M130. Homeworks assigned. Dr. Leisinger, Summer 2016. Name of this file: http://math.umb.edu/~aleising/M130/Homeworks.txt ================ THIS FILE WILL BE CONTINUALLY REVISED ======= Updated 6/28/2016, 7:21 pm ------------------------------------------------------- NOTE added 7/28/2016. All homeworks have now been assigned. NOTE: Many homeworks are now due on 6/28, 7/5 and 7/7. Do them as soon as you can. I realize you might not be able to finish them all on time. I recommend you START all of them, then finish them as you can. HOMEWORKS DO NOT need to be in homework number order in your HW notebook. ------------------------------------------------------- ============================================================= 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 My OFFICE HOURS: to be announced ============================================================= 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 0:6/2/16 6/07 Read http://www.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 above) Also: read: http://www.math.umb.edu/~aleising/Preparation_For_My_Classes.txt 1:5/31 6/02 Inventory Test Turn in the Inventory test. 2:5/31 6/07 Number Systems and Basic Operations. This is a reading assignment. Study, learn, and read very carefully, the document "NumberSystems_notes.pdf" in this directory. OPTIONAL PROBLEMS (extra credit:) * You may if you wish, do the Exercise and Challenge Problem. * Work these problems on paper arranged in the format * described as in HW#0. 3:5/31 6/07 Number system properties [NO WRITTEN WORK; STUDY ONLY] But carefully study the properties of the number systems found in sections 1-1 and 1-2. 4:6/02 6/07 Variables & Order of Operations NOTE: the first 20 pages of the textbook are found on this website in: --- Foerster_p1-20.pdf --- Read Section 1-3. IN YOUR HW NOTEBOOK: * p 14-15 Q1-Q10 * p 15-16 ODD #1-39 AND #14,#40 5:6/02 6/07 Graphing Linear Equations, part I. See "Linear Equations.pdf". on this website. This is the same as the handout given in class. THIS HW IS DONE ON THE GRAPH PAPER, NOT IN YOUR NOTEBOOK. Study very well and learn this handout. * Graph the two columns of linear equations from the bottom of the handout. You need TWO copies of the graph handed out in class. Or, you may print another from GraphForLinearEquationGraphs.pdf in this directory. Column 1 goes on piece of the graph paper; Column 2 goes on the other piece of graph paper. LINES SHOULD BE VERY PRECISE, DRAWN WITH A STRAIGHTEDGE, AND SHOULD RUN ALL THE WAY ACROSS THE GRAPH 6:6/02 6/07 Circles. Read pp461-464. Do not read the example on p464, yet. READ AND LEARN WELL: distance formula p463, all 3 forms. Understand the picture 9-2d (p465). The "<" sign means that the solution points are INSIDE. IN YOUR HW NOTEBOOK: * p466 ALL #1-18. * How to do #13: * p466 #13 (a) find the distance from (7,5) to (3,-2). (b) Using that distance as the radius, Write the equation for that circle. [ Work should be done in your HW notebook. ] 7:6/02 6/07 Factoring a natural number Learn: the notes on FactoringNaturalNumbers.pdf IN YOUR HW NOTEBOOK: * Work the exercise at the end. 8:6/02 6/07 Graphs of Functions; Lines Read text p51-56 DO THESE IN YOUR HW NOTEBOOK: * p52 ALL #1-5 * p56-57 ODD #1-11,#4; ALL 13-20. Read text p73-81. * Sketch the following graphs in your HW notebooks. * put each line on a different graph. * p81-82 ODD #1-23 and #22. 9:6/2 6/09 Inequalities and Absolute Value See: Solving_Absolute_Value_Expressions.pdf in this directory. Read pp 27-31. IN YOUR HW NOTEBOOK: Work examples #1-5. * pp 31-32 Q1-Q7, #1-4,#7-10. Do ODD#15-31, PART (a) ONLY. (That means, always use the Real Numbers for #15-31.) Give answers in two forms: GRAPH, and UNION of INTERVALS 10:6/02 6/07 Products and factoring, #1 Read and try to understand the "Factoring Anything" handout. (on this website: Factoring_Anything.pdf) Do not write anything on the "Factoring Anything" sheet. * Work the problems on that sheet, IN YOUR HW Notebook. * Work these problems from the "Factoring_Anything.pdf" sheet: #1-30 (all) Do the work in your HW notebook. 11:6/02 6/09 Products and factoring, #2 Read Textbook, section 7.3 pp 328-332. Especially: Conjugate Binomials (box, p329) Product of any polynomials (p329-330) p331, Example #3 Last 12 lines of page 331 * Textbook, p333-4 ODD #23-49,#63-85 12:6/02 6/13 Pascal's Triangle * complete the worksheet: Pascal_Triangle.pdf, to be turned in. 13:6/02 6/13 Factoring #3 * Finish "Factoring Anything" (EXCEPT #31,32) THIS IS THE SAME WORK AS HW#10. Check your HW#10 work in your HW notebook. * Put the answers on your Factoring Anything" worksheet. 