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lecture notes 138

# lecture notes 138 - Day 1 Welcome Role Why general...

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Day 1 Welcome Role Why general education math classes? Learning – book, lecture, homework, classmates ["not what you know, but what can you communicate"] Syllabus Responisibilities Professor Prepare quality lectures Examine fairly and predictably Return grades efficiently Answer questions Both Come to class, Be respectful Be honest Don’t complain Student Prepare Complete work outside of class Participate in class Prepare for exams Exponents and Radicals Recall: a n =a a … a [n times] Consequences (properties) 1. a m a n =a (m+n) 2. a m /a n =a (m-n) 3. (ab) m =a m b m 4. (a/b) m =a m /b m 5. (a m ) n =a mn 6. a -m =1/a m Let n be a positive integer. If a=b n then b is the n th root of a . Is this unique? 16 / \ (-4)(-4) The (principal) n th root of a is the number x, that when multiplied by itself n times, gives us a. Principal means that it has the same sign at a . It is denoted .

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We also write which is called a rational exponent . Watch out for : -3 2 , ((-3) 2 ) 1/2 HW: worksheet Alternate material: R2.1, R2.6 Linear Equations and Inequalities A linear equation with one variable is one that can be written as ax+b =0 where a and b are real numbers. "Reverse order of operations" Solve Katy makes \$18 per hour (after taxes) but has to pay a baby sitter \$6 per hour to take care of her son. Write an equation to calculate how much time, t , she worked if she need \$400 for living expenses. Solve for t . Joe robs nail salons for a living. If he has made \$18000 from January to September, and plans to go on thieving at the same rate for the rest of the year, how much can he expect to make in the year? (In case you're in doubt, he doesn't pay taxes.) HW – review both review chapters particularly pages R21 and R30.
Day 2 – 2.1 and 2.2 Graphs of Equations & Lines in the Plane Review : Pre-Exam Rectangular coordinate axis or the Cartesian plane – draw and label "pictures hold information" - input, output. Distances One Dimesion: | Two Dimensions ------------|---|---|---|---|---|---|---- d=|x 2 -x 1 | | Midpoints: (x 1 +x 2 )/2 | ((x 1 +x 2 )/2, (y 1 +y 2 )/2) Sketching the graph of an equation 1. If possible isolate one of the variables 2. Construct a table of values 3. Plot these points on the xy-plane 4. connect the points with a smooth curve Intuitively, what should slope mean? hills, planes Def The slope of a non-verticle line passing through the point (x 1 ,y 1 ) and (x 2 ,y 2 ) is . Point-slope form y-y 1 =m(x-x 1 ) Slope-intercept form y=mx+b Find the line through (3,4) and (-5,3). If your rent was \$300 per month last year, you know it will be \$600 per month next year and you expect it to continue to increase at the same rate (slope), what to you expect it to be two years from now? HW - 1.1: 6,7,51-56,95,96 1.2: 9,11,17,40,69

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Day 3 – 1.3 & 1.4 Linear Modeling and Direct variation & Functions Recall: A special kind of linear relationship: y varies directly as to x, or y is directly proportional to x, means y=mx where m is called the constant of proportionality .
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lecture notes 138 - Day 1 Welcome Role Why general...

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