NASS 2026 AM-O S4E5N Prelim P1 (QP)

Name: .............................................................. Register no: ........... Class: ........... NGEE ANN SECONDARY SCHOOL O PRELIMINARY EXAMINATION ADDITIONAL MATHEMATICS 4049/01 Paper 1 28 August 2026 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, register number and class 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 90. For Examiner’s Use Total /90 Checked by student: ………………………………. Date: ………………… This document consists of 21 printed pages and 1 blank page.

2 NAS/2026/Prelim/AM-O/P1 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 02  cbxax , a acbbx 2 42  Binomial expansion   1 2 2 ... ...1 2 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       1 ... 1 ! ! ! ! n n n n rn r r n r r          2. TRIGONOMETRY Identities 2 2sin cos 1A A  2 2sec 1 tanA A  2 2cosec 1 cotA A    BABABA sincoscossinsin   cos cos cos sin sinA B A B A B     BA BABA tantan1 tantantan   AAA cossin22sin  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 ΔABC sin sin sin a b c A B C  2 2 2 2 cosa b c bc A   1 sin2 bc A 

3 NAS/2026/Prelim/AM-O/P1 1 The percentage Gross Domestic Product (GDP) growth of a country from 2014 to 2024 can be modelled by the quadratic equation 2G( ) 0.7 7 11.2t t t   , where t is the number of years after 2014. (a) By completing the square, find the year in which the percentage growth is the lowest, and state this minimum percentage GDP growth. [4] (b) Explain why this model may not be suitable for predicting the country’s percentage GDP growth in the long run. [1]

4 NAS/2026/Prelim/AM-O/P1 2 Do not use a calculator in this question. It is given that 2 12a b  , where a and b are positive real numbers. (a) Show that   2 2 3 216 2 6a b b    . [4] (b) Hence state the least possible positive value of 1 2 3a b . [1]

5 NAS/2026/Prelim/AM-O/P1 3 (a) Express   1 1n n  in partial fractions. [3] (b) Hence show that   1 1 1 1 1 2 ...3(4) 4(5) 5(6) 1 ( 1) 3( 1) n n n n n n          . [3]

6 NAS/2026/Prelim/AM-O/P1 4 (a) Find the coefficient of 3x in the binomial expansion of 1221 .2 x x     [3] (b) The coefficients of x and 2x in the binomial expansion of  3 2 n x are equal. Find the value of n. [4]

7 NAS/2026/Prelim/AM-O/P1 5 (a) The graph of logby a x  , where a and b are constants, passes through the points with coordinates  9,0 and  243,3 . Find the values of a and b, and hence express x in terms of y. [5]

8 NAS/2026/Prelim/AM-O/P1 (b) One student was infected with HFMD in a school of 2900 students. The spread of the disease through the school population was given by 0.65 2900 1 2899 tN e  , where N was the total number of students infected after t days. The school would suspend lessons for a week when more than 40% of the students were affected. Find, correct to the nearest whole number, the number of days after the first student was infected with HFMD that the school would suspend lessons. [4]

9 NAS/2026/Prelim/AM-O/P1 6 (a) Prove that 1 1tan . tan sin cosx x x x  [2] (b) Hence solve 2 1 3 tansin cos xx x   for 0 . x   \ [4]

10 NAS/2026/Prelim/AM-O/P1 7 The diagram shows an open cylinder tank with O as the centre of the base and 0 90   . It is given that angle 2EOF  and OF = 5 cm. (a) Prove that the total surface area of the cylinder is  25 2sin 2 cos 2 12S      . [4]