M115. Homeworks assigned. Dr. Leisinger, Fall 2013. Updated 12/10/2013, 7:26 pm. Name of this file: http://math.umb.edu/~aleising/M115/Homeworks.txt ============================================================= Syllabus for course: http://math.umb.edu/~aleising/M115/Math_115_Syllabus.txt Note that other information for the course is provided in Homework # 0, below ============================================================= Tutoring available: see Tutoring.txt in this directory. ============================================================= Please note that the numbers below in the first column are the homework # for each assignment ! ======= NOTE: "*" means "written work" HW#, Date Date Assignment Assigned Due 0:8/28 9/04 Read math.umb.edu/~aleising/General_Information.txt and follow the directions there. (DO YOU UNDERSTAND THAT THIS IS Homework #0 ?) (The Homework # is found in the first column three lines back) Also: read: math.umb.edu/~aleising/Preparation_For_My_Classes.txt 1:9/04 9/06 Inventory Test (worksheet) DO NOT DO THIS IN YOUR HW NOTEBOOK! All work should be done on the worksheet, on the back of the worksheet, or clearly labeled with problem numbers, the way you would write the problem in you 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. 2:9/06 9/09 Field Properties. This homework is done in your HW notebook. It starts 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 3:9/9 9/11 Variables;Expressions;Order of Operations Read textbook pp9-14. * Text p15-16. ODD problems #1-41. 4:9/11 9/13 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; * pp 19-20 (section 1.4) Q1-Q10 (all); ODD problems #1-33;34 quinntic polynomial, or fifth degree polynomial. 5:9/11 9/13 Multiply & Divide Polynomials Worksheet (done on separate paper) H5_Polynomials.pdf (in this directory) 6:9/16 9/18 Graphing Linear Functions. Read Linear Equations.pdf (handed out to some of you in class) Graph the first column on the first side of the Graph Paper (see GraphForLinearEquationGraphs.pdf ) Graph the second column on the second side of the Graph Paper (see GraphForLinearEquationGraphs.pdf ) 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. LABEL each line with the LETTER of its equation. 7:9/18 9/20 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. Read text p73-81. * p81-82 ALL #1-22. 8:9/20 9/23 More lines; point-slope form of a line. Equation of a line with given slope, and through a given point. Slope of a line perpendicular to a given line. (box p.88) Read text pp86-90. Study carefully examples #1-5. In your HW notebook: * Work each example by yourself, and compare with the text. Or, if that is too difficult, copy each example into your HW notebook. * p90-91 ALL #1-10,11,13 9:9/23 9/25 Shifting Functions: * worksheet: ShiftingFunctions.pdf Factoring: * worksheet: FactoringAnything.pdf; problems #1-10 NOTE: We will go over the ShiftingFunctions.pdf worksheet later. Don't worry about it for now. 10:9/25 9/27 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 ALSO: re-study graphing lines. Read and carefully study examples, pp78-80, #1,2,3 SEE: Tutoring.txt 11:9/27 9/30 More factoring. * worksheet: FactoringAnything.pdf; problems #11-30 Note: a few of these problems cannot be factored. We will study that some more next week. 12:9/30 10/02 The discriminant * worksheet: FactoringAnything.pdf; problems #11-30 Finish the problems. Use the discriminant when necessary to show when the trinomials do not factor. * Text, p340, ODD#17-35; #28,30 13:9/30 10/02 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 NOTE: FinalExamSchedule.txt in this directory 14:10/3 10/4 Inequalities Read Section 1.6,pp 27-30. * pp 31-32 ALL #1-4,7-10. Part (a) only,ALL #15-20. NOTE: See MathReviewSession.txt in this directory 15:10/4 10/7 Inequalities & Absolute Value * p 32 ALL Part (a) only,ALL #21-32 Give answers in two forms: GRAPH, and UNION of INTERVALS More factoring practice: * Text, pp 340-341, ODD #37-57 AND #56 16:10/8 10/9 Introduction to Linear Systems Read text, Sections 4.1 and 4.2, pp 110-116. * p111-112 #1-6 * Work p114-115 example 1 and 2 in your HW notebook. Follow along with the text, and write these solutions the way they are done in the textbook. * Copy the three graphs on p.116 into your HW notebook. Learn the names of these three types of systems. 17:10/9 10/16 Solving linear systems by Gaussian Elimination (Add/subtract) This method is called either of these names: (a) Gaussian Elimination (b) Elimination (c) Linear Combination method (d) Add-Subtract method Study the example at the bottom of p112. * Copy this example into your HW notebook. * P117 ALL #1-14; solve by Gaussian Elimination 18:10/16 10/18 Solving linear systems by Cramer's Rule Carefully read text p120-123. Study the example, p122. * p124 ALL #1-16. Solve by Cramer's rule. Compare your answers to the first ten problems to the previous homework. (they should be the same). Check the last 6 problems by substituting x and y values into both equations. 