MGS 2025 Sec 4 Prelim AM P2

This question paper consists of 22 printed pages and 2 blank pages. Class Index Number Name : __________________________________________ METHODIST GIRLS’ SCHOOL Founded in 1887 PRELIMINARY EXAMINATION 2025 Secondary 4 Wednesday ADDITIONAL MATHEMATICS 4049/02 27 August 2025 PAPER 2 2 hours 15 mins Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your class, index number and name in the spaces at the top of this page. Write in dark blue or black pen You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all 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. 90

Page 2 of 24 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2025 1. ALGEBRA Quadratic Equation For the quadratic equation , Binomial Expansion , where n is a positive integer and . 2. TRIGONOMETRY Identities Formulae for DABC a2 = b2 + c2 - 2bc cos A D = bc sin A !" =++ !"#$# ! !"##$ ! "!!±!= ( ) !""!!!!! ##$" !#$!#$!$#$ ++!! " # $$ % &++!! " # $$ % &+!! " # $$ % &+=+ ''' !!!!" !" ( ) ! " #$%%%" #$ !! ! ! !! ! ! " " "!" " !" ## +==$% #&' !"#$$%& '' =+ !! !! !! "#$%&'( += !!"#$ %" & "#'!!=+ !"!"!" !"#$%!$%!!"#&!"#' ±=± !"!"!" !"#!"#$%!$%!&$%!' !=± !" !"!" !"#!"#$ !"#!"#%!"#& ! ±=± !!!!"##$%&&#$%=!!!!! !!!! "#$!%%&'"!"#$&'"!&'" !=!=!= ! !! !"#$% "#$!!"#$ ! = !"# !"# !"# !"# ABC== !"

Page 3 of 24 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2025 1 A piece of raw meat is accidentally left out at room temperature, and bacteria begin to grow on it. Initially, there are 500 bacteria presents, and the number of bacteria doubles every 3 hours. The number of bacteria, N, after t hours can be modelled by the formula . (i) Show that k = . [2] (ii) It is considered unsafe for consumption when the number of bacteria on the meat exceeds 3 000. Determine the maximum number of hours that it will still be safe to consume the meat. [3] !""#$%!"#= !"

Page 4 of 24 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2025 2 (a) Given that , find the range of values of x such that . [4] !!" "=! ! ! "" #"" !!" "" +>

Page 5 of 24 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2025 2 (b) A curve is such that . Given that the curve has a gradient of 3 at the point , find the equation of the curve. [4] ! ! "# $! #" ! "" = ! ( )!" #

Page 6 of 24 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2025 3 A circle C1 passes through . Its centre, B, lies on the line . AB is perpendicular to . (a) Find the equation of the circle. [5] !" # $ %!!! !"# $!"+= !"# $!"+=

Page 7 of 24 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2025 3 (b) A second circle C2 has centre at . The line y = 0 is a tangent to circle C2. Find the equation of the circle in the form of , where p, q and r are integers. [2] !" # $ %!!! !! "!"# ! $ " %+++ + =

Page 8 of 24 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2025 4 The diagram shows two intersecting circles and . The line CF intersects at E, and at D, such that . BAD is a straight line, where A is the centre of . The tangent to at F meets EG produced at H. Stating your reasons clearly, prove that (i) and are similar, [2] !!!! !!!! !" "#=!! !!!"#!!"#! C2 C1

Page 9 of 24 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2025 4 (ii) , [2] (iii) [3] !!" !# $!=! !! !!" !# #"=+

Page 10 of 24 Methodist Girls’ School Additional Mathematics Paper 2 Sec 4 Preliminary Exam 2025 5 (a) Show that can be expressed as , where a and n are constants to be determined. [4] (b) Solve the equation , giving values of y in logarithmic form. [4] !"#$ % & $ % & '!"!= !"# $= !" #!!"" !!=