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### lesson5outline

Course: MA 15300, Spring 2011
School: Purdue
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Word Count: 166

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153 Lesson MA 5 Outline Quiz Solutions (Practice problems for distance learning students) 1. Subtract and express as a polynomial. ( 3x 4 + 2 x 2 4 x + 1) ( x 4 5 x 2 + 7 ) = 3x 4 + 2 x 2 4 x + 1 x 4 + 5 x 2 7 = 2 x4 + 7 x2 4 x 6 2. Multiply. Express your answer as a polynomial. ( 2 x 1) ( x 2 3x + 5 ) = 2 x ( x 2 3 x + 5 ) 1( x 2 3 x + 5 ) = 2 x 3 6 x 2 + 10 x x 2 + 3 x 5 = 2 x 3 7 x 2 + 13...

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153 Lesson MA 5 Outline Quiz Solutions (Practice problems for distance learning students) 1. Subtract and express as a polynomial. ( 3x 4 + 2 x 2 4 x + 1) ( x 4 5 x 2 + 7 ) = 3x 4 + 2 x 2 4 x + 1 x 4 + 5 x 2 7 = 2 x4 + 7 x2 4 x 6 2. Multiply. Express your answer as a polynomial. ( 2 x 1) ( x 2 3x + 5 ) = 2 x ( x 2 3 x + 5 ) 1( x 2 3 x + 5 ) = 2 x 3 6 x 2 + 10 x x 2 + 3 x 5 = 2 x 3 7 x 2 + 13 x 5 Answering of homework questions over lesson 4. Lesson 5 Section 1.4 Rational Expressions polynomial polynomial Reducing rational expressions Example: (a) 15 35 (b) 2x2 + 9x 5 3 x 2 + 1 7 x + 10 Multiplying and dividing expressions Example: (a) 3 rational 18 49 (b) 4 x2 9 x2 x 6 2x2 + 7 x + 6 x+5 (c) 6 x 2 5 x 6 2 x 2 3x x2 4 x+2 Adding/Subtracting rational expressions Example: (a) 57 + 69 (b) 3 2 x+5 x (c) 4x 8 2 +2 + 3x 4 3x 4 x x Quiz (Practice problems for distance learning students) 1. Factor each of the following as much as possible: (a) 2 x 2 5 x 1 2 (b) 16 x 4 1 (c) 27 x12 + 8 Given: x 3 + y 3 = ( x + y ) ( x 2 xy + y 2 ) Answers to above quiz (a different version of quiz #3 is shown on lesson 6) (a) ( 2 x + 3) ( x 4 ) (b) (4x (c) ( 3x 2 + 1) ( 2 x + 1) ( 2 x 1) 4 + 2 ) ( 9 x8 6 x 4 + 4 )
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Purdue - MA - 15300
MA 153Lesson 6 OutlineQuiz Solutions (Practice problems for distance learning students)1. Factor each of the following as much as possible:(a) 3 x 2 + 1 0 x 8(b) 1 6 x 4 1= ( 3x 2 ) ( x + 4 )= (4 x 2 + 1)(4 x 2 1)= ( 4 x 2 + 1) ( 2 x + 1) ( 2 x 1)
Purdue - MA - 15300
MA 153Lesson 7 OutlineAnswering of homework questions over lesson 6.Lesson 7 Section 2.1 Equations(I) Linear EquationsExample:4 ( 2 y + 5) 3( 4 y ) = 0(II) Rational Equations(a) Example (Method 1):538 = 2+xx(a) Example (Method 2):538 = 2+
Purdue - MA - 15300
MA 153Lesson 8 OutlineAnswering of homework questions over lesson 7.Lesson 8 Section 2.2 ApplicationsExample:Kathy invested \$50,000 into two different accounts. One account earns 7% simpleinterest and the other pays 5% simple interest. How much is i
Purdue - MA - 15300
MA 153Lesson 9 OutlineQuiz Solutions (Practice problems for distance learning students)1. Solve for x:7 ( 2 x 1) 3 ( 4 x ) + 2 = 814 x 7 12 x = 62 x = 13x=1322. The following equation is an identity in which 0=0. What is the solution for x?32
Purdue - MA - 15300
