Manjusri 4049 01 PRELIM 2021 QP Ans Key Marking Scheme

This document consists of 21 printed pages and 3 blank pages. Name Register Number Class Calculator Model MANJUSRI SECONDARY SCHOOL PRELIMINARY EXAMINATION 2021 Subject: Additional Mathematics Paper: 4049/01 Level: Secondary 4 Express Date: 26 August 2021 Duration: 2 hours 15 minutes Setter: Mdm Neo Chai Meng 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 on both sides of the paper. 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. Marks Obtained 90

2 4049/01/PRELIM/2021 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation , . Binomial Theorem , where n is a positive integer and . 2. TRIGONOMETRY Identities Formulae for ΔABC . .

3 4049/01/PRELIM/2021 . Answer all the questions. 1 Given that find the value of x and of y. [4]

4 4049/01/PRELIM/2021 2 The volume of a right square pyramid of length cm is cm3. Without using a calculator, find the height of the pyramid in the form cm, where a and b are integers. [5]

5 4049/01/PRELIM/2021 3 (i) Given , find the value of x. [3] (ii) Given and , find the value of k where k is an integer. [3]

6 4049/01/PRELIM/2021 4 It is estimated that the percentage of Singapore’s population ( P) responding to the Save Electricity Campaign is given by the equation P = 100 (1−e-0.05t), where t is the number of weeks after the launch of the campaign. (i) Find the percentage of population responding to the Save Electricity Campaign after 8 weeks of its launch. [1] (ii) Form an inequality to find the number of weeks it takes for at least 65% of the population to respond after the launch of the Campaign. [3] (iii) Is it possible for the percentage of Singapore’s population responding to the Campaign to reach 100%? Explain your answer by showing your working clearly. [2]

7 4049/01/PRELIM/2021 5 The diagram shows part of the graph . Find the (i) set of values of x for which y is a decreasing function of x. [4] (ii) the gradient of the curve at the point where it cuts the x-axis. [2] x y 0

8 4049/01/PRELIM/2021 6 (i) By expressing cos 3x as cos (2x + x), show that . [3]

9 4049/01/PRELIM/2021 (ii) Hence, in radians, find angles of x between 0 and 2π which satisfies the equation [4]

10 4049/01/PRELIM/2021 7 (a) The acute angles A and B are such that cos (A − B) = and cos A cos B = . Without using a calculator, find the exact value of (i) sin A sin B, [2] (ii) tan A tan B. [2]