MCCC MAT 135 - MAT135 In Class Assignments

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MAT 135 In Class Assignments Fall 2009MAT135 In-Class Assignment 2MAT135 In-Class Assignment 3 Introduction to Set Notation Set Notation and Definitions A set is a collection of objects. The members or objects in a set are called elements. There are three ways to describe a set:1. We can use words.2. We can make a list.3. We can use set-builder notation. Some NotationUnionIntersection Is an element of:Is not an element of: Examples of Sets1. Words:Nis the set of natural numbers or counting numbers.2. List:N= {1, 2, 3, …}3. Set-builder notation:N= {x| x N}MAT135 In-Class Assignment 4 Introduction to Set Notation (continued) Examples of Sets A={1,2,3} B={1,4,5}1,2,3,4,5AB1AB22AB Examples of Sets A={1,2,3} B={5,6,7} The Empty Set is the set containing no elements. It may be denoted by1,2,3,5,6,7AB???AB 1. List the elements in each set: a. { | is a natural number and 5}A x x x b. { | is an odd whole number and 11}B x x x c. { | is an integer and 5}C x x x 2. Find the union of the sets: a. {1,3,7,8} {2,3,8} b. {1,3,7} {2,4,8} c. { , , , } { , , , }r e a l e a s yMAT135 In-Class Assignment 5 Introduction to Set Notation (continued) 3. Find the intersection of the sets: a. {1,2,3,4} {2,4,5} b. {1,3,7} {2,4,8} c. { , , } { , , }w h y h o w 4. Let {1,2,3,4,5,6} {2,4,6,9,11,12}A B. Are the following statements true or false? a. 6 A b. 6 B c. {2,4,6}AB d. 6 AB e. AB f. {1,2,3,4,5,6,9,11,12}AB g. 12 A h. 5 A i. 9 B j. 8 B 5. Write the following in set-builder notation: a. {1,2,3,4}A b. { 4, 3, 2, 1,0}AMAT135 In-Class Assignment 6MAT135 In-Class Assignment 7 Section 2.1 Solving Linear Equations 1. Solve the following equations: 5) 4 8 3 7 ) 3 23 3 1 1 1 5)7 3( 2) 4( 1) ) 2 4 3 4 ) (3 2) 26 )2 3(3 5) 6a a a b tc x x d x xe x x f x x 2. The taxi meter was invented in 1891 by Wilhelm Bruhn. Chicago charges $1.80 plus $0.40 per mile for a taxi ride. a) If the fare is $6.60, write an equation that shows how the fare is calculated. b) How many miles were traveled if the fare was $6.60? 3. In 1992, twice as many people visited their doctor because of a cough than an earache. The total number of doctor’s visits for these two ailments was reported to be 45 million. a) Let x represent the number of earaches reported in 1992. Write an expression for the number of coughs reported in 1992. b) Write an equation that relates 45 million to the variable x. c) How many people visited their doctor in 1992 to report an earache?MAT135 In-Class Assignment 8 Section 2.2 Formulas and Function 1. Solving for a Variable Although you can’t print most of these out without signing up at the site, there are some useful presentations to help with this topic. http://www2.guhsd.net/algebra2/Alg2Show/Chapter01/1_5LiteralEquations.htm http://www.slideshare.net/crainsberg/solving-literal-equations http://www.scribd.com/doc/6932127/Algebra-1-Notes-YORKCOUNTY-FINAL-Unit-3-Lesson8-Solving-Literal-Equations 2. For each formula, express y as a function of x, then find y given that2x. a. 36xy b. 4 5 10xy c. 143xy d. 28xy 3. Solve for the indicated variable: a. for p q rs t r b. ( ) for x u v r y v c. 2( ) for P l w w d. 1 2 1( ) for A s r r r (Lateral area of a frustrum) e. 1 2 11( ) for 2A h b b b (Area of a trapezoid)MAT135 In-Class Assignment 9 Section 2.3 Applications Choose the equation that best describes the situation. 1. 2. 3. 4. 5.MAT135 In-Class Assignment 10 Section 2.3 Applications (continued) 6. 7. 8. 9. 10. You may also want to view http://www.slideshare.net/ejboggs/translating-algebraMAT135 In-Class Assignment 11 Section 2.4 Inequalities 1. Solve the inequalities, graph each solution, and write the solution in interval notation: 1) y>4 ) 12 2 3 1)5 115 )10 y 36 2 )2(3 1) 10 )1 3 4(3 1)a b xc x de x f a 2. A store selling art supplies finds that x sketch pads are sold each week at a price of p dollars each according to the formula x=900-300p. What price should they charge if they want to sell: a) at least 300 pads each week? b) fewer than 525 pads each week? c) more than 600 pads each week? d) at most 375 pads each week? 3. What about the solutions to these problems? a. 2 3 2( 4)xx b. 43xx c. 6 4 4 7xx d. 2 4 5 4 2 1xxMAT135 In-Class Assignment 12 Section 2.5 Compound Inequalities 1. Solve the following inequalities. Use a line graph and interval notation to write each solution set. ) 60 20 20 60 )7 5 2 or 3 2 3 12)5 +1<9 )8 12 and >1 43 )3 1 2 4 or 5 2 3 4 a a b x xc x d x xe x x x x ) 2 5 2fm 2. A factory’s quality control department randomly selects a sample of 5 lightbulbs to test. In order to meet quality control standards, the lightbulbs in the sample must last an average of at least 950 hours. Four of the selected bulbs lasted 925 hours, 1000 hours, 950 hours, and 900 hours. How many hours must the fifth lightbulb last for the sample to meet quality control standards? 3. A worker earns $12 per hour plus $16 overtime pay for every hour over 40 hours. How many hours of overtime are needed to make between $600 and $800 per week? 4. Write each union or intersection as a single interval, if possible. .(6, ) (8, ) .( 6, ) ( 8, ).(6,10) (4,12) .[ 5, ) ( , 8]abcdMAT135 In-Class Assignment 13 Section 2.6 Absolute Value Equations and Inequalities Some tutorials: http://www2.bc.cc.ca.us/mperrone/LECTURES_PDF/Ch4/Microsoft%20PowerPoint%20-%20bia5e_ppt_4_3.pdf http://www.purplemath.com/modules/absineq.htm 1. Solve: 2 2 2 3 13x. a. {-5} b. {3 } c. {-5 , 3} d. no solutions 2. Find all real solutions: 1 2 1xx. a. {-2 } b. {-2 , 0} c. {0} d. no solutions 3. Find all real solutions: 3 3 18.x a. 3x b. 3, 9xx c. 9, 3xx d. 4. Find all real solutions to the equation. 1422x. a. -4 b. no solutions c. 4 d. all real numbers 5. Solve the inequality: 2434x. a. ( , 7/3) b. (7/3 , ) c. (-7/3 , 7/3) d. ( , ) 6. Solve the inequality: 1 2x. a. [3 , ) b. ( , -1] U [3 , ) c. (- , -1] d. (- , )MAT135 In-Class Assignment 14 Section 2.6 Absolute Value Equations and Inequalities (continued) 7. Solve


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