KSS 2021 Prelims 4E AM P1 (Solutions)

2021 KSS AM Prelim P1 (Solutions) 1 2 The solution set is , hence x = 5 does not satisfy the inequality. 3 0 5 8 3 0 5 8

3i 3ii Since there are no real roots for the quadratic factor, f(x) has only 1 real root, x = -1. 3iii 4ai 4aii [M1] Since distance of A to center = 12.6 units (3s.f.) > 12 = radius, The person will not be able to make use of free WiFi. Since 147>131, i.e. standing outside the circumference of the coverage, hence the person will not be able to make use of free WiFi. 4bi 4bii

4biii and ABCD is given as a rhombus, i.e. AB = AD ABCD is a square. 5i , there is no turning point for all values of x. (shown) 5ii 6

7i 7ii 8i 8ii 8iii Since the displacement of the particle changes from a positive value. (when t = 24) to a negative value (when t = 25), the particle passes through O at some instant during the twenty-fifth sec. [A1]

9a 9bi 9bii 10i h = 2(1 – cos kt). Since the diameter of the carousel = max value of h, h = 2 (1 – (-1)) = 4 m 10ii Period = 20 s 10iii

11a 11bi 11bii 12