M129. Homeworks assigned. Spring, 2016 See: "Solving_Absolute_Value_Expressions.pdf" in this directory. File updated 5/10/2016 3:56 pm THIS FILE WILL BE CONTINUALLY UPDATED !!! WHEN YOU REFERENCE IT, ALWAYS "refresh" the page in your browser. ================================================= Math129 : Dr. Leisinger. Name of this file: math.umb.edu/~aleising/M129/Homeworks.txt ================================================= Syllabus for this course: math.umb.edu/~aleising/M129/Math_129_Syllabus.txt Note that other information for this class is provided in Homework #0, below ================================================= ALL WORK IS TO BE DONE IN THE HW notebook, unless noted below. NOTE: "*" means "WRITTEN WORK". ================================================= HW# Date Date Assignment assigned due 0:1/22 1/26 Read www.math.umb.edu/~aleising/General_Information.txt and follow the directions there. (Do you understand that this is HW#0 ? ) ( The HW # is found in the first column, 3 rows back ) Also: read: www.math.umb.edu/~aleising/Preparation_For_My_Classes.txt 1:1/22 1/26 Inventory Test (worksheet) * "www.math.umb.edu/~aleising/M129/Inventory_Test_B.pdf" DO NOT DO THIS IN YOUR HW NOTEBOOK! All work should be done on the worksheet, on the back of the worksheet, or on separate sheets clearly labeled with problem numbers, the way you would write the problem in your HW notebook. Answers go in the answer column. Use only ink. Show all of your work. No calculator. Time yourself and write down how many minutes you spent on this assignment. You are graded only for completeness; but do not worry if you really can't do some of the problems. Just try them all. The purpose of this assignment is for me to see what you know. Turn this HW in at the first class. 2:1/22 1/28 Field Properties. This homework is done in your HW notebook. You should wait until after the 1/26 class before writing it. Of course, you could read the section in the text. (see "Foerster_p1-20.pdf" in this directory) This HW is to be written starting on side 5 of your HW notebook. Please write your answers in correct format. Textbook: read "Preliminary Information". Read pp 1-7. * Text pp2-3:#1,2,3,5,7,8,9 Read and learn very well: Field Axioms, pp 4-5 (blue box) There is one more important Field Axiom which the book omits: "One is not equal to zero." * Text pp7-8:#1-10 PLEASE ALSO CONSULT the file NumberSystems_Notes.pdf in this directory. 3:1/22 1/28 HW Notebook setup You receive credit for this assignment when your HW notebook is in the correct format. 4:1/22 1/28 Variables;Expressions;Order of Operations (Done in HW notebook) Read textbook pp9-14. * Text p15-16. ODD problems #1-41. 5:2/3 2/4 Graphing Linear Functions. Worksheet (done on separate paper, not in HW notebook) Read "LinearEquations.pdf" (on this website) Use 2 copies of "GraphForLinearEquationGraphs.pdf" (on website) Graph the first column on one copy of the Graph Paper Graph the second column on the second copy of the Graph Paper Use the method described on the notes for graphing a line from the slope-intercept form of the line equation. Graph each line neatly. Use a ruler or straightedge to make a good line. Extend each line all the way across the graph. If it's too sloppy, you'll need to do it over again. LABEL each line with the LETTER of its equation. 6:2/4 2/9 Distance formula;Circles Read text, pp 462-465. ESPECIALLY p463. Learn VERY WELL the three forms of the distance formula. Equation for a circle. Completing the square for a circle (p464-465 ex.#2) * p467 ALL #13-18 * p466 ALL #1-12 7:2/4 2/9 Factoring a natural number Learn: the notes on FactoringNaturalNumbers.pdf IN YOUR HW NOTEBOOK: * Work the exercise at the end. 8:2/4 2/9 Graphs of Functions; Lines Read text p51-56 DO THESE IN YOUR HW NOTEBOOK: * p52 ALL #1-5 * p56-57 ODD #1-11, ALL 13-20. 9:2/4 2/9 Point-Slope form of a Line Read text p73-81. * p81-82 ALL #1-22. Equation of a line with given slope, and through a given point: Read text pp86-90. Study carefully examples #1-5 * p90-91 ALL #1-10 Slope of a line perpendicular to a given line. (box p.88) 10:2/4 2/11 Inequalities & Absolute Value See: "Solving_Absolute_Value_Expressions.pdf" in this directory. FOR ABSOLUTE VALUE PROBLEMS: THE METHOD TAUGHT IN CLASS SHOULD BE USED, INSTEAD OF THE METHOD GIVEN IN THE TEXTBOOK. Read Section 1.6,pp 27-30. * pp 31-32 ALL #1-4,7-10. Part (a) only,ALL #15-20. * p 32 Part (a) only for each problem in the list: ALL #21-32 Give answers in two forms: GRAPH, and UNION of INTERVALS 11:2/11 