BBSS 4 Express Add Maths Prelims Paper 1 4049 2021 Final

Class Register Number Name Bukit Batok Secondary School GCE ‘O’ Level Preliminary Examination 2021 Secondary 4 Express ADDITIONAL MATHEMATICS 4049/01 Paper 1 24 August 2021 Tuesday 08 00 – 10 15 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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. If you need additional writing space, you may request for writing/graph papers from the invigilators. At the end of the examination, you will insert the additional writing/graph papers into your Question Paper. 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 This document consists of 19 printed pages. HOM: Striving for accuracy and precision

2 BBSS/Prelim/2021/Sec4E/AMaths/Paper1 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation Binomial expansion , where n is a positive integer and 2. TRIGONOMETRY Identities sin² A + cos² A = 1 sec² A = 1 + tan² A cosec² A = 1 + cot² A sin (A  B) = sin A cos B  cos A sin B cos (A  B) = cos A cos B ∓ sin A sin B sin 2A = 2sin A cos A cos 2A = cos2 A – sin2 A = 2cos2 A – 1 = 1 – 2sin2 A tan 2A = Formulae for ABC a² = b² + c² 2bc cos A Answer all the questions

3 BBSS/Prelim/2021/Sec4E/AMaths/Paper1 1 The quadratic function 3 − 2𝑚 + 𝑚𝑥 − 𝑥2 is always negative for . Determine the value of p and of q. [4]

4 BBSS/Prelim/2021/Sec4E/AMaths/Paper1 2 Given that prove that . [4]

5 BBSS/Prelim/2021/Sec4E/AMaths/Paper1 3 A watermelon is assumed to be spherical in shape while it is growing. Its mass, M kg, and radius r cm, are related by the formula 𝑀 = 𝑘𝑟3, where k is a constant. It is also assumed that the radius is increasing at a constant rate of 0.1 cm per day. On a particular day the radius is 10 cm and the mass is 3.2 kg. (i) Find the value of k. [2] (ii) Find the rate at which the mass is increasing on this day. [3]

6 BBSS/Prelim/2021/Sec4E/AMaths/Paper1 4 The reflex angle is such that where 0 < k < 1. (i) Find an expression, in terms of k, for (a) [2] (b) [1] (ii) Explain why is negative for 0 < k <1. [2]

7 BBSS/Prelim/2021/Sec4E/AMaths/Paper1 5 (a) Find the term independent of x in the expansion of (2𝑥 − 1 3𝑥) 6 . [2] (b) In the expansion of (3 − 2𝑥) (1 + 𝑥 2) 𝑛 , the coefficient of x is 7. Find the value of the constant n and hence find the coefficient of x2. [5]

8 BBSS/Prelim/2021/Sec4E/AMaths/Paper1 6 The population P, in millions, of a country is given by , where t is the number of years after January 2000 and A and b are constants. In January 2010 the population was 40 million and had increased to 45 million by January 2013. (i) Show that b = 1.04 correct to 2 decimal places and find A correct to the nearest integer. [4] (ii) Find the population in January 2020, giving your answer to the nearest million. [1] (iii) Find the year when the population will be over 100 million for the first time in the month of January. [3]

9 BBSS/Prelim/2021/Sec4E/AMaths/Paper1 7 In the diagram, BC is a diameter of the circle, ABC is a straight line and AD is a tangent to the circle at D. AD = DC and AB : BC = 1 : 2 . (i) Explain why is similar to . [3] (ii) Hence, or otherwise, show that [3] (iii) Hence find [3] [NOT TO SCALE] C B O A D

10 BBSS/Prelim/2021/Sec4E/AMaths/Paper1 8 (a) The equation of a curve is . (i) Obtain an expression for . [2] (ii) Explain why the curve has no stationary points. [1] (b) A curve has equation = (2𝑥 − 1)√4𝑥 + 3 , 𝑥 > − 3 4 . (i) Find 𝑑𝑦 𝑑𝑥 in the form 4(𝐴𝑥+𝐵) √4𝑥+3 where A and B are integers. [3]