AISS 2023_4E_Add Math Paper 1_Prelim solution

_____________________________________________________________________________ This document consists of 19 printed pages. AISS PRELIM/4E/4049/P1/2023 [Turn over AHMAD IBRAHIM SECONDARY SCHOOL GCE O-LEVEL PRELIMINARY EXAMINATION 2023 SECONDARY 4 EXPRESS Name: Class: Register No.: SOLUTION ADDITIONAL MATHEMATICS Paper 1 Candidates answer on the Question Paper. 4049/01 7 August 2023 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. 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 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. 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. For Examiner’s Use /90

2 AISS PRELIM/4E/4049/P1/2023 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ + = , 2 4 2 b b acx a −  −= Binomial expansion 1 2 2() 12 n n n n n r r n n n na b a a b a b a b b r − − −     + = + + + + + +           where n is a positive integer and ! ( 1) ( 1) !( )! ! n n n n n r r r n r r  − − +== − 2. TRIGONOMETRY Identities 1cossin 22 =+ AA AA 22 tan1sec += 22cosec 1 cotAA=+ sin( ) sin cos cos sinA B A B A B =  cos( ) cos cos sin sinA B A B A B= tan tantan( ) 1 tan tan ABAB AB = sin 2 2sin cosA A A= 2 2 2 2cos 2 cos sin 2cos 1 1 2sinA A A A A= − = − = − 2 2 tantan 2 1 tan AA A= − Formulae for ABC sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − 1 sin2 bc A=

3 AISS PRELIM/4E/4049/01/2023 [Turn over 1 The variables x and y are related by the equation 2 hy xk= − . The diagram below shows the graph of 1 y against x. Calculate the value of h and of k. [4] 2 hy xk= − 1 2 2 x k k xy h h h −= = − Gradient of line = 1 ( 4) 1 2 10 0 2 h −− ==− 4h= y-intercept at 4 k h− =− 16k = ( )0, 4− x B1: setting up linear form M1: finding gradient A1 A1

4 AISS PRELIM/4E/4049/01/2023 2 The Richter scale measures the intensity of an earthquake using the formula 0 lg IM I =   , where M is the magnitude of the earthquake, I is the intensity of the earthquake, and 0I is the intensity of the smallest earthquake that can be measured. (a) Calculate the magnitude of an earthquake if its intensi