M115. Homeworks assigned. Dr. Leisinger, Summer 2013. Updated 8/14/2013, 8:11 am. Name of this file: http://math.umb.edu/~aleising/M115/Homeworks.txt ============================================================= Syllabus for course: To be provided sometime. ============================================================= 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 0:7/14 7/15 Read math.umb.edu/~aleising/General_Information.txt and follow the directions there 1:7/15 7/16 Properties of the number system Read and understand: Textbook, p. 4-5, blue box. Learn names of all of the properties. Learn to use each property. * Textbook, p 7, #Q1-Q10 ALL * Textbook, p 7-8, #1-9. Learn: p 10-12, blue boxes. Read examples, p 10-13, Examples #1-5. * WORK OUT THESE EXAMPLES IN YOUR HW NOTEBOOK. * p. 15 ODD PROBLEMS ONLY, #1-37 If you do not have a textbook, the photocopied pages are here as: Foerster_p1-20.pdf and the answers to odd-numbered problems as: Foerster_Answers_p983.pdf 2:7/15 7/16 Graphing Lines Read and study: "Linear Equations.pdf" (on this website) * use two copies of the GraphForLinearEquations.pdf, Use one for the FIRST column of exercises on the LinearEquations.pdf; Use the other for the SECOND column of exercises. DO NOT CHANGE THE SCALE ON THE GRAPH. One block is one unit in x- and y-. Use a straightedge or ruler to make NEAT lines that run all the way across the graph. I don't want tiny, short lines. Your lines should be very accurate. 3:7/16 7/17 Solving and graphing inequalities Read pp 27-31 in the text. Do this set of problems ASSUMING THE DOMAIN IS ALL REAL NUMBERS. The textbook asks for various domains. Ignore that. FOR EACH PROBLEM, give the answer in two forms: (a) the graphical form (b) in interval notation * pp 31-32 ODD PROBLEMS #1-31, and #14 and #26 4:7/18 7/22 Shifted Parabolas. * Worksheet. Shifted_Parabolas.pdf * Do the work on your worksheet. * In your HW notebook, make a better (and a bit bigger) sketch of each parabola #1-8. 5:7/22 7/23 Graphing Parabolas * Worksheet: GraphingQuadraticFunctions.pdf * Do the FIRST SIX COLUMNS (up to and including the vertex). Calculate the x- and y- coordinate of the vertex. * If you need to do work, you may do it in your HW notebook. DO NOT WORK DOWN!!! Do each row, one by one. That way you get thinking practice and you are not a robot. Please don't go ahead. Also: review the inequalities quiz. Please read your UMB email and respond appropriately to my email sent over the weekend. 6:7/23 7/24 Graphing Parabolas * Worksheet: GraphingQuadraticFunctions.pdf * Finish the worksheet. Use the graph paper handed out in class to do a quick sketch of each parabola. You should show all five of these points (or lines), if they exist: 1. vertex 2. y-intercept 3. symmetric point 4. roots, if they are real roots. (these are also called x-intercepts) 5. line (or axis) of symmetry 6. At least one other point of your choice PLEASE NOTE: THIS HW# HAS CHANGED: (it was 6, now it is 7) 7:7/24 7/25 Factoring Worksheet: FactoringAnything.pdf Read the first side of the worksheet and try to understand it. * Work the first ten problems on the worksheet. Do the work in your HW notebook. Study your multiplication tables. Prepare for a quiz on graphing parabolas, like the worksheet from HW#6. 8:7/25 7/29 More factoring problems [ because you asked... ] * Textbook, p333, ODD #3-23 * Textbook, p341, ODD #43-71 << Note page number correction Prepare for a quiz on simple factoring problems. Prepare for a quiz on graphing parabolas, like the worksheet from HW#6. 9:7/29 7/30 Check answers to your factoring problems. Turn in the FactoringAnything worksheet on 7/30. (no other written work) 10:7/29 7/30 Completing the square to solve quadratic equations. See CompletingTheSquare.htm for the method. * Use the completing the square method to find the roots of #1-14 on the GraphingQuadraticFunctions.pdf worksheet. Do the work in your HW notebook. Check these roots against the ones you found in HW#6. 11:7/30 7/31 Complete the square to put a quadratic equation in vertex form. * text pp 198-199 ALL #7-12. DO NOT FOLLOW BOOK DIRECTIONS! For each of these problems, change the equation to vertex form. Ignore the y-values given. 12:7/31 8/1 Systems of Linear Equations (= Simultaneous Equations) Read: text pp111-116. * Work examples 1,2 pp 114-115 in your HW notebook. Learn these definitions: (see picture p.116) Inconsistent equations Dependent equations Independent equations * Solve these systems by the ELIMINATION (Add-Subtract) method p117 ODD #1-19. * Check your answer by substituting in EACH equation. 13: 8/1 8/5 Substitution method. * p124 ODD #1-15 AND #2, #4. solve by substitution Quiz Monday: changing to vertex form by completing the square. 14: 8/1 8/6 Cramer's rule (Determinant method) Introduction to Determinants * p124 ODD #1-15 AND #2, #4. * solve by Cramer's method * check eacn problem 15:8/5 8/6 Matrix inverse method for 2x2 matrices (a) elementary matrix operations (book, appendix A) Read pp 937-940. DO NOT GO ON TO "inverse of a higher order matrix" * p942-943 Exercise A #1-24 (all problems). 16:8/5 8/7 Matrix inverse method for 2x2 matrices Solve the following systems by the Matrix Inverse method: * p124 ODD #1-15 AND #2, #4. (same problems as HW#14) * check eacn problem 17:8/7 8/8 Determinants of 3x3 and 4x4 matrices. Refer to pp150-152 for methods. * p152-153 # 1,2,3,4. Use Cramer's rule, and 3x3 determinants, to solve these systems. When evaluating the 3x3 determinants, don't forget the "checkerboard" sign system we discussed in class: + - + - + - + - + On p. 151, the bottom 4 lines, these signs are described in a different way. ("minor is subtracted from..." 17a:8/8 8/12 Matrix inverse method for 3x3 and 4x4 systems. * p152-153 # 1,2,3,4. SOLVE BY MATRIX INVERSE METHOD 18:8/8 8/12 Elimination method for 3x3 and 4x4 systems. * p152-153 # 1,2,3,4. SOLVE BY GAUSSIAN ELIMINATION 19:8/8 8/12 Matrix inverse and elimination for 4x4 systems. * p141 # 13. SOLVE BY ELIMINATION * p141 # 13. SOLVE BY MATRIX INVERSE METHOD 20:8/12 8/13 Laws of Exponents. Read carefully" pp 231-233. See the 3 examples p233. * p234 #1-14 <<< added to HW that I mentioned in class. Learn thoroughly: b lue box p237. Read examples #1,#2 p 238 * p239-240 #1-32 <<< HW that I gave in class. 21:8/13 8/14 Rationalizing the denominator Read: p416-420 Learn: blue box p419 (definition of SIMPLE RADICAL FORM) Read examples: #1-#4 * p420-422 ODD #5-19; ODD #29-37 Note: #37: multiply top & bottom of the fraction by sqrt(5) 22:8/14 8/15 Fractional Exponents; Simplifying Radicals Read pp 242-244. Learn the blue boxes * Work through p244-245 examples 1,2,3 * p245 ALL Q1-Q10 * p246 ALL #1-4,10,ODD #11-45. 23:8/14 8/16 Powers & Radicals without calculators * pp 251-252 ODD#1-59 Remainder of the course: Review, retest. Final Exam 8/22. YOU MUST BE PRESENT ON THAT DAY.