M130. Homeworks assigned. Dr. Leisinger, Summer 2013. Updated 8/12/2013, 7:39 pm. Name of this file: http://math.umb.edu/~aleising/M130/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 Circles; Distance Formula; completing the square. Read: text, section 9-2, pp 462-466 LEARN VERY WELL: the distance formula, p 463. There are 3 forms of the distance formula on p463. They have little circled numbers (1) (2) (3) at the right. You should know all three of these forms. Read carefully and understand the Example p 464-6. * In your HW notebook, pp 466-467 ALL #1-21 You should draw sketches of each figure #1-12. The text pp 462-466 is posted on this website as: Foerster_p462ff.pdf 4:7/16 7/17 Factoring. READ VERY WELL AND LEARN: "Factoring_Anything.pdf" * Work the first ten problems on the sheet in your HW notebook. ====> Check back later for more problems!!! 5:7/17 7/18 Factoring (continued) READ VERY WELL AND LEARN: "Factoring_Anything.pdf" * In your HW notebook, work the first thirty problems from the sheet "Factoring_Anything.pdf". * When you are sure you are correct, put the answers on the worksheet. Be ready to hand in both the worksheet and your HW notebook. 6:7/22 7/23 Function shifting and mirroring. * Worksheet: FunctionTransformations.pdf Work all of the problems EXCEPT: #3,4,5,8,12,14,15. 7:7/22 7/23 More Factoring. * Textbook, p340, ODD #1-37 READ: section 7.6, pp347-350. * Textbook, p353, #1,2,3,4. [using the Factor Theorem] Check by multiplying. 8:7/23 7/24 Definitions: an EVEN function f(x) obeys the rule: f(-x) = f(x). That is, if you mirror it about the y axis, you get the same picture. Example: y = x^2 + 1 A polynomial that is an EVEN function will have ONLY even-degree terms. an ODD function f(x) obeys the rule: f(-x) = -f(x). That is, if you mirror it about the y axis, and then mirror the result about the x axis, you get the same picture. Example: y = x^3. (x-cubed) A polynomial that is an ODD function will have ONLY odd-degree terms. * Finish all the remaining problems on the worksheet: FunctionTransformations.pdf 9:7/24 7/25 Still more factoring: * Textbook, p340, ODD #39-69 * Textbook, p353, #5-10 all. [using the Factor Theorem] [NOTE: I know I posted this late. If you can't do it all by 7/25, please try some of the problems on each set. 10:7/24 7/25 Laws of exponents Read Textbook, pp229-233. * p234 #1,3,5,7 LEARN VERY WELL: blue box p237 (properties of exponentiation) * p239-240 ODD #1-31 11:7/24 7/25 Graphing exponential functions * Worksheet: GraphingExponentialFunctions.pdf (do the work on the worksheet) 12:7/25 7/29 More properties of exponentials * p247-248 #13,17,ODD #19-41 13:7/25 7/29 Logarithmic functions READ: p269-270; READ AND UNDERSTAND examples pp270-271 * p272 ODD #1-41 NOTE THAT HW#14 IS DUE AFTER HW#15. I HAVE CHANGED THE HW# to HW#15.(was #14) 14:7/30 7/31 Graphing Logarithms. Handout: GraphLogs.pdf (also on website) 15:7/29 7/30 Unit Circle assignment. * HW15_UnitCircle.pdf Do this assignment on the worksheet. Make sure you GRAPH and LABEL every solution point. NOTE THAT HW#14 IS DUE AFTER HW#15. I HAVE CHANGED THE HW# to HW#15.(was #14) 16:7/30 7/31 Trigonometry introduction. (A) measurement of arcs. radians and degrees (book p711) (B) the reference angle (book p713) Read examples pp 714-716. * p717 odd #1-23 (C) Definition of sine and cosine function The textbook makes this distinction (we won't). (book p717-718) (D) trig function (degree input) (E) circular function (radian input) (F) special triangles (30-60-90; 45-45-90) (G) special angles: 30 degrees, 45 degrees, 60 degrees. Read examples pp 723-724. 17:7/30 8/1 Graph the cosine function. * H28_GraphCosine.pdf (but this is NOT HW#28) FOLLOW DIRECTIONS !!! 18:7/31 8/1 Graph the cosine function. * H28_GraphCosine.pdf (but this is NOT HW#28) * (A) Using your calculator in RADIAN mode, find cos(x) for every value of x 0.0, 0.1, 0.2 ... 