MA 153Lesson 10 OutlineAnswering of homework questions over lesson 9.Lesson 10 Section 2.3 Solving Quadratic Equationsax 2 + bx + c = 0Solving:(1) By factoring: If ab = 0 , then a=0 or b=0.Example:x ( 3x + 10 ) = 77Example:5x36+ +2=x2 xx (
Purdue - MA - 15300
MA 153Lesson 11 OutlinePractice Quiz Solution (Practice problems for distance learning students)1. If Jon and Kathy work together, they can do a job in 35 minutes. If Jon works alone,he can do the same job in 55 minutes. How long would it take Kathy t
Purdue - MA - 15300
MA 153Lesson 12 OutlinePractice Quiz Solution (Practice problems for distance learning students)1. Solve for x:x ( 3x + 7 ) = 23x 2 + 7 x + 2 = 0(3 x + 1)( x + 2) = 03 x + 1 = 0, x + 2 = 01x = , x = 232. Solve for x:( x 4)2=5x4= 5x = 4 5A
Purdue - MA - 15300
MA 153Lesson 13 OutlinePractice Quiz Solution (Practice problems for distance learning students)1. A ball is thrown upward with an initial velocity of 48 ft./sec. The number of feet, s,above the ground after t seconds is given by s ( t ) = 16t 2 + 48t
Purdue - MA - 15300
MA 153Lesson 14 OutlineAnswering of homework questions over lesson 13.Lesson 14 Section 2.5 Other Types of EquationsAbsolute ValueExample:(a) x = 4(b) 4 x + 1 3 = 9Example:x=3Square both sides:x2 = 9Solve for x:x = 3, x = 3x = 3 is called an
Purdue - MA - 15300
MA 153Lesson 15 OutlineAnswering of homework questions over lesson 14.Lesson 15 Section 2.6 InequalitiesNotationInequalityInterval NotationGraph(a) 2 &lt; x 1(b) x 2(c) x 4 or x &gt; 2If you do not include an end value, use parantheses.If you do inc
Purdue - MA - 15300
MA 153Lesson 16 OutlineAnswering of homework questions over lesson 15.Lesson 16 Section 3.1 Rectangular Coordinate SystemyQ IIQIxQ IVQ IIIExample:Plot the point ( 2, 4 ) on the above axesDistance FormulaIf A ( x1 , y1 ) and B ( x2 , y2 ) , th
Purdue - MA - 15300
MA 153Lesson 17 OutlineReivew of lesson 16 formulas:Distance formula: d ( A, B ) =( x2 x1 ) + ( y2 y1 )22x +x y +y Midpoint formula: 1 2 , 1 2 22Answering of homework questions over lesson 16.Lesson 17 Section 3.2 GraphsExample:Graph y = x 2
Purdue - MA - 15300
MA 153Lesson 18 OutlineAnswering of homework questions over lesson 17.Lesson 18 Section 3.3 LinesExample: A ( 2, 3) and B ( 1, 2 )ySlope (m)m=rise y2 y1=run x2 x1xExample: x = 2Example: y = 3yyxxEquations of lines(1) Point-slope formy
Purdue - MA - 15300
MA 153Lesson 19 OutlineQuiz Solutions (Practice problems for distance learning students)1. Find the x intercept for the following equation:y = x 30 = x 33= xx = 9;( 9, 0 )2. Find the center and the radius of the circle given by the equation:x2 +
Purdue - MA - 15300
MA 153Lesson 20 OutlineQuiz Solutions (Practice problems for distance learning students)21. Find the slope of the line perpendicular to the line y = x + 1 .32Slope of given line = 3Slope of line perpendicular is negative reciprocal or322. Find
Purdue - MA - 15300
MA 153Lesson 21 OutlineLesson 21 Section 3.4 (cont) FunctionsGraphing Functions(1) IncreasingyAs x gets bigger, y gets bigger also.What values of x make the ys larger?5Increasing on [1, 4]21x4(2) DecreasingAs x gets bigger, y gets smaller.
