MATH.14

# Q8 the points r t and u lie on a circle that has

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Q8: The points R , T, and U lie on a circle that has radius 4. If the length of arc RTU is 3 4 π , what is the length of line segment RU ? A. 3 4 B. 3 8 C. 3 D. 4 E. 6 Answer: ------------------------------------------------------------------------------------------------------------ Q9: For all integers n , the function f is defined by f ( n ) = a n , where a is a constant. What is the value of f (1)? (1) f (2) = 100 (2) f (3) = -1,000 ------------------------------------------------------------------------------------------------------------ Q10: What is the value of ( x - y ) 4 ? (1) The product of x and y is 7. (2) x and y are integers. 3

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------------------------------------------------------------------------------------------------------------ Q11: Mary persuaded n friends to donate \$500 each to her election campaign, and then each of these n friends persuaded n more people to donate \$500 each to Mary’s campaign. If no one donated more than once and if there were no other donations, what was the value of n ? (1) The first n people donated 16 1 of the total amount donated. (2) The total amount donated was \$120,000. ------------------------------------------------------------------------------------------------------------ Q12: When n liters of fuel was added to a tank that was already 3 1 full, the tank was filled to 9 7 of its capacity. In terms of n , what is the capacity of the tank, in liters? A. 9 10 n B. 3 4 n C. 2 3 n D. 4 9 n E. 3 7 n Answer: ------------------------------------------------------------------------------------------------------------ Q13: 4
If n is a positive integer, what is the remainder when 3 8 n +3 + 2 is divided by 5? ------------------------------------------------------------------------------------------------------------ Q14: Of all the students in a certain dormitory, 2 1 are first-year students and the rest are second-year students. If 5 4 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major? 1 1 4 1 2 ------------------------------------------------------------------------------------------------------------

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