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