14:6/7 6/13 Factoring #4: * p340 ODD #17-43,47-51; ALL #55-61 ============================================================= NOTICE: You'll need a non-graphing scientific calculator by 6/16/2015. If you want one from me, I have some Casio FX-260 Solar calcs at $10.00 ... I will have them in class on 6/9,6/14,6/16. ============================================================= ======================================================== =========== Start of Trigonometry ===================== ======================================================== 15:6/7 6/14 Unit Circle. Complete the handout: UnitCircle.pdf (in this directory). Follow the instructions given on the worksheet. 16:6/7 6/14 Calculating sin(x) and cos(x) for special angles. DO NOT DO THIS ASSIGNMENT UNTIL IT IS EXPLAINED IN CLASS! * For each angle below, calculate sin(x) and cos(x) . * DO NOT USE A CALCULATOR. * Find the exact values (e.g. (1/2)sqrt(2),not .707 * Convert each angle to radians first. (these values are in degrees:) x = 0,30,45,60,90,120,135,150,180; x = 180,210,225,240,270,300,315,330,360. 17:6/7 6/14 Graph cos(x). Use "HW28_GraphCosine.pdf". NOTE: due to circumstances beyond my control, the worksheet and its title are incorrectly labeled. After you print the worksheet, please CHANGE THE HW # to HW#17 at the top of the page. * Step 1. At the bottom of the page is a table. * Commplete the row for x using all special angles * up to 2 pi = 360 degrees. * Step 2. On that table, write the values of x as DECIMALS. * Do that JUST ABOVE the row that says "x 0 pi/6 ..." * Step 3. NOT USING A CALCULATOR, write the values of cos(x) * in exact form ( e.g. cos (pi/6) = sqrt(3)/2. ) * Step 4. write the values of cos(x) as decimals. * Step 5. CAREFULLY graph all of these points on your graph. * (DO NOT TRY TO TRACE THE CURVE!!!) 18:6/7 6/14 Graph cos(x) [second method] Use the SAME GRAPH that you used for HW#17. This time, use your calculator in RADIAN MODE. * In your HW notebook, make a table of [x, cos(x)] * for x = {0,0.1,0.2,0.3, .... 6.1,6.2,6.3}. * That is, start with zero and go up 1/10 at a time up to 6.3. * Then, plot these points on that same graph. * Record the points with an "x" mark, or use a different color * of ink from your marks for HW#18. The points from this HW, and those from HW#18, should agree. 19:6/7 6/16 Six trig. functions of special angles. Note: the book uses the terms "Circular Function" if the input is in radians, and "Trigonometric Function" if the input is in degrees. We are not making this distinction. Learn the definitions of all six functions. The new ones are: tan(x) = [ sin(x) /[ cos(x) ] cot(x) = [ cos(x) /[ sin(x) ] sec(x) = 1/[ cos(x) ] csc(x) = 1/[ sin(x) ] * p726 ODD #1-35; also #6 and #36. 20:3/4 7/7 Graphs of sinusoidal functions. Use "Al's Box Method". See "Al's Box Method_2.docx" Graph the following sinusoidal functions: * p749 #5,6,10,12. <== the last one is a sin() function. In your HW notebook: Remember the formula "p = [2 pi]/B" First, find the numbers A,B,C,D,p from the equation. Second, make a box in your HW notebook with the correct A,C,D,p. (That box is NOT the final graph). Third, using "GraphPaper.pdf" for your graph, transfer each box to the graph paper; then graph all four sinusoidal functions on the same graph paper. Make sure that you continue the graph all the way across the graph paper from left to right. You may need multiple boxes. The box repeats across the page. 21A:6/9 7/7 Right Triangle Trig Read pp 864-866. Learn the three SOHCAHTOA formulae for sin,cos,tan (box p866) * p868 ODD ##1-13 21:6/28 7/7 Equations of Sinusoidal Functions from their graphs * pp752-754 ALL #1-10 22:6/28 7/7 Using the identity cos(A+B) = cos(A) cos(B) - sin(A) sin(B). Worksheet: Trig_Exercise_cos_A+B.docx 23:6/28 7/7 Elementary Trig Identities * p805 ODD #1-25 * work all examples pp 808-810 24:6/28 7/7 More Trig Identities * pp 811-812 ALL #1-20,23,24 25:6/28 7/7 Properties of Trig functions Learn boxes p816-817. See boxes 820-821 Learn especially formulae for cos(A+B) and sin(A+B) * p822 ODD #1-11 * p823 ODD #21-43 NOTE The proof of this is posted. See: Proof_CosOfSumFormula_V2.pdf 26:6/28 7/7 Law of Cosines; law of sines; solving triangles Using the law of cosines, solve these problems: * p879 ODD #1-13 NOTE: DO NOT ROUND OFF ANY ANSWERS. The book answers were obtained by trig. tables and are only correct to about 3 or 4 decimal places. See: Proof_LawOfCosines.pdf 27:6/28 7/5 Area of a triangle. Use the area formula in the box at the top of p881. Read example 1 and example 2, p881. * p883 ALL #1-7. 