Purdue - MA - 15300
MA 153Lesson 22 OutlineQuiz Solution (Practice problems for distance learning students)1. Given the graph below, find the following:(a) DomainDomain is the smallest x to the largest x, so D : [ 0, 4](b) RangeRange is the smallest y to the largest y
Purdue - MA - 15300
MA 153Lesson 23 OutlineReview of Changes in GraphsA vertical change is something being done to the function and changes the y-values.A horizontal change is something being done within the function and changes the xvalues.Start with graph of y = f ( x
Purdue - MA - 15300
MA 153Lesson 24 OutlineAnswering of homework questions over lesson 23.Lesson 24 Section 3.5 (cont) Piecewise FunctionsExample:x + 3f ( x) = 4i f x 1if x &gt; 1Find:(a) f ( 4 )(b) f ( 1)(c) f ( 2 )(d) f (100 )GraphingExample (same as above):x
Purdue - MA - 15300
MA 153Lesson 25 OutlineQuiz Solutions (Practice problems for distance learning students)1. Given a function y = f ( x ) whose graph contains the following points:( 3, 4 ) , ( 2, 6 ) , ( 1, 3)Find the points of the function y = f ( x 2 ) + 5(You do n
Purdue - MA - 15300
MA 153Lesson 26 OutlineReview from last lesson:Parabolas:1. Standard Equation : y = a( x h) 2 + kVertex: ( h, k )2. Quadratic form: y = ax 2 + bx + cVertex can be found one of two ways:b. Substitute the x-coordinate (once2aknown) into the equat
Purdue - MA - 15300
MA 153Lesson 27 OutlineAnswering of homework questions over lesson 26.Lesson 27 Section 3.7 Operations on FunctionsLet f(x) and g(x) be two functions:(1)( f + g )( x) = f ( x) + g ( x)(2) ( f g ) ( x ) = f ( x ) g ( x )( 3) ( fg ) ( x ) = f ( x )
Purdue - MA - 15300
MA 153Lesson 28 OutlineQuiz Solutions (Practice problems for distance learning students)1. Find the maximum or minimum value (specify whether it is a max or a min):2y = 2 ( x 3) 5Min value = -5(It is a min because a is positive so parabola opens up
Purdue - MA - 15300
MA 153Lesson 29 OutlineAnswering of homework questions over lesson 28.Lesson 29 Section 4.1 Polynomials with degree greater than 2Degree 1: y = 7 x + 3 is a lineDegree 2: y = 3 x 2 2 x + 1 is a parabolaDegree 3: ?Example:Given the sign chart below
Purdue - MA - 15300
MA 153RLesson 30 OutlineQuiz Solutions (Practice problems for distance learning students)1. Find all the values that would be included on the top of the sign chart for:( x + 2 ) ( x 1) 0Would needx = 2,1, and 5 on thetop of the sign chartx+5(Do N
Purdue - MA - 15300
MA 153Lesson 31 OutlineQuiz Solutions (Practice problems for distance learning students)1. Given below is the sign chart for a function, y = f ( x ) . Assume all valuesrepresent x-intercepts. Sketch a possible graph for this function.+sign of f ( x
Purdue - MA - 15300
MA 153Lesson 32 OutlineLesson 32 Section 9.2 Systems of EquationsSolve a system of equations:(1) By substitution(2) By elimination (today)Given a system of two equations and two unknowns, you can:(1) interchange the equations(2) multiply or divide
Purdue - MA - 15300
MA 153RLesson 33 OutlineQuiz Solutions (Practice problems for distance learning students)1. Solve. Express your answer as an ordered pair.3 x 6 y = 25 x + 4 y = 1Multiply the top equation by 2 and the bottom by 3(one of many options):6 x 12 y = 4
Purdue - MA - 15300
MA 153Lesson 34 OutlineQuiz Solutions (Practice problems for distance learning students)1. Solve each system using either elimination or substitution. Express your answer as anordered pair. If no solution exists, write none.2 x + 3 y = 9(a) 3 x +
Purdue - MA - 15300
MA 153Lesson 35 OutlineAnswering of homework questions over lesson 34.Lesson 35 Section 5.2 Exponential Functionsf ( x) = axExample:yGraph(a) f ( x ) = 2 xx1(b) f ( x ) = 2xyx#11. Graph:y(a) f ( x ) = 2 xx(b) f ( x ) = 2 xyx(d) f (
Purdue - MA - 15300
MA 153Lesson 36 OutlineQuiz Solutions (Practice problems for distance learning students)1. Given the function y = f ( x ) below, find the domain of the inverse function, f 1 .(2, 5)yy = f (x )Range of the original functionis [ 3, 5] so the domain
Purdue - MA - 15300
MA 153Lesson 37 OutlineReview of Lesson 36: Logarithmsbe sure to be able to switch from log form toexponential form and vice versa.Definition of a logarithmy = log a x a y = x(log form)(exponential form)Domain: x &gt; 0 which means that you cannot ta
