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# The Spirit and Uses of Mathematics 1 MATH 1110

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This 3 page Study Guide was uploaded by Cydney Conroy on Thursday October 29, 2015. The Study Guide belongs to MATH 1110 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 40 views. For similar materials see /class/231828/math-1110-university-of-colorado-at-boulder in Mathematics (M) at University of Colorado at Boulder.

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Date Created: 10/29/15

Math 1110 The Spirit and Uses of Mathematics Fall 2008 Review for Exam 1 1 Find 45 46 200 201 Show your work 2 If nA 7 113 8 and 110 9 what is the greatest and least number of elements in each of the following aA B C bAUBUC cAUBiC dAUBiC 3 Each part of this problem contains both an expression and some equations First evaluate the expression Then put parentheses if necessary into the equation to make it true a3gtlt24764 3X247612 3X24760 b4gtlt36215 4X36218 4X36224 4X3629 4 Use a block model that is an area model to illustrate the fact that a ba c a2 baac be 5 List all elements of each of the following sets a is an even number between 1 and 11 b is a circle and a is a square 6 List all subsets of each of the following sets a Your 1110 instructor 1 a c is a circle and a is a square 7 Describe all one to one correspondences between each given pair of sets a 17 2 and 1w 1 17 2 3 and U7 1 b 17 2 3 and U7 v w 8 For each of the following determine whether the sequence is arithmetic geometric or neither Write down the next four terms in the sequence Also nd the 50th and the nth term in the sequence a 246810 b 0246810 c 16111621 d1525125625 e 111111 f 124816 g 0 1 00 1 00 0 1 0 00 01 h 75 5 755 75 9 For each of the following draw the next three gures in the sequence Also draw the 100th gure in the sequence a EZZEZEZZ 0 ODODDOODODDO lt gt DDODDOODDOOO 10 The Yo Fuggetaboutit Pizza and Mathematics Club in New York City has a reunion and all 60 members attend Available Pizza toppings at the reunion are mushroom onion and Tootsie Roll All members have some pizza 9 have pizza with no toppings 35 have at least mushroom 23 have at least onion 20 have at least mushroom and Tootsie Roll 7 have at least onion and Tootsie Roll 9 have at least mushroom and onion 2 have all three toppings a Draw a properly labeled Venn diagram depicting the situation Describe the major sets in question including the universe using set builder notation b How many members had Tootsie Roll only on their pizza c In terms of the sets from part a and unions and intersections and so on describe the set discussed in part b of this problem 11 Write down a word problem that leads to the equation 940 403 7 12 20 Then solve that equation and answer your word problem in words 12 Explain why it s impossible to diVide a whole number that is any of the numbers 0 1 23 by zero 13 A woman earned 45 000 the first year she worked If she received a raise of 100 000 at the end of each year how much was she earning during her 11th year 14 A woman earned 45 000 the rst year she worked If her salary doubled at the end of each year how much was she earning during her 11th year 15 The symmetric dz erence denoted AAB of two sets A and B is de ned as follows AAB AiBU Bil a Indicate by shading the appropriate region the symmetric difference AAB in the following Venn dia ram U b Why do you think it s called the symmetric difference c Indicate by shading the appropriate region the set A U B A B in the following Venn dia ram U d What can you deduce by comparing parts a and c above 16 Suppose j k E and m stand for distinct whole numbers from 1 to 9 and that jk m a What s the smallest possible value that m can have b What digits can j kl never be 17 Write down the rst ve terms in each of the following sequences a The sequence start with 1 multiply by 2 each time b The sequence start with 1 then add 1 then add 2 then add 3 and so on b The sequence start with 1 then write down successive whole numbers skipping multiples of 3 18 What7s the moral of the previous problem 19 Consider a sequence that starts like this 5abcd 160 Find 110 and d if the sequence is a arithmetic b geometric 20 How many one to one correspondences are there between the sets 110 d e f and 123456 if a a must correspond to 6 and 6 must correspond to 2 b Each vowel must correspond to a multiple of 3 c a must correspond to a number larger than 2 d a must correspond to a number larger than 2 and f must correspond to a number no larger than 2 21 Write an algebraic expression for each of the following a Height h of a box with volume V length E and depth d b Seconds 3 in hours h c Yards y in inches i d Hours h in weeks w

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