M115. Homeworks assigned. Dr. Leisinger, Spring 2013. Updated 5/6/2013, 12:25 pm. Name of this file: http://math.umb.edu/~aleising/M115/Homeworks.txt ============================================================= Syllabus for course: To be provided by 1/30/2013 ============================================================= 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 0:1/28 1/30 Read math.umb.edu/~aleising/General_Information.txt and follow the directions there 1:1/28 1/30 * Graph lines (handout) WORK IS TO BE DONE ON THE GRAPH PAPER HANDED OUT! 2:1/28 1/30 Read math.umb.edu/~aleising/M130/Homeworks.txt Read math.umb.edu/~aleising/M130/Textbook.txt Get a hardbound homework notebook! Only the sew-in, 9 3/4" x 7 1/4" 100-page is acceptable. Carefully number its pages as directed. Set up your contents on sides 1,2,3,4. The next two homeworks are due on Monday 2/4. I advise you to get started on them now. They are due on Monday because not everyone has a textbook yet. ====> For good and bad examples of setting up your HW notebook: see: math.umb.edu/~aleising/HwNotebookSetup.pdf 3:1/30 2/4 Graph lines; Equations of lines from their graphs WORK IS TO BE DONE IN YOUR HW NOTEBOOK * textbook pp 81-82 #1-19 ODD PROBLEMS ONLY * textbook pp 85-86 #1-13 ODD PROBLEMS ONLY 4:1/30 2/4 Write the equations of lines WORK IS TO BE DONE IN YOUR HW NOTEBOOK textbook pp 90#1-19 ODD PROBLEMS ONLY; #20,22,24 Also, study these forms of the line equation: (a) slope-intercept form (b) point-slope form (c) two-intercept form (c) standard form For those still without a book, the TEXTBOOK PAGES 81-91 are on the file: Foerster_pp_81_91.pdf 5:2/4 2/6 Finding equations of lines from descriptions of lines. This assignment is a bit long. Allow enough time to do it. VERY CAREFULLY READ the text pp 86-90. WORK IS TO BE DONE IN YOUR HW NOTEBOOK * Work through all examples #1,2,3,4,5 in this section. This means, try to do each example in your HW notebook. When you get stuck, look at the book's solution. * p 90-91: Q1-Q10 (ALL); #21-31 ODD PROBLEMS ONLY 6:2/4 2/8 See handout "How to Factor (almost) anything)" NOTE THE DUE DATE! This is posted on the website as "FactoringAnything.pdf". * IN YOUR HW NOTEBOOK, work as many problems as you can. [These problems will be due in finished form on 2/15.] 7:2/7 2/11 Text section 7-3. START this HW assignment now. Try to do as much as you can. DUE DATE: 2/11 Carefully read pp 328-332. LEARN box p329; box p331. * Carefully work examples 1,2,3,4 on pp 330-331 in your HW book. Follow the book's method. * p333 ODD PROBLEMS 3-31, 43-61, 63-81. DO NOT COPY ANSWERS FROM THE BACK OF THE BOOK. WORK THE PROBLEMS; THEN CHECK YOUR ANSWERS. 8:2/11 2/13 Distance Formula; Circles READ: Text pp462-464. (Disregard the example for now.) LEARN VERY WELL the three forms of the distance formula, p463. [These forms have circled numbers 1,2,3 on the right] UNDERSTAND:the distance formula IS the Pythagorean Theorem. Write the equation of each of these circles: a. Radius 5, center (0,0) b. Radius 5, center (1,3) c. Radius 7, center (-1,-3) d. Radius 1, center (-1,0) e. Radius = (square root of 2), center (5,7) f. Radius = (square root of 7), center (1,-6) g. Radius = (square root of 11), center (2,4) h. Radius = 11, center (2,4) CONTINUE TO STUDY FACTORING !!! 9:2/13 2/15 More factoring. Note that HW#6 WILL BE COLLECTED on Friday, 2/15. [Don't worry about #31,32 on the Factoring Anything sheet]. * p334 83,85. Learn BOX p. 338 (the Discriminant) * p340 ODD #5-35 10:2/17 2/19 Circles: Completing the Square. Read Example and discussion, pp464-466. * pp466-467. ALL problems #1-12 11:2/21 2/22 Circles: Finding the equation of a circle, if you know the center and a point on the circle. This is a two-step problem. Suppose the circle has center at C=(c,d), and it contains the point A(a,b). Step 1. use the distance formula to find the distance from C to A. d^2 = (c-a)^2 + (d-b)^2. That distance is the radius of the circle. Step 2. Now write the equation of the circle using the method you already know. * p 467 ALL #13-18,20. STUDY ALL PAST WORK, ALSO. 12:2/23 2/25 Quadratic functions (Section 5.1) Read carefully Section 5.1 pp 174-175. * Do exercise 5.1 p 175 ALL #1-7. Use a piece of graph paper for the graph. You can use "GraphPaper.pdf" in this directory as graph paper. STUDY ALL PAST WORK, ALSO. 13:2/25 2/27 Handout: Graphing Quadratics * (put answers on sheet) * (no graphing yet; don't calculate roots.) 