M130. Homeworks assigned. Dr. Leisinger, Spring 2014. Updated 5/14/2014, 11:27 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 0:1/26 1/28 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 back) Also: read: http://www.math.umb.edu/~aleising/Preparation_For_My_Classes.txt 1:1/26 1/28 Prerequisite Bring me either a printed placement test result or a printed copy of your transcript with a B or better in Math115. 2:1/26 1/30 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. 3:1/26 1/30 Field Properties. REMARK (1/28): YOU CAN READ THESE PROBLEMS, BUT YOU CAN'T DO THEM YET, BECAUSE YOU DON'T HAVE PERMISSION TO WRITE IN YOUR HW NOTEBOOK!!! However, you can do the reading !! So please start this HW; It will be due on Tuesday, 2/4. This HW is from the textbook. The first 21 pages of the text are in a file in this directory. That file is Foerster_p1-20.pdf ; the answers to the problems are in "Foerster_Answers_p983.pdf a) carefully study the table on the left page facing page 1. There are two errors on this table. Error 1: the definition of transcendental numbers is almost OK. Error 2: the "Whole Numbers" are left out. Where would you put them? b) carefully read section 1.1 and 1.2. Learn the table on pp 4-5 VERY WELL. You will be tested on it soon. 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. * Textbook 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." * Textbook pp7-8:#1-10 [NOT Q1-Q10] 4:2/1 2/4 Variables & Order of Operations Read Section 1-3. * p 14-15 Q1-Q10 * p 15-16 ODD #1-39 AND #14,#40 5:2/4 2/6 Graphing Linear Equations, part I. (handout in class, also on the website as: "Linear Equations.pdf". Study very well and learn this handout. * Graph the two columns of linear equations from the bottom of the handout. Column 1 goes on one side of the graph paper; Column 2 goes on the other side of the graph paper. The graph paper is also posted on the website as: GraphForLinearEquationGraphs.pdf ALSO: study the inventory test and try to understand how correctly to work the problems that you missed. 6:2/08 2/11 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. 7:2/08 2/11 More lines; point-slope form of a line. Equation of a line with given slope, and through a given point. Slope of a line perpendicular to a given line. (box p.88) Read text pp86-90. Study carefully examples #1-5. In your HW notebook: * Work each example by yourself, and compare with the text. Or, if that is too difficult, copy each example into your HW notebook. * p90-91 ODD #1-13 8:2/11 2/13 Parallel and perpendicular lines Learn box, p.88. Read example 3, p.88. Do this HW on a sheets of paper small enough to be glued, taped or stapled into your HW notebook. * p91 ODD# 15-31; p92 #34. Read p94-95 and examples #1,2. * p98 # 1,5,8,9,15 9:2/11 2/18 Inequalities and Absolute Value Read pp 27-31. 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.) 10:2/18 2/20 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. * p466 #13. Read section 7.3 pp 328-331, Examples #1,2,3. * p333 ODD #3-19, and #20. 11:2/21 2/25 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. Re-read 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 12:2/21 2/25 More circles * p466 #13 (again, see HW#9, first part). (a) find the distance from (7,5) to (3,-2). (b) Using that distance as the radius, Write the equation for that circle. * p466 #14-18 13:2/25 2/27 Factoring #2; more circles NOTE: p466 #49 has a CORRECT answer in the book. Read section 7.4 pp 336-337. * p340 #5-10,11,13,15,16 (READ TEXTBOOK DIRECTIONS for #15,16) * In your HW notebook: work the first ten problems on the * "Factoring_Anything.pdf" sheet. Completing the square in the circle formula: Carefully read and understand the EXAMPLE on pp464-465. * p466#1,2,7,8 14:3/01 3/04 Factoring #3; more circles * In your HW notebook, work these problems from the * "Factoring_Anything.pdf" sheet: #11,12,15-18,22,23,28,30 * Textbook p466#3-6,9-12. First, by completing square, find the equation in standard form. Then, sketch the graphs in your HW notebook. ==> prepare for a quiz on factoring and circles. 15:3/04 3/06 Factoring #4; * complete the worksheet: Pascal_Triangle.pdf, to be turned in. * Finish "Factoring Anything" (EXCEPT #31,32) * Put the answers on your Factoring Anything" worksheet. ==> Prepare for a quiz on factoring and circles. ==> Be ready for another quiz on inequalities. 