Peicai Prelims_4049_4E_AMath_P2_2021_solutions

[Turn over PEICAI SECONDARY SCHOOL SECONDARY 4 EXPRESS PRELIMINARY EXAMINATION 2021 CANDIDATE NAME CLASS REGISTER NUMBER ADDITIONAL MATHEMATICS 4049/02 Paper 2 27 August 2021 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your register number, class and name 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. DO NOT WRITE IN ANY BARCODES. 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. This document consists of 20 printed pages. Setter: Mrs Ho Thuk Lan SOLUTIONS

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the quadratic equation ax 2 + bx + c = 0, Binomial expansion , where n is a positive integer and 2. TRIGONOMETRY Identities Formulae for ∆ABC

3 [Turn over 1 Solve the equation for . [5] x = 0.253, 1.57, 2.89 2 The diagram shows two circles and with centres P and Q respectively. Both circles and is tangent to the x axis at R (1.5, 0). The radius of is 6 units. (i) Find the coordinates of the centre, P of circle . [1] P = (ii) Find the equation of the circle . [1] (iii) Given that the area of is 18 times the area of , find the coordinates of the centre, Q of . [3] Q = (1.5, ) P(1.5,6) x Q R(1.5, 0) R a d i u s

4 3 (i) Using , show that . [3] (ii) State the amplitude and period of . [2] Amplitude = 2 Period = 120 (iii) Sketch the graph of for . [3]

5 [Turn over 4 A glass of hot water was left to cool in the fridge. The temperature, T C, of the water decreases with time, t minutes. The table shows the measured values of T and t. t (min) 10 20 30 40 50 T (C) 60 37 23 14 9 It is known that t and T are related by the equation where a and k are constants. (i) Explain clearly how a and k can be calculated when a graph of ln T against t is drawn. [2] k = gradient ln a is the ln T – intercept, c ln a = c a = t (min) 10 20 30 40 50 ln T (C) 4.09 3.61 3.14 2.64 2.20 (ii) On the grid below, plot ln T against t for the given data and draw a straigh