ACSBR 2023 4E5N Add Maths Prelim P1_updated

Full Name Class Index No Class Anglo-Chinese School (Barker Road) PRELIMINARY EXAMINATION 2023 SECONDARY FOUR EXPRESS / FIVE NORMAL (ACADEMIC) ADDITIONAL MATHEMATICS 4049 PAPER 1 2 HOURS 15 MINUTES Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number and name on all the work you hand in. Write in dark blue or black pen. Answer all questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For  , use either your calculator value or 3.142, unless the question requires the answer in t erms of  . 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. This question paper consists of 18 printed pages and 2 blank pages. For Examiner’s Use

Anglo-Chinese School (Barker Road) 2 Preliminary Examination 2023 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 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 nn n na b a a b a b a b b r − − −     + = + + + + + +           , where n is a positive integer and ( ) ( ) ( )11! ! ! ! n n n n rn r r n r r − − + == − 2. TRIGONOMETRY Identities 22sin cos 1AA+= 22sec 1 tanAA=+ 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=

Anglo-Chinese School (Barker Road) 3 Preliminary Examination 2023 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 1 A cuboid has a square area ( ) 26 35 m .− The capacity of the cuboid is ( ) 345 5 38 7 m .− Find the height of the cuboid, in m, in the form ( )57ab − , where a and b are integers. [3]

Anglo-Chinese School (Barker Road) 4 Preliminary Examination 2023 Secondary 4 Express / 5 Normal (Academic) Additional Mathematics 4049 Paper 1 2 (a) Show that ( 1)x− is a factor of 32f ( ) (2 1) ( 2 )x x h x k h x k= − + − − + ,where h and k are constants. [1] (b) Explain with working why the equation f ( ) 0x = will have 3 real roots if 2 0hk+ . [4]

Anglo-Chinese School (Barker Road) 5 Preliminary Examination 2023 Secondary 4 Express / 5 Normal (Academic) Additional M