2/16 Polynomials NOTE: answers to odd-numbered textbook problems may be found in this directory in: Foerster_Answers_p983.pdf Carefully read textbook pp 16-19. Learn the definitions of: term; monomial; binomial; trinomial; exponent; power; coefficient; degree of a term; degree of a polynomial. [to be discussed in class: total degree] constant; linear polynomial, or first degree polynomial; quadratic polynomial, or second degree polynomial; cubic polynomial, or third degree polynomial; quartic polynomial, or fourth degree polynomial; quintic polynomial, or fifth degree polynomial. * pp 19-20 (section 1.4) Q1-Q10 (all); ODD problems #1-33;34 12:2/11 2/16 Multiplying polynomials. Read pp 328-332. Understand blue boxes, p329,p331. Product of Conjugate Binomials (box, p329) Completely Factored Form (box, p331) * pp 330-331: work examples #1,2,3,4 in your HW notebook. * pp 333: #3-41 (ODD), #40. 13:2/11 2/16 Factoring: READ AND UNDERSTAND: the worksheet, methods #1,2,3,4,5. DO THESE PROBLEMS IN YOUR HW NOTEBOOK. DO NOT WRITE ON THE WORKSHEET YET. * worksheet: FactoringAnything.pdf; problems #1-10 NOTE ADDED 2/18/2016: Prepare for quizzes on: Solving Inequalities; Simple factoring of polynomials. 14:2/18 2/23 The discriminant * Text, p340, ODD#17-35; #28,30 15:2/18 2/23 More factoring. * Finish the worksheet: FactoringAnything.pdf (except #31,32) Note: a few of these problems cannot be factored. Finish the problems. Use the discriminant when necessary to show when the trinomials do not factor. DO WORK IN YOUR HW NOTEBOOK. COPY THE ANSWERS ONTO THE WORKSHEET. 16:2/18 2/23 More factoring Read and study examples p330-331 #1,2,3 * p333 ODD#3-23. Check your answers AFTER doing the problems. * p334 ALL #63-78. Read and study p338, example 1. * p340 ALL #5-14 17:2/18 2/25 More factoring. * pp340-341 ODD #37-57 and 56. * p353 ALL#5-8 18:2/18 2/25 Exponents. Read text, Section 6.2, pp 230-234. * Text, p234 ODD #1-9 Read text, Section 6.3, pp 236-238. * Text, p239-240 ODD #1-31 * pp341-342 ODD #59-79. 19:2/18 3/1 The factor theorem. Factoring cubic and quartic polynomials. Learn and understand: blue box p349. * Work example 1, p349, in your HW notebook. You should follow along with the example. * p353 #1,2,3,4 20:2/18 3/3 Graphing Exponential Functions * worksheet: GraphingExponentialFunctions.pdf The sheet is posted on this website. 21:2/18 3/8 Rational and fractional exponents. Simplifying radicals,#1. Read text, section 6.4, pp 241-245. Learn thoroughly the 4 blue boxes in that section. Read the 3 examples pp 244-245. * p246-247 #1-6,10; #11-14 (Those are calculator problems.) * p247 ODD#19-45. 22:2/18 3/8 Powers without calculators * p251-2 #1,2, and ODD#3-59 Scientific notation * p257 ODD #1-27 23:3/1 3/10 Introduction to Logarithms. Read section 6-9, pp269-271. Study examples #1,2,3. * p272-3 ODD #1-41 and #2,14,32 24:3/1 3/12 Graphing Logarithmic functions * Worksheet: GraphingLogarithmicFunctions.pdf The worksheet is posted on this website. 25:3/1 3/22 Simple Log properties Learn Log Properties, blue box p276 * write out examples p276-277 #1,2,3 in your HW notebook * p278 ALL #1-6. Use a calculator to evaluate each side of each equation. * p278 ALL #7-14. NO CALC! use "facts" given before problem 7. 26:3/1 3/24 More log properties * p279 ALL # 33-44 See Example 2, p. 277 for help in doing these problems. 27:3/1 3/29 Change of Base law for Logarithms LEARN blue box p283. * p284 #1-10 all. Use the change of base law, and the "log" button of a calculator, to find answers to these problems. ( the letter "a" in the blue box p283 would be =10). Note that the answers in the book are only correct to a few decimal places. DO NOT ROUND OFF YOUR CALCULATOR ANSWERS. 28:3/1 3/31 Solving exponential equations by logs Read p264-265 examples #1,2 * p267 ODD #1-23 and #22. Solve by taking the log of both sides. But in #19 and #23, you will need to divide by something first. ==> Expect a quiz on Friday on: HW#22,23,25,26 29:3/31 4/5 Function composition; Function inverses Read text, p290, blue box only. Read text, p291-2, examples 1,2 * p293#1,7,9. (part (a) only) * worksheet: Function_Composition_&_Inverses.pdf 30:3/31 4/5 Exponentials as mathematical models Read text section 6-14, pp 300-302. * Copy the Bacteria Problem example from pp301-302, in your HW notebook. Write out the full solution! Your answer should follow the textbook answer. 31:3/31 4/7 Exponentials as mathematical models * p303 #2, #6. Use the exponential equation f(t) = (A) b^t. 32:3/31 4/7 Exponentials as mathematical models * p307 #9. Use the exponential equation f(t) = (A) b^t. * p321 #T9. 