PHS 2021 4EXP Prelim AM P1 MS

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 MARK SCHEME Setter: Mrs Yim Meng Choo Vetter: Mr Tan Chee Wee

2 Presbyterian High School4049/01/4E5N Prelim/2021 This question paper consists of 16 printed pages and 0 blank pages. Answer all questions in the space provided. 1 Solve the following simultaneous equations. [4] M1 M1 A1 A1 2 (i) Express in the form , where a, b and c are constants. [2] M1 A1 (ii) Hence, determine with explanation, whether the curve lies entirely below the x-axis. [2] From part (i), the maximum point is , the curve does not lie entirely below x-axis. M1 A1

3 Presbyterian High School4049/01/4E5N Prelim 2021 [Turn Over 3If the line is a tangent to the curve , find the possible values of k. [5] M1 (Substitution) M1 (Expansion) M1 (Discriminant), M1 (=0) A1 4 Given that , where , express in terms of p, (i) , [2] (ii) . [3] (i) (ii) M1 A1 M1 M1 (Either ratio) A1

4 Presbyterian High School4049/01/4E5N Prelim/2021 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] M1 M1 (Expansion), B1 ( seen) A1 (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] M1 M1 (Conjugate) A1

5 Presbyterian High School4049/01/4E5N Prelim 2021 [Turn Over 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] B1 (ii) The value of the gem after 5 years is $10000. Find the value of k. [4] M1 M1 (Taking lg on both sides) M1 (Power Law) A1 (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] After 15 years, the value of the gem based on the equation is $6944.93 which is more than the amount offered by the dealer. So, he should not sell it to the dealer. M1 A1(o.e.)

6 Presbyterian High School4049/01/4E5N Prelim/2021 7 A curve has equation . (i) Find the gradient of the curve when , leaving your answer in the exact form. [5] M1 (Quotient Rule), M2 (1 for each correct derivative) M1 A1 (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] M1 A1

7 Presbyterian High School4049/01/4E5N Prelim 2021 [Turn Over 8 The function is defined for (i) State the amplitude and period of f. [2] Amplitude = 3 Period = 180o B1 B1 (ii) Sketch on the same diagram below, the graphs of and for . [4] x y O

8 Presbyterian High School4049/01/4E5N Prelim/2021 G2 for each curve Deduct I mark for wrong period/amplitude/shape for each curve (iii) Hence determine the value of k for which the equation has 3 solutions for . [1] k = 3 B1

9 Presbyterian High School4049/01/4E5N Prelim 2021 [Turn Over 10 (a) (i) Find the first three terms in the expansion, in ascending powers of x, of . [2] M1 (any two terms correct) A1 (ii) Hence find the value of p, where p is an integer, such that the coefficient of in the expansion of is . [3] M1 (any two terms correct) M1 A1 (b) Explain why there is no independent term in the expansion of . [4] M1 M1 (Correct power) B1 (Power =0) AG1

10 Presbyterian High School4049/01/4E5N Prelim/2021 11 [The volume of a sphere of radius r is and the surface area is .] Mr Lim wants to make a solid cylinder with a hemisphere on top as shown in the diagram below. The cylinder has radius 4x cm and height h cm. The volume of the entire solid is 896𝜋 cm3. (i) Show that . [2] M1 (Any attempt to have two vols) AG1 (ii) Show that the total surface area of the solid is given by cm2. [3] M1 (Any attempt to have two SA) M1 AG1 4x h