2022 AHS AMath Prelims P1

Secondary Four Additional Mathematics Preliminary Examinations 2022 [Turn over NAME: _______________________________ ( ) CLASS: 4 ( ) 9o ADDITIONAL MATHEMATICS 4049 / 01 Paper 1 29 August 2022 Candidates answer on the Question Paper. 2 hours 15 mins No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, index number and class in the space at the top of this page. Write in dark blue or black pen. You may use a 2B pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters and glue or correction fluid. Answer all the 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. ------------------------------------------------------------------------------------------------------------------------- For Examiners’ Use Question Marks Question Marks Table of Penalties 1 8 2 9 Clarity/Logic 3 10 Accuracy/Precision 4 11 Units 5 12 Total: 6 13 7 Parent’s Name & Signature: Date: This document consists of 18 printed pages. S4 ANGLICAN HIGH SCHOOL SECONDARY FOUR PRELIMINARY EXAMINATIONS 2022 90

2 Secondary Four Additional Mathematics Preliminary Examinations 2022 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  AAec 22 cot1cos  BABABA sincoscossin)sin(   cos cos cos sin sinA B A B A B     tan tantan 1 tan tan A BA B A B    AAA cossin22sin  AAAAA 2222 sin211cos2sincos2cos  A AA 2tan1 tan22tan   Formulae for ABC C c B b A a sinsinsin  Abccba cos2222  Area of Cabsin 2 1

3 Secondary Four Additional Mathematics Preliminary Examinations 2022 [Turn over 1 A polynomial, P( )x , is 3 22 6 27x ax x   , where a is a constant. The quadratic expression 2 9x bx  is a factor of P( )x , where b is a constant. (a) Find the remaining factor of P( )x . [2] (b) Show that the equation P( ) 0x  has only one real root. [3