Math141Sols1AF11

Math141Sols1AF11 - QUIZ 1A - SOLUTIONS (CHAPTER 0) MATH 141...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
QUIZ 1A - SOLUTIONS (CHAPTER 0) MATH 141 –FALL 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 (48 POINTS TOTAL: 2 POINTS EACH, UNLESS OTHERWISE SPECIFIED) 1) (6 points total). a) Write the converse of this statement: “If I win the election, then I am clever.” “If I am clever, then I win the election.” b) Write the contrapositive of this statement: “If I win the election, then I am clever.” “If I am not clever, then I do not win the election.” c) Which of the following is logically equivalent to the given statement? (Box in one.) Its converse Its inverse Its contrapositive 2) The symbol ± means which of the following? (Box in one.) For all There exists Is a member of 3) Give the piecewise definition of a (where a is real) that we have given in class. a = a ,i f a ± 0 ² a f a < 0 ³ ´ µ
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4) Use absolute value notation to mathematically express the distance between x and 9 on the real number line. x ± 9 or 9 ± x 5) Factor completely over ± , the integers: 5 x 2 ± 11 x + 2 . 5 x 2 ± 11 x + 2 = 5 x ± 1 () x ± 2 There’s only one way to break up 5 x 2 here: 5 x and x , or vice-versa. The constant term of the given trinomial, + 2 , is positive, so the constant terms of the factors on the right must have the same sign. Because the linear term of the trinomial, ± 11 x , has a negative coefficient, the constant terms of the factors must be negative. 6) (6 points). Factor completely over ± , the integers: 2 x 6 ± 54 x 3 . 2 x 6 ± 54 x 3 = 2 x 3 GCF ± x 3 ± 27 Factor this difference of two nice cubes. ²³ ´µ ´ = 2 x 3 x ± 3 x 2 + 3 x + 9 Difference of Two Cubes template: A 3 ± B 3 = A ± B A 2 + AB + B 2 Here, A = x and B = 3. Note : The last factor, x 2 + 3 x + 9 , is irreducible over the integers by the Test for Factorability. 7) (6 points). Factor completely over ± , the integers: x ± 7 ± 4 x ± 5 , as we have done in class. We factor out the power of x with the least exponent; here, it is x ± 7 .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/07/2012 for the course MATH 2203 taught by Professor Ellermeyer during the Fall '10 term at FIU.

Page1 / 10

Math141Sols1AF11 - QUIZ 1A - SOLUTIONS (CHAPTER 0) MATH 141...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online