XMSS 2024 AM Prelim P2_QP

This document consists of 19 printed pages and 1 blank page. [Turn over XINMIN SECONDARY SCHOOL SEKOLAH MENENGAH XINMIN Preliminary Examination 2024 CANDIDATE NAME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS Paper 2 Secondary 4 Express Setter: Ms Joanne Kong Vetter: Ms Low Yan Jin Moderator: Ms Pang Hui Chin 4049/02 26 August 2024 2 hour 15 minutes Candidates answer on the Question Paper 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 staples, paper clips, glue or correction fluid. Answer all the questions. Give non-exact numerical answers 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. 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 Errors Qn No. Errors Qn No. Accuracy Simplification Brackets Units Geometry Marks Awarded Presentation Marks Penalised For Examiner’s Use 90 Parent’s/Guardian’s Signature:

2 1. ALGEBRA Quadratic Equation For the quadratic equation ax 2 + bx + c = 0, a acbbx 2 42 −−= Binomial Expansion ( ) nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− 221 21 , where n is a positive integer and ( ) ! )1)...(1( !! ! r rnnn rrn n r n +−−=−=      2. TRIGONOMETRY Identities sin 2 A + cos 2 A = 1 sec 2 A = 1 + tan 2 A cosec 2 A = 1 + cot 2 A sin (A ± B) = sin A cos B ± cos A sin B cos (A ± B) = cos A cos B  sin A sin B tan ( A ± B ) = tan tan 1 tan tan AB AB  sin 2A = 2 sin A cos A cos 2A = cos2 A – sin2 A = 2cos2 A – 1 = 1 – 2 sin2 A tan 2A = 2 2 tan 1 tan A A− Formulae for  ABC sin sin sin a b c A B C== a 2 = b 2 + c 2 − 2bc cos A  = 2 1 bc sin A

3 [Turn over 1 A company purchased a colour copier machine at a cost of $8500. The value of this machine decreases with time such that its value, $ V, after t months of usage is given by 8500 ktVe −= , where k is a constant. (a) The value of the copier machine is expected to fall to $6400 after 8 months of usage. Estimate the value, to the nearest dollar, of the machine after 2 years of usage. [4] (b) Copier machines are to be replaced when its value reaches 1 7 of its initial value. The company’s manager, Mrs Lee, claims that the machine will last for at least 5 years before a replacement is due . Showing all necessary working, explain whether you agree with Mrs Lee. [2]

4 2 (a) Differentiate 2 sin 2 xx