M130. Homeworks assigned. Dr. Leisinger, Fall 2013. Updated 12/12/2013, 2:00 pm. Name of this file: http://math.umb.edu/~aleising/M130/Homeworks.txt ============================================================= Syllabus for course: Math_130_Syllabus.txt http://math.umb.edu/~aleising/M130/Math_130_Syllabus.txt Note that other information for this course is provided in Homework #0, below ============================================================= TUTORING: 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 0:7/14 7/15 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. 2:9/6 9/9 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 in class) Graph the first column on the first side of the Graph Paper (handed out in class) (see GraphForLinearEquationGraphs.pdf ) Graph the second column on the second side 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. 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;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 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) 9:9/23 9/25 Shifting Functions: * worksheet: ShiftingFunctions.pdf Factoring: * worksheet: FactoringAnything.pdf; problems #1-10 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 TUTORING: See Tutoring.txt in this directory 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 More factoring. * pp340-341 ODD #37-57 and 56. * p353 ALL#5-8 [Math 130-01: do on a separate sheet. attach to HW notebook later] NOTE: See MathReviewSession.txt in this directory 15:10/4 10/7 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. <<<< CORRECTION SINCE 10/4 16:10/7 10/9 Graphing Exponential Equations * worksheet: GraphingExponentialFunctions.pdf [ section M130-02: you might not be able to do #5,#6.] 17:10/9 10/11 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. 18:10/11 10/16 Powers without calculators * p251-2 #1,2, and ODD#3-59 Scientific notation * p257 ODD #1-27 19:10/16 10/18 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 20:10/19 10/21 Introduction to Logarithms. Read section 6-9, pp269-271. Study examples #1,2,3. * p272-3 ODD #1-41 and #2,14,32 21:10/22 10/23 Log properties Learn Log Properties, blue box p276 * write out examples p276-277 #1,2,3 in your HW notebook * p278 ODD #7-29. NO CALC! use "facts" given before problem 7. Expect a quiz on 10/23 on: HW#15 HW#16 problems 1-4 HW#17 HW#18 NEXT MATH REVIEW SESSION: Wed. Oct 23, 4-6pm See MathReviewSession.txt in this directory 22:10/22 10/23 More log properties * p279 ALL # 33-44 See Example 2, p. 277 for help in doing these problems. 23:10/26 10/28 Change of Base law 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. 24:10/29 10/30 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. 25:10/30 11/01 Exponentials as mathematical models *p300: Read the example , and do this example in your HW book. * p303-308 #1,2,6. ==> Expect a quiz on Friday on: HW#20,21,22,23,24 26:11/02 11/04 One more exponential model * p307-308 #9. 27:11/04 11/06 The Unit Circle * HW27_UnitCircle.pdf 28:11/06 11/08 Arcs & Angles Read section 13-2, pp 711-715. Learn the definitions of: standard position (p712) coterminal angles (p712) reference angle (p713) Be able to convert between degrees and radians Read examples 1-3 pp 714-715 * p717 Q1,Q4,Q6,Q7,Q8,Q10;ODD #1-23. * Convert to radians: (a) 72 degrees; (b) 75 degrees; (c) 270 degrees; (d) -30 degrees; (e) 210 degrees; (f) 60 degrees; (g) 12 degrees; (h) 360 degrees. 29:11/08 11/13 Sin, Cosine, Tangent Read p717-725 * p726 #1-12 (ONLY DO sin and cos) * p726 #13-19,25-30 30:11/08 11/15 Graph Cosine, part 1 * HW30_GraphCosine.pdf (NOTE: the HW# on the sheet should be: HW30) 31:11/14 11/18 Graph Cosine, part 2 HW30_GraphCosine.pdf part 2 * Use your CALCULATOR (in radian mode!) to find the values: cos(0),cos(0.1),cos(0.2)...cos(6.2),cos(6.3). * MAKE A TABLE OF THESE VALUES in your HW notebook.(x,cos(x)) * Then, on the SAME graph you used in HW#30, plot these points with a different color ink (or a different mark) than the mark or color used in HW#30. NOTE CORRECTED DUE DATE: 32:11/14 11/20 The six trigonometric functions * pp 726-727. #1-12: Find ALL six functions [note that sin,cos were done in HW#29] * pp 726-727. #19-24;#31-36. NO CALC (you may check using a calculator) NOTE CORRECTED DUE DATE: 33:11/18 11/20 Graphing sinusoidal functions * p 749 #5,6,9,10. Use the box method. Note: the formulae are given in the form: y = C + A cos(B(x-D)) before starting each problem, change it to the form: y - C = A cos(B(x-D)) by subtracting "C" from both sides. * Sketch the boxes for the graphs in your HW notebook. * Use GraphPaper.pdf (in this directory) to make accurate graphs of the problems. 34:11/21 11/22 Equation of sinusoids from their graphs * pp 752-755 #1,3,5,7,9,11 More graphs of sinusoids: * p 749 #1,7,8,13 __11/23 11/25 No new HW. Please catch up in all of your old and missing assignments. Review trigonometry up to HW#34. Plan for another quiz like the one we had on Friday 11/22. 35:11/30 12/02 cos(A+B);sin(A+B) LEARN and MEMORIZE the SECOND and FOURTH blue boxes on p820, the formulae for the cos or sin of the sum of two angles. *I p822 #1,2.8,10,12. THE FOLLOWING ARE TO BE DONE WITHOUT A CALCULATOR: USE AND GIVE EXACT VALUES (in radicals) for the answers. *II use the fact that 75 degrees = 45 degrees + 30 degrees, and the sin(A+B) and cos(A+B) formulae, to find (a) sin(75 degrees) and (b) cos(75 degrees), using the sin(A+B) and cos(A+B) formulae the formulae that you memorized from p820. *III Find sin(-30 degrees) and cos(-30 degrees). *IV use the fact that 15 degrees = 45 degrees + -30 degrees, and the sin(A+B) and cos(A+B) formulae, to find (a) sin(15 degrees) and (b) cos(15 degrees) 36:12/03 12/04 Law of cosines. LEARN and MEMORIZE the law of cosines (box, bottom p874). * work pp 876-878 examples #1,3 and write a complete solution in your HW notebook. Use a calculator; DO NOT ROUND OFF; give answers to as many digits as your calculator produces. * p879 #1,3,4;7,8,9. NOTE: book answers are given only to a few decimal places. But your answers should be given with no round-off. 37:12/04 12/06 cos(x+y); sin(x+y); cos(2x) * p822 #13-16 NOTE: for #11 and #12, DO NOT memorize tan(x+y). Instead: Find sin(x+y) and cos(x+y); then divide to get tan(x+y). * p828 #9-12 [ double angle formulae ] NOTE: (1) find the cosine of the angle. (2) use the double angle formula for cosine. (3) use the quadrant information and the first Pythagorean Identity to find the sine. (4) find the other trig.functions by their definitions. 38:12/04 12/09 Difference Quotient. Study the handout carefully. * work the example problems on the handout. 39:12/04 12/11 The quadratic function. [YOUR NEXT-TO-LAST HOMEWORK] Worksheet on this directory: GraphingQuadraticFunctions.pdf * (A) Complete all columns on this worksheet. * (B) Graph the quadratics on graph paper (provided in class) 40:12/12 12/20 Change quadratic to vertex form [YOUR LAST HOMEWORK] * Following the method taught in class, * work the problems on the sheet H40_QuadraticVertexForm.pdf PLEASE READ YOUR UMB EMAIL AND FILL OUT THE SURVEY AS DIRECTED!