YTSS 4NA Additional Mathematics with Answer Key Question Paper 1 2023

NAME: ( ) CLASS: YISHUN TOWN SECONDARY SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY 4 NORMAL ACADEMIC ADDITIONAL MATHEMATICS PAPER 1 (4051/01) DATE : 14 August 2023 DAY : Monday 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 5 3 4 4 5 5 4 6 4 7 4 8 4 9 6 10 3 11 6 12 4 13 8 14 9 TOTAL 70 This question paper consists of 17 printed pages including this cover page and 1 blank page.

2 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/01) 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 (4051/01) [Turn over 1 Express 2 2 2 ( 2) ( 4) x xx   in partial fractions. [4]

4 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/01) 2 Do not use a calculator in answering this question. ABCD is a trapezium where AB is parallel to DC. The area of the trapezium is 31112 cm2. AB = 8 48 cm and 1212DC cm. Find the perpendicular distance between AB and DC, leaving your answer in the form 3ba , where a and b are integers. [5] D C B A

5 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/01) [Turn over 3 Solve the simultaneous equations 22 7 0,x xy y    3 7 0.yx   [4]

6 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/01) 4 The function f ( )x is defined by f ( )x  323 + 4 x hx kx for all real x. Given that 31x is a factor of f ( )x and that when f ( )x is divided by 1x , the remainder is 4 , find the value of each of the constants h and k. [5]

7 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/01) [Turn over 5 Find the set of values of the constant k for which the curve 2 12 4 41y x x k    lies completely above the line 9 4y kx k . [4]

8 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/01) 6 (a) Factorise 327 125x  . [2] (b) Explain why 5 3x is the only real root of the equation 327 125 0x  . [2]

9 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/01) [Turn over 7 (a) Show that sin( ) sin( ) tancos( ) cos( ) A B A B AA B A B       . [2] (b) Hence, find the exact value of sin105 sin15 .cos105 cos15 oo oo   [2]

10 2023 Preliminary Exam Secondary 4 Additional Mathematics NA (4051/01) 8 Given that cos 2 pecA , where A is obtuse, express each of the following in terms of p. (a) cot ,A [2] (b) cos2 .A [2]