −−= and the line 5 2 7xy− =− intersect at the points A and B. Find the coordinates of A and B. [5]

4 AMKSS 4E5N AM PRELIM 4049/01/2024 2 (a) Express 3 32− in the form pq+ where p and q are integers. [2]

5 AMKSS 4E5N AM PRELIM 4049/01/2024 [Turn Over (b) The diagonals of a rhombus are 30 and 3 32− and the perimeter of the rhombus is P. Calculate P2, giving your answer in the form of a b c+ where a, b, and c are integers. [4]

6 AMKSS 4E5N AM PRELIM 4049/01/2024 3 The cost per submarine, $y in millions, of assembling x submarines can be modelled by 25 20 1002y x x= − + , where 8x  . (i) Explain the meaning of the constant term 100 in this model. [1] (ii) Express 25 20 1002y x x= − + in the form of 2()y a x h k= − + . [2] (iii) Explain the significance of xh= in (ii). [1]

7 AMKSS 4E5N AM PRELIM 4049/01/2024 [Turn Over 4 (a) Solve the equation ( )4 44 log 3log 2 3log 2 2 yy −−= . [4]

8 AMKSS 4E5N AM PRELIM 4049/01/2024 (b) Given that 27 9log logzy= , express z in terms of y. [3]

9 AMKSS 4E5N AM PRELIM 4049/01/2024 [Turn Over 5 Express 32 2 2 6 1 ( 1)( 2) xx xx ++ −+ in partial fractions. [5]

10 AMKSS 4E5N AM PRELIM 4049/01/2024 6 The diagram below shows a quadrilateral ABCD in which A is (0, 6) and AB is parallel to the x-axis. D is a point on the x-axis such that the equation of DC is 56xy+ =− . AC is perpendicular to the line 27yx=+ . (a) Find the coordinates of point C. [4] y C D B A x O