28:6/28 7/7 Trigonometric Equations First, read the text and all six examples in section 14.9, on pp 850-855. Then, solve the following problems: * Section 14.9, pp 856-857, ODD #1-21 ======================================================== =========== Exponents and Logarithms =================== ======================================================== 29:6/07 6/14 Exponents Learn the properties of exponents. boxes, p237,242-244. * p233 ALL #Q1-Q10. Notice the difference between Q8 and Q10 * p234 ODD #1-7 (parts a,b,c) and 8-10 (no calculator). * p234 ALL #10-14; use your calculator for these. * p239 ODD #1-31,22,30,32 30:6/07 6/14 Graphing Exponential Equations * Complete the work sheet GraphingExponentialFunctions_A.pdf [Section 130-08: omit #5 and #6 before in-class explanation.) Expect a quiz on this material on 4/11. 31:6/07 6/14 More exponentials. * p246-7 #10,11,18,ODD#19-45. * p251 ODD#1-41 32:6/07 6/16 Solving exponential equations by brute force p261: Read example. For the next problems,DO NOT use the log button on a calculator. Instead, try values of x until your answer is close enough. * p262: #1,2,3,4,5,6. 33:6/07 6/16 Solving exponentials by logs. Read examples pp 264-266. * p267 ODD #1-21. and #2,14 34:6/28 6/30 Graph logarithms sheet * GraphingLogarithmicFunctions.pdf 35:6/28 6/30 Logarithms by inspection Without using a calculator, solve these problems: * p272 ODD#1-41; and #12,#20,#36,#40 If you need help, then convert the logarithmic form to the exponential form 36:6/28 6/30 Properties of logarithms Learn VERY WELL: box, p276 and box, p283 * Work the examples pp276-278,#1-3, in your HW notebook * READ THE DIRECTIONS on p278 between #6 and #7 * p278 ALL #7-14; ODD #15-31 37:6/28 6/30 Change of Base for logarithms Read section 6-11, p282-284. Learn: box, p283. Recall the alternate form taught in class. * Use the change-of-base formula and an appropriate calculator: * p284-285 Q1,Q10,ALL #1-10, ODD#13-19,21. 38:6/28 6/30 Difference Quotient Read the sheet (on this website) and work the problems in: * DifferenceQuotient_B.pdf NOTE: for the f(x) = cos(x) problem, you will need to use the cos(A+B) formula. NOTE: for the f(x) = e^(x) problem, you will need the fact that e^(a+b) = (e^a)(e^b) ================================================================= ============= Quadratic Equations ============================= ================================================================= 39:6/28 7/5 Quadratic Function skills sheet Learn the skills on the sheet handed out in class. The skills sheet is at: GraphingQuadraticFunctions_N.pdf * Complete the table:see GraphingQuadraticFunctionsExercises.pdf 40:6/28 7/5 Graphing quadratic functions * On the graph paper provided in class, graph the 14 quadratic * functions given as HW#14. * [This graph paper is also at: GraphForQuadraticGraphs.pdf 41:6/28 7/5 Vertex form of the quadratic. See the handout: ConvertQuadraticToVertexForm_N.docx Be able to change a quadratic from polynomial to vertex form. Use the method shown on the handout. * Convert to vertex form: * y = 3x^2 - 2x + 7 * y = -2x^2 - 3x - 4 42:6/28 7/5 Fractional Equations Read p378-379. * What is an extraneous root? (give the answer!) * p 380-381 #1,2,3,5, ODD#21-31 43:6/28 7/5 Radical Equations Read p425-427. * p428 ODD#1,5-13,23-27. ===================================================================== THIS IS THE END. THERE IS NO MORE HOMEWORK FOR THIS COURSE after HW#43. ===================================================================== =========== NOT FOR HUMAN CONSUMPTION!!!!! ========================= ============================================================ ============ PRACTICE PROBLEMS FOR FINAL EXAM ============== ============================================================ Please see: in this directory: ASampleFinalDec2014.pdf ASampleFinalDec2014Solns.pdf ASampleFinalMay2015.pdf ASampleFinalMay2015Solns.pdf ================================================================= ================================================================= ============= DO NOT READ BELOW THIS LINE ==================== ============= NO HOMEWORK BELOW THIS LINE ==================== ============= EVERYTHING BELOW HERE IS SUBJECT TO CHANGE ====== ================================================================= ================================================================= 37:4/02 5/04 Functions of Two Variables. * FunctionsOfTwoVariables.pdf (in this directory) Do this in your HW notebook. 39:4/02 5/13 Solving equations of special types: exponential equations logarithmic equations trigonometric equations [ no definite assignment yet; updates will follow ] 40:4/02 5/13 Solving quadratic equations by completing the square [ no definite assignment yet; updates will follow ] 41:8/03 8/20 Additional topics Functions and relations graphing functions new functions from old even/odd functions Complex numbers graphing higher-degree polynomial functions Factoring; using the factor theorem The general quadratic in two variables: The ellipse, the hyperbola; the xy term. [ no definite assignment yet; updates will follow ] =================================================================