[FFM] [2023] 4E AM 4049 Prelims P1_QP

NAME: ____________________________ ( ) CLASS: _______ ADDITIONAL MATHEMATICS 4049/01 Paper 1 Date: 24 August 2023 Duration: 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 on all the work you hand in. 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. 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 Table of Penalties Question Number 90 Presentation  1  2 Rounding off  1 Parent’s/Guardian’s Signature Setter: Mdm Haliza This question paper consists of 21 printed pages including the cover page. FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2023 SECONDARY 4 EXPRESS

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Express Preliminary Examination 2023 2 Additional Mathematics Paper 1 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02 =++ cbxax , a acbbx 2 42 −−= Binomial expansion ( ) nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− ......21 221 , where n is a positive integer and ! )1)...(1( )!(! ! r rnnn rnr n r n +−−=−=      2. TRIGONOMETRY Identities 1cossin 22 =+ AA AA 22 tan1sec += cosec 2 A = 1 + cot 2 A BABABA sincoscossin)sin( = BABABA sinsincoscos)cos( = BA BABA tantan1 tantan)tan(  = AAA cossin22sin = AAAAA 2222 sin211cos2sincos2cos −=−=−= A AA 2tan1 tan22tan −= Formulae for ABC C c B b A a sinsinsin == Abccba cos2222 −+= Cabsin2 1=

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Express Preliminary Examination 2023 3 Additional Mathematics Paper 1 Answer all the questions. 1 Without using a calculator, find the exact value of (i) cosec , given that  is acute and 3cos 4 = , [1] (ii) cos30 (tan 45 sin 60 ) +  . [2]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Express Preliminary Examination 2023 4 Additional Mathematics Paper 1 2 Find the set of values of a for which the curve 227yx=+ lies entirely above the line 3y ax=− . [4]

Name: __________________________________ (