YTSS 4NA Additional Mathematics with Answer Key Question Paper 2 2023

NAME: ( ) CLASS: YISHUN TOWN SECONDARY SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY 4 NORMAL ACADEMIC ADDITIONAL MATHEMATICS PAPER 2 (4051/02) DATE : 15 August 2023 DAY : Tuesday DURATION : 1 hour 45 minutes MARKS : 70 READ THESE INSTRUCTIONS FIRST Do not turn over the cover page until you are told to do so. Write your name, class and class index number 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 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 70. MARKS OBTAINED FULL 1 4 2 4 3 5 4 5 5 6 6 8 7 9 8 10 9 10 10 9 TOTAL 70 This question paper consists of 14 printed pages including this cover page.

2 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/02) Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation , 2. TRIGONOMETRY Identities 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 02  cbxax a acbbx 2 42  AA AA AA 22 22 22 cot1eccos tan1sec 1cossin          A AA AAAAA AAA BA BABA BABABA BABABA 2 2222 tan1 tan22tan sin211cos2sincos2cos cossin22sin tantan1 tantantan sinsincoscoscos sincoscossinsin         

3 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/02) [Turn over 1 Integrate with respect to x (a) 22( 1)x  , [2] (b) 32 .2 xx x  [2]

4 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/02) 2 (a) Write down the period of 12 tan .2y  [1] (b) On the axes below, sketch the graph of 12 tan 2y  for 22     radians. [3] 2   3 2  2 y 2 3 2   2  

5 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/02) [Turn over 3 (a) Show that 2f ( ) 3 9 7x x x   can be written as 2f ( ) ( ) ,x a x b c   where a, b and c are constants to be found. [4]