6.3 and record these values in a table in your HW notebook. * (B) Then, using a DIFFERENT COLOR OF INK from the color you used in HW#17, plot each (x,cos(x)) point on the same graph you used for HW#17. 19:7/31 8/1 The six trigonometric functions. Learn the definitions of the six trig/circular functions given in class. Learn them PERFECTLY. Read and understand the table p.721. Work the examples #1,#2 pp 723-724 in your HW notebook. * p726 ODD #1-36. 20:8/1 8/5 Graphing Sinusoidal Functions Read the handout "Al's Box Method" * Handout: HW20_Sinusoids.pdf (see HW20_Sinusoids.pdf on the website) * make the final graphs for this HW on the graph paper given. (see GraphPaper.pdf on the website) DO NOT CHANGE THE SCALE ON THE GRAPH PAPER! 1 box = 0.5 units. 21:8/5 8/6 Writing the equation of a sinusoidal function, from its graph. In these problems, DO NOT convert between degrees and radians. If the graph is in degrees, use degrees for D and period. If the graph is in radians, use radians for D and period. Notice that A, B, and C are pure numbers with no units. * pp752-755 #1-14 ALL Quizzes expected on or after 8/6: (a) elementary trig Definition of sin and cos in terms of the unit circle Angles in degrees and in radians Converting between degrees and radians Special triangles 30-60-90 and 45-45-90 degrees Trig functions of special angles (0,30,45,60,90 degrees) (b) Functions Definition of a function Domain, range, and image of a function Function addition, subtraction, multiplication, division Function composition Function inverses (definition; notation) Calculating a function inverses by the verbal string method Calculating a function inverse by algebra [WE DIDN'T DO THIS YET ! Not on a quiz on 8/6] (c) Graphing a sinusoid from its equation (d) Writing the equation of a sinusoid from its graph 22:8/6 8/7 Inverse Trig/Circular Functions, part I. * p733 #21-26, 33,34,35,39,40 Here, #21-26 are in degree mode; #33-40, in radian mode. Read pp 767-768 including the blue box. Understand the differences between: arcsin(x), Arcsin(x), sin-1(x), Sin-1(x) arccos(x), Arccos(x), cos-1(x), Cos-1(x) (the -1's are all written above as if they were exponents) Look at the first two graphs at the top of p771. These graphs show the ranges of Arcsin and Arccos. Compare with the first two lines of the lower blue box p770. 23:8/6 8/7 Solving right triangles, part I. Read pp 863-865 (water tower example). Look at blue box p866. * p868 #1,3,5,7. ` 24:8/7 8/8 Solving (oblique) triangles Learn very well: Law of cosines (p874, box) Refer to examples p876-878 exs#1,2,3,4 Law of sines (p884, first box) Refer to examples p 884-886 ex. 1,2. * p887 ODD#1-9. * p893 ODD#1-5. (the SSA case) 25:8/7 8/12 Solving (oblique) triangles: general case p896 ODD #1-23. NOTE 1: Convert degrees and minutes to decimal degrees. NOTE 2: Remember to give all answers to 10 sigfigs. NOTE 3: The book answers are only correct to 4 or 5 places. 26:8/8 8/12 Using cos(A+B) formula. * pp 822-823 #1,2,3,4; * pp 822-823 parts (a) and (b) of #7,#8,10,12 Use the cos(A+B), sin(A+B), tan(A+B) formulae to prove: * pp 823 #13,14,15 (Hint: set B = 90 degrees) * pp 824 ALL #27-32; #45 NO NEW HW for 8/13. (study multiplication facts) (prepare for quiz on solving triangles SAS,SSS,ASA (no SSA) 27:8/13 8/14 Difference Quotient Worksheet (read carefully. Do problems in HW notebook) DifferenceQuotient_B.pdf 28:8/14 8/15 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) 29:8/14 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. 30:8/14 8/15 Powers & Radicals without calculators * pp 251-252 ODD#1-59 31:8/14 8/19 Radicals, Radical Equations Read pp 425-427. Read and understand the examples pp425-427. * p428 ODD#1-35 32:8/14 8/20 Fractional Equations [ LAST HW ASSIGNMENT ] << RENAMED HW32 ! Read pp 378-379 Use the method of the blue box p379 to work these problems: * p381 ODD #3-15; #21-37 Remainder of the course: Review and re-test. Final exam Thursday, 8/22. YOU MUST BE PRESENT ON THAT DAY.