M130. Homeworks assigned. Dr. Leisinger, Fall 2015. ================ THIS FILE WILL BE CONTINUALLY REVISED 4/02/2015 ======= Updated 12/07/2015, 5:24 pm. NOTE: NEAR THE BOTTOM OF THIS FILE: PRACTICE PROBLEMS FOR FINAL EXAM Name of this file: http://math.umb.edu/~aleising/M130/Homeworks.txt ============================================================= NOTE (9/21/2015): TUTORING IS NOW AVAILABLE (see Tutoring.txt in this directory) ====================================================================== Math 130 Final Exam: Friday, December 18, 2015, 6:30 pm - 9:30 pm. DO NOT miss this exam! Do not plan to leave Boston before the exam is finished!! ====================================================================== ============================================================= 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 ============================================================= 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 0:9/5/14 9/9 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 1:9/5 9/9 Prerequisite Bring me either a printed placement test result or a printed copy of your transcript with a B or better in Math115. 2:9/5 9/9 Number Systems and Basic Operations. This is a reading assignment. Study, learn, and read very carefully, the document "NumberSystems_notes.pdf" in this directory. * 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. 6A:9/10 9/11 Graphing Linear Equations, part I. [Note: this is HW#6] 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 3A:9/10 9/14 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. 3:9/10 9/14 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 4:9/15 9/18 Circles. [ Note: this HW was assigned on 9/15. ] [ Please start it. We'll discuss it more on 9/16. ] 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. * 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. 5:9/15 9/18 Factoring a natural number Learn: the notes on FactoringNaturalNumbers.pdf * Work the exercise at the end. 6B:9/15 9/18 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. 7:9/15 9/21 Inequalities and Absolute Value 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.) 8:9/15 9/23 Products and factoring, #1 Read and try to understand the "Factoring Anything" handout. (on this website: Factoring_Anything.pdf) Don't work the problems on that sheet yet. 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 * p333-4 ODD #23-49,#63-85 * Work these problems from the "Factoring_Anything.pdf" sheet: #1-10 Do the work in your HW notebook. Do not write anything on the "Factoring Anything" sheet. 9:9/15 9/25 Products and factoring, #2 * (Show work in your HW notebook or on a half-sheet of paper * to be glued/taped into your HW notebook: * "Factoring_Anything.pdf" sheet #11-12,15-18,22,23,28,30 10:9/27 9/30 Pascal's Triangle * complete the worksheet: Pascal_Triangle.pdf, to be turned in. 11:9/27 9/30 Factoring #3 * Finish "Factoring Anything" (EXCEPT #31,32) Do the work in your HW notebook. * Put the answers on your Factoring Anything" worksheet. 12:9/27 10/02 Factoring #4: * p340 ODD #17-43,47-51; ALL #55-61 ============================================================= NOTICE: You'll need a non-graphing scientific calculator by 10/7/2015. If you want one from me, I have some Casio FX-260 Solar calcs at $10.00 ... I will have them in class on 10/5. ============================================================= ======================================================== =========== Start of Trigonometry ===================== ======================================================== 13:9/30 10/05 Unit Circle. Complete the handout: HW27_UnitCircle.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#13 at the top of the page. 14:9/30 10/07 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. 15:9/30 10/09 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#15 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!!!) 16:9/30 10/14 Graph cos(x) [second method] Use the SAME GRAPH that you used for HW#18. 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. 17:10/4 10/16 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. 18:10/4 10/19 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. Third, using "GraphPaper.pdf" for your graph, graph all four sinusoidal functions on the same graph paper. 19:10/4 10/21 Equations of Sinusoidal Functions from their graphs * pp752-754 ALL #1-10 Right Triangle Trig Read pp 864-866. Learn the three SOHCAHTOA formulae for sin,cos,tan (box p866) * p868 ODD ##1-13 20:10/4 10/23 Using the identity cos(A+B) = cos(A) cos(B) - sin(A) sin(B). Worksheet: Trig_Exercise_cos_A+B.docx 21:10/4 10/26 Elementary Trig Identities * p805 ODD #1-25 * work all examples pp 808-810 22:10/26 10/28 More Trig Identities * pp 811-812 ALL #1-20,23,24 23:10/26 10/30 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 24:10/26 11/02 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 25:10/26 11/04 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. ======================================================== =========== Exponents and Logarithms =================== ======================================================== 26:11/5 11/06 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 27:11/5 11/09 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 11/11. 28:11/5 11/11 More exponentials. * p246-7 #10,11,18,ODD#19-45. * p251 ODD#1-41 29:11/5 11/13 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. 30:11/5 11/16 Solving exponentials by logs. Read examples pp 264-266. * p267 ODD #1-21. and #2,14 31:11/5 11/18 Graph logarithms sheet * GraphingLogarithmicFunctions.pdf 32:11/5 11/20 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 33:11/5 11/23 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 34:11/5 11/25 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. 35:11/5 11/30 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 ============================= ================================================================= 36:11/05 12/2 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 37:11/05 12/4 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 ============================================================ ============ 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. 37:4/02 5/08 Fractional Equations This will be discussed in class on 8/19 Read p378-379. * What is an extraneous root (give the answer!) * p 380-381 #1,2,3,5, ODD#21-31 38:4/02 5/11 Radical Equations This will be discussed in class on 8/19 Read p425-427. * p428 ODD#1,5-13,23-27. 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 ] =================================================================