PHS 2021 4EXP Prelim AM P2 MS

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 Marking Scheme

2 This question paper consists of 17 printed pages (including this cover page) and 1 blank page.

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] M1, M1 A1 (ii) Explain whether y is an increasing or decreasing function. [2] For all x, and , M1 y is a increasing function. A1

5 2 The equation of the curve is , where a is a constant. (a) When , find the set of values of x for which . [3] M1 M1 A1 (b) (i) Find the range of values of a for which the curve has no real roots. [3] M1 M1 A1 (ii) Hence explain why the curve cannot lies completely below the x-axis. [1] For curve to lie below x-axis, , but , hence the curve cannot lies completely below the x-axis

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] M1 M1 A1 A1 (ii) Determine by showing all necessary working, the number of real root(s) of the equation . [4] (ii) M1, M1 Discriminant of = There is no real solution of M1 has only one real roots A1

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8 4 (i) Prove the identity . [4] M1 M1 M1 AG1 (ii) Hence find all the angles between 0 and 2π for which . [5] M1 M1 M1 (rejected) M1

9 A1 5 It is given that is such that . Given that , show that where a and b are constants. [7] M1, M1 M1, M1 M1 M1 A1

10 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 1.80 2.10 2.41 2.71 3.00 3.32 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] (ii) Use your graph to find the value of x when . [1] (iii) Explain how would you use the graph to find the value of x for which . [2] M1