PHS 2021 4EXP Prelim AM P2 QP

Name: Index No.: Class: PRESBYTERIAN HIGH SCHOOL ADDITIONAL MATHEMATICS 4049/02 Paper 2 26 August 2021 Thursday 2 hrs 15 min PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL 2021 SECONDARY FOUR EXPRESS PRELIMINARY EXAMINATIONS INSTRUCTIONS TO CANDIDATES DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. Write your name, index number and class on the spaces provided above. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. Write your answers on the spaces provided below each question. 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. Qn 1 2 3 4 5 6 7 8 9 10 11 Marks Deducted Marks Catego ry Acc ura cy Unit s Sy mb ols Oth ers Questi on No. Total Marks

2 Setter: Mr Tan Chee Wee Vetter: Mrs Yim Meng Choo This question paper consists of 18 printed pages (including this cover page) and 0 blank page. 90

3 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation , . Binomial Theorem , where n is a positive integer and 2. TRIGONOMETRY Identities . . Formulae for Δ ABC . . .

4 Answer all questions in the space provided. 1 The equation of a curve is . (i) Find an expression for . [3] (ii) Explain whether y is an increasing or decreasing function. [2]

5 4 The equation of the curve is , where a is a constant. (a) When , find the set of values of x for which . [3] (b) (i) Find the range of values of a for which the curve has no real roots. [3] (ii) Hence explain why the curve cannot lies completely below the x-axis. [1]

6 3 The expression , where a and b are constants, is exactly divisible by and leaves a remainder of when divided by . (i) Find the value of a and of b. [4] (ii) Determine by showing all necessary working, the number of real root(s) of the equation . [4]

7 4 (i) Prove the identity . [4] (ii) Hence find all the angles between 0 and 2π for which . [5]

8 5 It is given that is such that . Given that , show that where a and b are constants. [7]

9 6 The table below shows the experimental values of two variables x and y. x 1 2 3 4 5 6 y 63 127 258 510 1000 2100 It is known that x and y are related by an equation of the form , where a and b are constants. (i) By plotting against x, obtain a straight line graph to represent the above data. [3] (ii) Use your graph to estimate the value of a and of b. [3] (iii) Use your graph to find the value of x when . [1] (iv) Explain how would you use the graph to find the value of x for which . [2]

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