Math 110 online work that was due today at the start of class Gateway Homework turn in worksheet now while I take roll The Syllabus Quiz can be redone till 8 PM next Monday night if you haven t yet gotten 100 PLEASE HELP US OUT WITH THIS When you go to the open lab next door in 203 please make sure you sign in on the log sheet and enter your instructor s name and your section number We need to collect this information to document lab usage and ensure future funding for tutors This is section number 00 My instructor s last name is Your instructor will write this information on the whiteboard please copy it into your notebook Removable stickers with tutoring schedules still available grab one now and stick it on your laptop Please CLOSE YOUR LAPTOPS and turn off and put away your cell phones Sample Problems Page Link Dr Bruce Johnston Gateway Quiz Information You will be taking an 8 question Gateway Quiz at the beginning of the class session after next without a calculator The Gateway Quiz will consist of 8 questions similar to the ones on fractions and the order of operations that were due at the beginning of today s class This Gateway Quiz will count just 2 points towards your 1000 course points and unlike in Math 010 you won t have to get 100 on it to pass the class HOWEVER if you aren t able to do most of these problems without a calculator you will very likely have a difficult time doing the polynomial factoring and rational expression problems in the last half of this course and you might want to consider taking Math 010 before taking this class to increase your chances of success and lower your stress in Math 110 More Gateway Quiz Information We will spend some time in the next class session on how to do these kinds of problems and you will have another set of eight practice Gateway problems to do at the end of the homework assignment due at the next class session along with a required practice quiz with a worksheet that will be due at the class session after next You can also view a set of slides or print a handout with either step by step solutions or just an overview of sample problems completely worked out just click the PowerPoint Lecture Slides link in today s assignment folder and then click on the Gateway link The TAs and teachers in the open help lab next door in 203 can also give you one on one help with the practice Gateway problems after class today up until 6 30 p m or tomorrow in the 203 open lab starting at 8 00 a m Section 1 2 OK time to take notes now A variable is a symbol used to represent a number Examples x y z t etc Algebraic expressions are a collection of numbers variables operations grouping symbols but NO equal or inequality signs Examples 2x 3 y 3 z 24 Sample problem from today s homework NUMBER LINES A number line used to represent ordered real numbers has negative numbers to the left of 0 and positive numbers to the right of 0 A number is graphed on a number line by shading the point on the number line that corresponds to the number See page 9 in either the paper or on line textbook for a good illustration of a number line Sample problem from today s homework Sets of numbers Natural counting numbers N 1 2 3 4 5 6 Whole numbers W 0 1 2 3 4 Integers Z 3 2 1 0 1 2 3 More sets of numbers Rational numbers the set Q of all numbers that can be expressed as a quotient of integers with denominator 0 Irrational numbers the set I of all numbers that can NOT be expressed as a quotient of integers Real numbers the set R of all rational and irrational numbers combined The information on sets is easy to forget come quiz or test time so make sure you have it written down in your notes Page 11 in your textbook online or hardcopy version provides a helpful diagram of all these number sets and their relationships to each other Access the online version in each Assignments folder Underneath this diagram on page 11 are some example problems EXAMPLE 5 that will be useful in preparing to do the homework problems More on sets and set notation In describing some of the previous sets we used the symbol called an ellipsis It means to continue in the same pattern The members of a set are called its elements The symbol means is an element of When we list the elements of a set the set is written in roster form Examples 1 5 8 11 or 1 2 3 A set can also be written in set notation This notation describes the members of a set but does not list them Example x x is an even natural number less than 10 The set of all x such that x is an even natural number less than 10 In roster notation this would be 2 4 6 8 Comment It is possible for a set to have no members at all For example the set described in set notation by x x is a natural number less than one has no elements because 1 is the smallest natural number A set with no members is called an empty set and is denoted by either the symbol or a set of empty set brackets Sample problem from today s homework Answer 9 36 Absolute Value The absolute value of a number is the distance of that number away from 0 on a number line a 0 always since distances are non negative We say non negative to include positive numbers and zero a a if a is 0 or a positive number Example 0 0 10 10 a a if a is a negative number Example 10 10 10 Examples 1 5 5 2 5 5 3 5 5 4 0 0 5 5 5 Note the difference the placement of the negative sign makes Translating Words into Algebraic Symbols Addition the symbol is denoted by the phrases sum plus added to more than increased by Subtraction the symbol is denoted by the phrases difference of minus subtracted from less than decreased Multiplication the symbol or is denoted by product times multiply twice Division the symbol or is denoted by the phrases quotient divide ratio divided by Examples Translate each phrase to an algebraic expression Use the variable x to represent each unknown number 1 Eight times a number 8 x or 8 x 2 Three more than 8 times a number 3 The quotient of a number and 7 8 x 3 x or x 7 7 4 One and six tenths subtracted from twice a number 6 2 x 1 6 or 2 x 1 10 Sample problem from today s homework 4 Answer 5 x Now open your laptops 1 Open …