16:3/08 3/11 Factoring #5: * p340 ODD #17-43,47-51; ALL #55-61 17:3/11 3/13 Factoring #6; Quadratic functions #1. ==> Be sure you know how to complete the square [see the top blue box on p177]. Quadratic functions: Learn the box, p174. * p179 ALL #1-8 * ALSO: work EXAMPLE #1 from the sheet: ConvertQuadraticToVertexForm_N.docx which is found on this website. Work the example THREE TIMES. COPY EXACTLY THE METHOD SHOWN!!! 18:3/16 3/25 Converting a quadratic to vertex form. USE THE METHOD POSTED ON-LINE, rather than the book method. See: ConvertQuadraticToVertexForm_N.docx [NOTE: the book gives the vertex as an answer. [But I am looking for the equation in vertex form: y - k = a (x - h)^2 , as well as the vertex and the graph. Convert each quadratic to vertex form: * p180 ALL #19-26. 19:3/28 4/01 Quadratic Function skills sheet Complete the table handed out in class. 20:4/01 4/03 Graphing quadratic functions * On the graph paper provided in class, graph the 14 quadratic * functions given as HW#18. Expect a quiz on this topic on 4/3. 21:4/01 4/03 Exponents Learn the properties of exponents. boxes, p237,242-244. * p234 ODD #1-9 (parts a,b,c) * p239 ODD #1-31,32 22:4/05 4/08 Graphing Exponential Equations * Complete the work sheet handed out in class. This work sheet is: GraphingExponentialFunctions.pdf Expect a quiz on this material on 4/10. 23:4/09 4/10 More exponentials. * p246-7 #10,11,18,ODD#19-45. * p251 ODD#1-35 24:4/09 4/15 Logarithms Read examples #1,2,3 p264-267 * p267 ALL Q1-Q10 and ODD#1-23. 25:4/12 4/15 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. 26:4/12 4/15 Properties of logarithms Learn VERY WELL: box,p276 and box,p283 * Work the examples pp 276-278,#1-3, in your HW notebook. * READ THE DIRECTIONS on p278 between #6 and #7. * p278 ALL #7-14; ODD #15-31. 27:4/14 4/17 Unit Circle. Complete the handout: HW27_UnitCircle.pdf 28:4/14 4/?? Solving Exponential and Logarithmic Equations NOT ASSIGNED OR DUE YET 29:4/20 4/22 Calculating sin(x) and cos(x) for special angles. * 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. 30:4/22 4/24 Graph cos(x). Use "HW30_GraphCosine.pdf". [Note, HW# on that sheet is 28; It should be HW#30.] * 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. 31:4/22 4/24 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. 32:4/24 4/29 Graph cos(x). Use the SAME GRAPH that you used for HW#30. 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#30. The points from this HW, and those from HW#30, should agree. NOTE NEW HW#. THIS WAS HW#33 33A:4/24 4/29 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. NOTE NEW HW#. THIS WAS HW#33 33B:4/29 5/01 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 34:4/29 5/6 Elementary Trig Identities * p805 ODD #1-25 * work all examples pp 808-810 35:4/29 5/6 More Trig Identities * pp 811-812 ALL #1-20 36:4/29 5/6 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 (added 5/6/2014): The proof of this is posted. See: See: Proof_CosOfSumFormula.pdf 37:5/03 5/8 Law of Cosines; 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. NOTE (added 5/6/2014): The proof of this has been corrected from the one given in clas. See: Proof_LawOfCosines.pdf 38:5/3 5/8 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. ========================== Practice for Final Exam ============== Practice materials for the final exam, produced by Prof. Kovitz, are posted in the subdirectory PracticeForFinal/ ================================================================= 39: 5/10 5/13 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. 40: 5/12 5/13 Graphing Logarithmic Functions * GraphingLogarithmicFunctions.pdf (handout,& in this directory) ========================== REVIEW SESSIONS for Final Exam ============== Prof. Kovitz review: Thursday, 5/15/2014, 9:30-12 noon, W1-0041 XueFen Chen review: Friday, 5/16/2014, 2-4 pm, S2-0065 Dr Leisinger review: Friday, 5/16/2014, 8-12, W1-0006 (room confirmed) The Friday morning review will be run by both Professors Leisinger and will continue at 10:30 or so, with subjects common to Math-130 and Math-115. ================================================================= FINAL EXAM: Friday, 5/23/2014, 6:30 pm - 9:30 pm, Wheatley W1-0004 Bring a scientific, non-graphing calculator, blue or black pens. DO NOT BRING: any other electronic devices. Phones may be turned off and given to the test proctor before the start of the exam. =================================================================