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# i) Sketch the following regions and find their areas. (1) The region enclosed by the curve f (x) = 2x − x2 and the x axis.

i) Sketch the following regions and find their areas. (1) The region enclosed by the curve f (x) = 2x − x2 and the x axis. (2) The region between the curves g(x) = 2(x − 1)2 + 3 and h(x) = 9 − 2x. ii) A student planning her university course for next year has a number of choices to make. Her course must consist of one out of five different business subjects, one of three different mathematics subjects, two out of six possible breadth subjects and either one of the four different history subjects or one of the three different literature subjects. How many different courses could she possibly choose? iii) If you are randomly dealt a poker hand of five cards from a standard deck of 52 playing cards, find the probability that you have: (1) four kings in your hand (2) all hearts in your hand

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