Manjusri 4049 02 PRE 2021

This document consists of 23 printed pages and 1 blank page. Name Register Number Class Calculator Model MANJUSRI SECONDARY SCHOOL PRELIMINARY EXAMINATION 2021 Subject: Additional Mathematics Level: Secondary 4 Express Paper: 4049/02 Date: 30 August 2021 Duration: 2 hours 15 minutes Setter: Mdm Tuan Chui Lin 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 questions. Give non-exact numerical answers corrected 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. At the end of the examination, fasten all your work securely together. 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 84. Marks Obtained 84

2 4049/02/PRELIM/2021 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, Binomial Expansion , where n is a positive integer and 2. TRIGONOMETRY Identities Formulae for ΔABC Δ = bc sin A

3 4049/02/PRELIM/2021 Answer all questions 1 Find the values of x and y which satisfy the equations , . [4]

4 4049/02/PRELIM/2021 2 (i) Express the function in the form h(x) = a(x + b)2 + c, where a, b and c are constants. [2] (ii) Hence determine the minimum value of h(x) and the corresponding value of x. Give reasons to support your answer. [2]

5 4049/02/PRELIM/2021 3 A curve has the equation , where k is a constant. (i) In the case where k = –3, find the range of values for x for which y ≥ 0. [2] (ii) Find the value of k for which the line is a tangent to the curve. [2]

6 4049/02/PRELIM/2021 4 It is given that . (i) Express a in terms of b. [3] (ii) State the conditions of a and b for the equation to exist. [2]

7 4049/02/PRELIM/2021 5 (a) Find the equation of normal to the curve at x = 1. [3] (b) Water is poured into a container at the rate of 94 cm3/s. The volume of water in the container is V cm3, where and h is the height of water in the container. Find the rate at which height of water is increasing when h = 3 cm. [3]

8 4049/02/PRELIM/2021 6 In the diagram, the points A, B, D and F lie on a circle. The lines AD and BF intersect at the point E. The tangents to the circle at B and D meet at the point C. (a) Prove that ∠BAD + ∠BFD + ∠BCD = 180°. [2] A C D E F B

9 4049/02/PRELIM/2021 (b) Prove that ΔAEF is similar to ΔBED. [2] (c) Prove that AF×BE = AE×BD. [2]

10 4049/02/PRELIM/2021 7 (a) By considering the general term in the binomial expansion of , (i) explain why there are no odd powers of x in this expansion. [3] (ii) explain why the term independent of x does not exist. [2]