19:10/18 10/21 Matrix operations Read pp 937-939. * p942 ALL #1-11 and #14. (Note: the book has no answers for these.) Here are some answers: #5: [ 1 59] [-22 -11] #8: [44 -37] [25 58] #14: [10 20] [30 40] 20:10/18 10/21 Solving linear systems by substitution * p117 ALL 1-10; solve by substitution. 21:10/22 10/23 Solving linear systems by the Matrix Inverse method Read the text starting with the paragraph halfway down p939 which begins, "An easy way to write the inverse..." and continue to read the following short section, "Matrix Solution of a Linear System" ending near the bottom of p940. * copy the example on p940 in your HW. * p943 #17,19,21. * p117 ALL #1-10; solve by the Matrix Inverse method. Expect a quiz on 10/23 covering: HW#16,#17,#18 NEXT MATH REVIEW SESSION: Wed. Oct 23, 4-6pm See MathReviewSession.txt in this directory 22:10/23 10/25 RETAKE of Quiz 8E See website: Quiz8E_SimultaneousEquations.pdf * Take this as a quiz at home. Rules: no calculator; no outside help. You MAY use your textbook as a resource. Turn it in by the start of class on Friday. 23:10/26 10/28 More linear systems. * p125 #19, part (a) - (e) In part (a), After graphing these two sets of equations (i) and (ii), attempt to solve each system by each of the following methods: A. Gaussian Elimination B. Substitution C. Cramer's Rule D. Matrix inverse method. Observe what happens when you use each method. * p124 #6. Solve by EACH of these methods: A. Gaussian Elimination B. Substitution C. Cramer's Rule D. Matrix inverse method. 24:10/29 10/30 More linear systems * p124 #7 Solve by EACH of these methods: A. Gaussian Elimination B. Substitution C. Cramer's Rule D. Matrix inverse method. E. Graphing 25:10/30 11/01 More linear systems; 3x3 determinants and Cramer's rule. * p124 #9 Solve by EACH of these methods: A. Gaussian Elimination B. Substitution C. Cramer's Rule D. Matrix inverse method. E. Graphing * p150-152. Carefully read section 4.9. Especially pay attention to p151. * Calculate the 3x3 determinants yourself. * Make sure you can get the solution to the example problem. * Check your solution by substituting your x,y,z values in ALL THREE equations. * p141 Use Cramer's rule to solve #1, #3. 26:11/02 11/04 3x3 Elimination Read text, p130-140, and read the example. * write the solution of example in your HW notebook. * Solve p141 #1, using elimination. Strategy: Multiply equation #I by 2; Subtract it from Equation #II. That gives you Equation #II-A, containing only y,z. Multiply equation #I by 3; Subtract it from Equation #III. That gives you Equation #III-A, containing only y,z. Now, use elimination to solve the system of two equations II-A and III-A. When you have found y and z, put them in to Equation #I and you will find the value of x. Check your (x,y,z) values in ALL THREE equations. 27:11/04 11/06 3x3 Augmented Matrix method Read text section 4-7, p142-144. Solve each of these problems by the Augmented Matrix method. If you like, you can also do them by Elimination. Compare the Elimination and Augmented Matrix methods. As in class, the two are precisely equivalent. * p145 #1,3,5. * p149 #3 28:11/06 11/08 Inverse of a 3x3 matrix. Carefully read and work through the section, "Inverse of a higher order matrix", pp 940-941. * calculate the matrix inverse in the example p940-941. (Do you get the same answer as the book?) * Check that example by multiplying the matrix by its inverse. * p940 #31,#32. Calculate each matrix inverse. Check by multiplying each matrix by its inverse. 29:11/08 11/13 Solving a 3x3 system by the matrix inverse method. * p149 #5,6,7 SOLVE EACH SYSTEM TWICE. Once, by either elimination or by augmented matrices (see pp 146-147 for the augmented matrix method). Also, by the matrix inverse method. 30:11/14 11/15 Graphing Quadratics, part 1 Read the worksheet carefully. 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. 31:11/15 11/18 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 __:11/18 11/20 No new homework. Finish HW#31. NOTE: see "Sample final Exam Math 115.pdf" on this website. It is a reasonable example of the final exam that you may expect on December 20. I will, of course, add more problems to that exam to cover some other things we have done in the class. ALSO SEE: M115_2013_Fall_FinalExamInformation.txt which is a note from the Math115 Course Coordinator. 32:11/21 11/22 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. __:11/23 11/25 No new HW. Please catch up in all of your older assignments. Begin reviewing for the final exam. Especially review HW#30,31,32. Be ready for another quiz like the one from Friday 11/23. 33:11/30 12/02 Quadradic equations, again.[complex roots] Solve each problem TWO ways: (a) by quadratic formula; (b) by completing the square. Then check one of the roots. * p193 #1,3,4. 34:12/03 12/04 Quadratic Vertex Form * 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 * (c) f(x) = 3x^2 + 3x + 4 35:12/04 12/06 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? 36:12/10 12/12 Radical and Fractional equations Read text and examples pp 425-427. * p428#1,5,7,29,43 Read text pp 378-379 * p381 #3, 13; 21,23,25,31 PLEASE READ YOUR UMB EMAIL AND FILL OUT THE SURVEY AS DIRECTED!