PHS 2021 4EXP Prelim AM P1 QP

1 Presbyterian High School4049/01/4E5N Prelim 2021 [Turn Over Name: Index No.: Class: PRESBYTERIAN HIGH SCHOOL ADDITIONAL MATHEMATICS 4049/01 Paper 1 25 August 2021 Wednesday 2 hours 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. Omission of essential working will result in loss of marks. 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 Qn 1 2 3 4 5 6 7 8 9 10 11 12 13 Marks Deducted Marks Total Marks 90

2 Presbyterian High School4049/01/4E5N Prelim/2021 ae ge ag ag ag ae ga gS he sd Categ ory Acc ura cy Unit s Sy mb ols Oth ers Questi on No. Setter: Mrs Yim Meng Choo Vetter: Mr Tan Chee Wee This question paper consists of 17 printed pages and 1 blank pages. Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation , . Binomial Theorem , where n is a positive integer and 2. TRIGONOMETRY

3 Presbyterian High School4049/01/4E5N Prelim 2021 [Turn Over Identities . . Formulae for Δ ABC . . .

4 Presbyterian High School4049/01/4E5N Prelim 2021 [Turn Over Answer all questions in the space provided. 1 Solve the following simultaneous equations. [4]

5 Presbyterian High School4049/01/4E5N Prelim 2021 [Turn Over 2 (i) Express in the form , where a, b and c are constants. [2] (ii) Hence, determine with explanation, whether the curve lies entirely below the x-axis. [2] 3If the line is a tangent to the curve , find the possible values of k. [5]

6 Presbyterian High School4049/01/4E5N Prelim/2021 4 Given that , where , express in terms of p, (i) , [2] (ii) . [3]

7 Presbyterian High School4049/01/4E5N Prelim 2021 [Turn Over 5 (i) PQR is an equilateral triangle whose side is cm. Find the exact value of the area of the equilateral triangle PQR, in the form where a and b are rational numbers. [4] (ii) A right prism with the equilateral triangle PQR as the cross-sectional base is to be made such that the volume of the prism is 8 cm3. Find the height of the prism, giving your answer in surd form. [3]

8 Presbyterian High School4049/01/4E5N Prelim/2021 6 A man buys a precious gem. The value, V dollars, of the gem after t years is given by , where N and k are constants. At the beginning, the value of the gem is $12000. (i) Find the value of N. [1] (ii) The value of the gem after 5 years is $10000. Find the value of k. [4] (iii) After 15 years, a gem dealer offers to pay the man $5000 for the gem. Based on the given equation, would you advise him to sell it? Justify your answer. [2]

9 Presbyterian High School4049/01/4E5N Prelim 2021 [Turn Over 7 A curve has equation . (i) Find the gradient of the curve when , leaving your answer in the exact form. [5] (ii) Given that x is increasing at a constant rate of 0.12 units per second, find the rate of change of y when . [2]

10 Presbyterian High School4049/01/4E5N Prelim/2021 8 The function is defined for (i) State the amplitude and period of f. [2] (ii) Sketch on the same diagram below, the graphs of and for . [4] (iii) Hence determine the value of k for which the equation has 3 solutions for . [1] x y O