2017 HCI H1 Maths Prelims Answers

1 2017 C2 H1 Prelim Solutions 1 Let x, y and z be the original selling price per pack of organic quinoa, organic feed eggs and chia seeds in dollars. 3 0.85 2 72.28xy z  --- (1)  2 2 0.85 5 93.85xy z  --- (2)  6 3 0.85 3 145.43xy z  --- (3) $14.90, $11.49, $8.90xyz 2(a)      2d1 ln 2 ln 1d 2 = ln 1 xx xxx x xx xx      2(b)  11 22 3 2 d1eed 22 xx x x        3 2.5 1.41x   or 1.41 1.41x  4(i) Using long division 221 3 3 2844 x xxx          2 2 421OR 44 21 4 AxBx Cx xx x Ax B x C        Compare coefficient: 28 3 3A,B ,C 4(ii) 266 55 62 5 21 3 3 d2 8 d44 83 3 l n 4 84 33ln 2 65 19 33ln 2 x xx xxx xx x           32x  0.5y   2.5,0.75  1.41,0.414  1.41, 2.41

2 5(i) 5(ii)    2 2 31 = 3 3 = 2 3 y xx x xx x x      2 2 23 33 0 x kx x xx k        2 2 40 34 30 94 1 20 42 1 52 5 ba c k k k k.       { : 5.25}kk 5(iii)   31 5yx xx     2 2 23 5 32 0 21 0 21 x xx xx xx x, x           1 2 2 1 2 2 132 2 2 area 2 3 5 d = 3 2 d 3 = 2 32 13 81 2 = 2 432 3 2 1 = units6 x xxx xx x xx x                         Or x y  30,  1, 4 10, 03,   31yx x 

3 1 2 2 132 2 2 1area ( 2 3)d (3 4) 1 2 27 3 32 2 1 = units6 xx x xx x             6(i) 221 π 33Area = 3 sin 2 223 4x xy xx y      2 2 33 21 54 3321 5 4 15 3 32 4 xx y xy x y xx    Let P be the perimeter. 52 15 3 35 4 Px y x xx   2 d3 3 1 5 = 5d4 P x x For cost to be minimum, perimeter has to be minimum. 2 2 2 d3 3 1 505 0d4 15 3.700962 4.053 2.0132 2.01, 2.42 P xx xx x xy         2 23 d3 0 0d P xx  Therefore P is a minimum.

4 6(ii) Let N be the perimeter of the fence in integral value Cost from Company 90A N    Cost from Company 10 95 84 10 110 84 BN N    110 84 90 61 1 0 18.3 18 NN N NN     6(iii) When x = 2.0132, y = 2.4177 14.902P Since 14.902 18 , therefore it is cheaper to choose Company A. 7(a) No. of words that can be formed 7! 1 5039    (b) No. of words if 3 vowels are altogether 3! 5! 720    No. of words 5040 720 4320   (c) 4 2No. of words 2! 5! 1440 C   8(i) Let B be the event that the lunch box is produced by production line B. Let F be the event that the lunch box is faulty.             PP P = P P (*) P 0.03 0.05 0.4 2P 3 FB B F B FB F B B      8(ii) Let A be the event that the lunch box is produced by production line A.   P 0.05 0.6 0.03 0.03P | 0.09 1 3 AF FA    8(iii)  2P ' 0.02 0.646673BF   0.64667 0.02 2 | only 1 faulty 0.95 0.05 2 0