Math141Sols1AS11

Math141Sols1AS11 - QUIZ 1A SOLUTIONS(CHAPTER 0 MATH 141...

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QUIZ 1A - SOLUTIONS (CHAPTER 0) MATH 141 – SPRING 2011 – KUNIYUKI 90 POINTS TOTAL No notes or books allowed. A scientific calculator is allowed. You may assume that two-dimensional graphs are in the usual Cartesian xy -plane. Give exact answers, unless you are told to approximate. SHORTER PROBLEMS (30 POINTS TOTAL: 2 POINTS EACH, UNLESS OTHERWISE SPECIFIED) 1) The symbol ± means which of the following? (Box in one.) For all There exists Is a member of 2) (6 points total). a) Write the converse of this statement: “If John is good, then I buy John the Harry Potter book.” “If I buy John the Harry Potter book, then John is good.” b) Write the contrapositive of this statement: “If John is good, then I buy John the Harry Potter book.” “If I do not buy John the Harry Potter book, then John is not good.” Note : Just because a person is “not good” does not necessarily mean that s/he is “bad.” c) Which of the following is logically equivalent to the given statement? (Box in one.) Its converse Its inverse Its contrapositive
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3) Use absolute value notation to mathematically express the distance between x and 4 on the real number line. x ± 4 or 4 ± x 4) (5 points). Factor completely over ± , the integers: 4 x 7 + 32 x 4 . First, factor out the GCF, 4 x 4 . 4 x 7 + 32 x 4 = 4 x 4 x 3 + 8 () We must now factor x 3 + 8 . Template for factoring a Sum of Two Cubes: A 3 + B 3 = A + B A 2 ± AB + B 2 . Here, A = x and B = 2 . 4 x 4 x 3 + 8 = 4 x 4 x + 2 x 2 ± 2 x + 4 Note : The last factor, x 2 ± 2 x + 4 , is irreducible over the integers by the Test for Factorability. 5) Is a 2 + b 2 equivalent to a + b ? Box in one: Y e s N o A counterexample is provided by the case a = 3 and b = 4 , for example. The square root of a sum does not typically equal the sum of the square roots.
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Math141Sols1AS11 - QUIZ 1A SOLUTIONS(CHAPTER 0 MATH 141...

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