Purdue - MA - 15300
MA 153Lesson 38 OutlineQuiz Solutions (Practice problems for distance learning students)1. Change to log form:4 5 = 1 02 4log 4 1024 = 52. Find the number:3. Solve the equation:log16 x =6=13662 =1log 6= _3613611216 2 = xx = 16x=4A
Purdue - MA - 15300
MA 153Lesson 39 OutlineQuiz Solutions (Practice problems for distance learning students)1. What would be done to the graph of y = log 5 x in order to graph y = log5 ( x + 2 ) .Shift left 22. Solve for x . Round your answer to the nearest tenth.log x
Purdue - MA - 15300
MA 153Lesson 40 OutlineAnswering of homework questions over lesson 39.Lesson 40 Section 5.6 Exponential and Log EquationsCalculator: log 4 3 =Change of Base Formulalog b u =log a ulog a bExample:Use your calculator to find log 4 3 =Example:log
Purdue - MA - 15300
MA 15300Assignment SheetSpring 2011Text: Algebra and Trigonometry with Analytic Geometry by Swokowski / Cole, Classic Twelfth Edition, Brooks /Cole (2010).Calculators are required, and only a one or two line, scientific calculator is allowed forquiz
Purdue - MA - 15300
MA 15300 Schedule, Spring 2011Exam 1: Lessons 1-9 ; Exam 2: Lessons 10-20 ; Exam 3: Lessons 21-33JanuaryFebruaryMarchAprilMay10MondayIntro/Lesson 117No classes24Lesson 631Lesson 97Lesson 1114Lesson 1421Lesson 1728Lesson 207Lesson
Purdue - MA - 15300
Overall average for the final exam=125A 180-200B 160-179C 120-159D 93-119F 0-92
Purdue - MA - 15300
MA 153Exam 1Spring 2011Following are the approximate letter grade cut-offs from exam 1:Overall average for Exam 1: 61.8A 90 - 100B 81 - 89C 60 - 80D 47 - 59F 0 - 44Also, this curve should not be used as an absolute determination of what letterg
Purdue - MA - 15300
MA 153Exam 2Spring 2011Following are the approximate letter grade cut-offs from exam 2:Overall average for Exam 2: 68A 90 - 100B 80 - 89C 60 - 79D 45 - 59F 0 - 44Also, this curve should not be used as an absolute determination of what lettergra
Purdue - MA - 15300
MA 153Exam 3Spring 2011Following are the approximate letter grade cut-offs from exam 3:Overall average for Exam 3: 60A 90 - 100B 80 - 89C 60 - 79D 45 - 59F 0 - 44Also, this curve should not be used as an absolute determination of what lettergra
Purdue - MA - 15300
Purdue - MA - 16100
Purdue - MA - 16100
Purdue - MA - 16100
MA161000Exam1AdvisoryLetterGrades Spring2011These advisory letter grades are unofficial and are partly based onguesses. The final letter grades will be based only on the sum of youractual numbers, as explained in the ground rules.A: 87-100B: 73-80C
Purdue - MA - 16100
Purdue - MA - 16100
Ground Rules for MA 16100, Spring 2011Homework: There are 37 online assignments using WebAssign(https:/www.webassign.net/purdue/login.html). Due dates and times are listed on the WebAssign CourseView by theAssignments. Generally, homeworks from Friday
Purdue - MA - 16100
ChangestotheschedulecausedbythesnowdaysI.Lectures.TheFebruary9lecturewillnowbeLesson11andhalfofLesson12,andtheFebruary11lecturewillbetherestofLesson12andallofLesson13.Afterthatthelectureswillbeaspreviouslyannounced.II.Homeworkduedates.Lesson12willno
Purdue - MA - 16600
Purdue - MA - 16600
MA16600Spring2011Exam3AdvisoryLetterGradesA 100 - 78B 77 - 60C 59 - 46D 45 - 41F 40 - 0
Purdue - MA - 16600
Purdue - MA - 16600
GROUND RULES FOR MA 166 SPRING 2011HOMEWORK: There are 35 online assignments using WebAssign(https:/www.webassign.net/purdue/login.html). Due dates and times are listed on the WebAsignCourseView by the Assignments. Generally, homework for a lesson cove
Purdue - MA - 16600
MA 166ASSIGNMENT SHEETSpring 2011Text: James Stewart Calculus, Early Transcendentals, Sixth Edition.Week Day Lesson Section StudyHomework Assignment1/10M112.1 allp769:6,14,16,26,29,35,36+12.2 beg.Ex. 2p777:3,5,6W212.2 after Ex. 2-Ex. 6p777
Purdue - MA - 16600
Purdue - MA - 16600
Purdue - MA - 16600
Purdue - MA - 16600
Purdue - MA - 16600
Purdue - MA - 16600
Purdue - MA - 16600
Purdue - MA - 16600
MA 166FINAL EXAM PRACTICE PROBLEMSSpring 20101. If a = i + j + k and b = 2i k , nd the vector projection of b onto a, proja b.111B. 3 aC. 5 aD. 3 bA. 1 a32. Find the angle between the vectors a = i + 2j and b = i + 3jB. C. 23D.A. 344E.5