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Do not refer to the text when taking this test A good score is at least 80 percent of the answers correct Answers are in the back of the book It s best to have a friend check your score the first time, so you won t memorize the answers if you want to take the test again This test is long Don t try to do it all 547in one sitting! 1 Which of the following procedures, if any, is not an acceptable way to modify an equation (a) Add a positive integer to the part of the equation to the left of the equals sign, and add the same positive integer to the part of the equation to the right of the equals sign (b) Subtract a positive integer from the part of the equation to the left of the equals sign, and subtract the same positive integer from the part of the equation to the right of the equals sign (c) Multiply the part of the equation to the left of the equals sign by a positive integer, and multiply the part of the equation to the right of the equals sign by the same positive integer (d) Divide the part of the equation to the left of the equals sign by a positive integer, and divide the part of the equation to the right of the equals sign by the same positive integer (e) All of the above procedures are acceptable 2 Consider the following pair of equations as a two-by-two linear system: x = 4y 3 and x = 4y + 2
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What is the solution to this system (a) (x, y) = (0, 4) (b) (x, y) = (3/4, 1/2) (c) (x, y) = ( 4/3, 2) (d) There are infinitely many solutions (e) There is no solution 3 If the discriminant in a quadratic equation is equal to 0, it means that (a) the equation has two different real roots (b) the equation has one real root with multiplicity 2 (c) the equation has one imaginary root with multiplicity 2 (d) the equation has two different nonreal, complex roots (e) the equation has no roots at all 4 Which of the following is not a rational number (a) 22/7 (b) 2525252525 (c) (d) 641/2 (e) (64/9)1/2 5 Suppose that m and n are integers, and p is a nonzero integer All of the following equations except one are generally true Which one is the exception (a) (m + n)/p = m/p + n /p (b) p/(m n) = p /m p /n (c) p(m + n) = pm + pn (d) (m + n)p = mp + np (e) (m n)p = mp np 6 Suppose we are trying to solve a three-by-three linear system using matrices We are sure we haven t made any mistakes along the way We come up with this matrix:
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We can conclude that the original three-by-three system has (a) no solutions (b) one solution (c) two solutions (d) three solutions (e) infinitely many solutions
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7 Fill in the blank to make the following statement true Suppose that a is a nonzero number Also suppose that m and n are rational numbers, with n 0 If we raise a to the mth power and then take the nth root of that quantity, we get the same result as if we ________ (a) raise a to the power of (m + n) (b) raise a to the power of (m n) (c) raise a to the power of mn (d) raise a to the power of m /n (e) raise a to the power of 1/(mn) 8 When we want to add two complex numbers, we must (a) add the real parts and multiply the imaginary parts, getting a real number (b) multiply the real parts and add the imaginary parts, getting a complex number (c) multiply the real parts and the imaginary parts separately, getting a real number (d) add the real parts and the imaginary parts separately, getting a complex number (e) find their absolute values and add them, getting a real number 9 In Fig FE-1, which of the following statements is true, assuming A, B, C, and D are all non-empty sets (a) Sets A and B are disjoint, and sets C and D are disjoint (b) Sets A and C are disjoint, and sets B and D are disjoint (c) Sets B and C are disjoint, and sets A and D are disjoint (d) Sets A and C are disjoint, and sets A and D are disjoint (e) None of the above 10 In Fig FE-1, which of the following statements is true, assuming A, B, C, and D are all non-empty sets (a) B A (b) B A (c) A B = A (d) A B = (e) A B = B 11 Suppose it s 12:00 noon on the twenty-fifth day of June How many 24-hour days will pass between this moment and 12:00 noon on the fourth day of July, in the same year and in the same time zone (June has 30 days) (a) Eight days (b) Nine days (c) Ten days (d) Eleven days (e) Twelve days 12 The numerical value of 13/( 3) is the same as the value of (a) 4-1/3 (b) 4-1/3
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