2014 H2 Maths Prelims 2 P1 Qn Paper

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2    IJC/2014/JC2 9740/01/S/2014 [Turn over 1 Adam bought a total of 50 fruits consisti ng of apples, oranges and pineapples. The apples, oranges and pineapples cost $0.80, $0.60 and $1.20 each respectively. The total cost of all the fruits he bought is $40. If the cost of apples is doubled and that of oranges is halved, then the total cost of all the fruits that he bought would be $53. Find the number of each type of fruit bought by Adam. [3] 2 It is given that x, y, z are the first three terms of a geometric progression. When the three terms are arranged in the order of z, x, y, they form three consecutive terms of an arithmetic progression. (i) Show that 2 20zz yy      . [4] (ii) Hence determine if the sum to infinity of the geometric progression exists. [2] 3 (i) Without the use of a calcul ator, solve the inequality    2 24 3 02 xx x x    . [5] (ii) Hence solve the inequality     2 24