33:3/31 4/12 Graphing Quadratics, part 1 Worksheet: GraphingQuadraticFunctions.pdf * Fill out the first 7 columns on the worksheet. but for the vertex, just do the x-value, not the y-value. 34:3/31 4/12 Compound Interest. Read pp 599-601 examples 2,3. pp 602-604 #5,6,7,8 35:3/31 4/14 Graphing Quadratics, part 2 Worksheet: GraphingQuadraticFunctions.pdf * Finish all of the columns on the worksheet. * Graph the quadratics on the graph paper provided in class 36:3/31 4/19 Graphing quadratics, part 3. * p187 #21,23,24,25,27,30 In the problems below, follow the text directions; but also, FIND THE ROOTS AS WELL. SKETCH THE LINE OF SYMMETRY, TOO. * p187 #33,35,38,42. 37:3/31 4/21 Use the method taught in class to convert each quadratic function into vertex form: (a) f(x) = 5x^2 + 3x - 1 (b) f(x) = 2x^2 + 3x - 4 For the correct method, see: ConvertQuadraticToVertexForm_N.docx 38:3/31 4/26 Linear Systems I: Gaussian Elimination * p117 #1-10 ALL; Solve by Gaussian Elimination 39:3/31 4/28 Linear Systems II: Substitution * p117 #1-10 ALL; Solve by Substitution 40:3/31 4/28 Linear Systems III: Graphing Method * p117 #1-10 ALL; Solve by Graphing. Use graph paper for each problem. Be precise. 41:3/31 5/03 Linear Systems IV: Cramer's Rule * p117 #1-10 ALL; Solve by Cramer's Rule 42:3/31 5/03 Linear Systems V: Matrix Inverse Method * p117 #1-10 ALL; Solve by Matrix Inverse Method 43:4/29 5/5 Systems of Linear Inequalities. Read text pp 153-155. * Copy examples pp154-155 #1,2 in your HW notebook. 44:4/29 5/5 Linear Programming #1. Read text pp 157-161. * Copy the example pp 157-161 in your HW notebook. * p162#1 [ Try to do this problem by 5/5. 45:4/29 5/5 Linear Programming #2. * p162-169 #2,9 USE GRAPH PAPER (on this website) to draw your graphs precisely. LABEL YOUR AXES CORRECTLY. 46:4/29 5/5 Quadratic Vertex Form, again [part A] Use the method taught in class to convert each quadratic function into vertex form: * (d) f(x) = -3x^2 + 4x - 5 * (e) f(x) = 6x^2 - 5x - 6 * (f) f(x) = 3x^2 - 18x + 27 [part B] Set y=0 in the vertex form, to find the roots of each. [part C] Use the Quadratic Formula to find the roots of each. Do the roots agree? [part D] Very quickly sketch the graph of each function. Use the vertex form and the y-intercept ONLY. You are sketching, not graphing. No need to be exact. [part E] Use the discriminant to see if the original f(x) can be factored over the integers. If so, factor it. Use the factored form to find the roots. Are these roots the same ones you found in part B,C? 47:4/29 5/10 Difference Quotient * Worksheet: DifferenceQuotient_129.pdf * do as many of the problems at the bottom of the sheet as you can. 48:4/29 5/10 Amortization and Sinking functions Reference and problem sheet: Amortization_&_SinkingFunds.pdf 49:4/29 5/10 Linear Programming Easy Problems * Linear_Programming_EasyProblems.pdf (in this directory) These are three easy problems. They are not "word problems". 50:5/10 5/20 3x3 systems of linear equations THIS IS AN EXTRA CREDIT HOMEWORK. Do it on 8 1/2 x 11 sheets of paper. * Method 1. Substitution * Method 2. Gaussian Elimination * Method 3. Cramer's Rule * Method 4. Matrix Inverse method * p141 ALL #1-4 [same problems are p152 #1-4 ] There WILL be a problem like this on the final exam. It will require the Matrix Inverse method. For detailed instructions for a 3x3 matrix determinant, see pp 150-152. For detailed instructions for a 3x3 matrix inverse, see pp 940-941. 51:5/10 5/20 Radical equations THIS IS AN EXTRA CREDIT HOMEWORK. Do it on 8 1/2 x 11 sheets of paper. * pp425-427: COPY examples #1 and #2 on your paper. * pp428-429: #1,2,7,8,25,26,27,28 ============================================================================= =========================== DO NOT READ BELOW THIS LINE ===================== =================== Material below is not yet fit for human consumption ===== ============================================================================= ========================= DO NOT READ BELOW THIS LINE ============== ===== HOMEWORK BELOW THIS LINE IS NOT YET FIT FOR HUMAN CONSUMPTION ===== ========================= DO NOT READ BELOW THIS LINE ============== 49:7/21 8/19 Q129. Practice exam (handout in class) 50:12/02 12/05 Graphing systems of linear inequalities (handout in class, title "QUIZ 33") 51:12/02 12/05 THIS DOES NOT NEED TO BE TURNED IN. Please see: M129_Practice_Problems_2014_12.pdf 52:9/15 9/24 Shifting Functions: * worksheet: ShiftingFunctions.pdf