14:2/27 3/01 Handout: Graphing Quadratics * (put answers on sheet) * calculate roots * graph #1-12 on graph paper handout page. DO NOT CHANGE THE SCALE ON THE GRAPH! 1 box = 1 unit. 15:3/1 3/4 Graphing Quadratics, again * p179-180 ODD #1-29 Please sketch any graphs in your HW notebook. 16:3/4 3/6 Examples on graphing quadratics Text, pp 181-186: study the examples. For the following equations, FIND THE ROOTS. If you can factor the polynomial, do so. Otherwise, use the Quadratic Formula to find the roots. * p186-187 #1-19 ODD and #16. Follow directions in the book for these problems: * p187 #21-29 ODD and #28. 17:3/7 3/8 Complete the Square to transform a quadratic to vertex form. Carefully work through example 1 on p. 178 of the text. Copy it into your HW notebook. The vertex form of a quadratic is: y - k = a (x-h)^2. The vertex is at the point (h,k). Just as with circles, the reference point [vertex] (h,k) is found as "y - (the y-center)" and "x - (the x-center}" The number "a" is the steepness. *THEN: for each equation below, transform to vertex form. *After that, find the roots using the Quadratic Equation. *What do you notice? *(a) y = 3x^2 + 4x - 5 *(b) y = 3x^2 + 4x + 5 3/8 NO NEW HOMEWORK 18:3/11 3/13 Inequalities in one variable; Absolute Value Read textbook, $1.6,pp 27-31 In the text, the following problems use various domains (Reals,Integers, Positive Numbers, Negative Numbers) But do each problem BOTH for the REAL numbers, and ALSO for the other domain given. Absolute Value: Read Example 4 (p. 29) very carefully. Notice it says " |x| " MEANS "the distance from the origin to x" " |x| > 29 " MEANS "The distance from the origin to x is greater than 29." Understand the box, p30, giving the meaning of |expression| * pp31-32 #1-14, ALL. 3/15 NO NEW HOMEWORK 19:3/15 3/25 Inequalities in one variable; Absolute Value * p32 ALL #15-32, part (c) (real numbers) only. For each problem: (1) graph the solution set (2) write the solution set as a union of intervals (3) write the solution set in set notation 20:3/25 3/29 Introduction to systems of linear equations Read text, chapter 4, pp 111-114. Study and work examples #1,2, p114-115. * Solve by the substitution method: P117 #1-10 (all) NOTE: due Friday 3/29 We will go over this in class. 21:3/27 3/29 Introduction to systems of linear equations * Check your answers to HW#20. Method: for problem #1, for example, the answer is: x = 1, y = 3. To check, substitute these values in BOTH equations. 5x + 2y = 11 5(1) + 2(3) = 11 5 + 6 = 11 (this checks) and x + y = 4 (1) + (3) = 4 1 + 3 = 4 (this checks, too) BOTH equations must check. 22:3/30 4/1 Solving systems of linear equations by elimination The "elimination method" is also called the "addition" method. * Solve by the "elimination method" (see examples #1,2 p114-115) p 117#1-10 (all) But if you already used this method on HW#21, then use the substitution method. How does the substitution method work? You have two equations with x and y. Solve the first equation for (say) x in terms of y. Substitute this value of x into the second equation. That gives you an equation with ONLY y. Solve that equation for y. This gives you a numerical value for y. Substitute that numerical value back for y in either equation to get the value of x. 23:4/1 4/3 Solving systems of linear eqs using Cramer's Rule(Determinants) Read section 4-3, pp 120-123. * Carefully work example on p122; copy it in your HW notebook. * p124 #1-10 (ALL). Use the determinant method. A system is DEPENDENT if the two equations represent the same line. A system is INCONSISTENT if the two equations represent two different parallel lines. * p125 #19 (parts a-e) 24:4/4 4/8 Graphing a linear equation with 3 or more variables Read carefully section 4.5, pp 133-137. * p137 #1,2,3 25:4/4 4/8 More Determinant solutions * p124 ALL #11-14 26:4/4 4/8 Multiplying matrices * p942 ODD #1-9; 10; 11,14,15. 27:4/8 4/10 Systems with 3 or more linear equations * p141 #1. Use ALL of the following methods: (a) substitution (b) Cramer's rule (determinants) (c) elimination * p141 #3,5. Use ANY of the above methods. 28:4/11 4/12 Systems with 3 or more linear equations * p141 #2. Use ALL THREE methods: (a) substitution (b) Cramer's rule (determinants) (c) elimination 29:4/12 4/17 Matrix inverse method for 2x2 systems. Appendix A, pp 937-944, is a good place to read about matrices. The inverse of a 2x2 matrix is described on p939, "Identities and Inverses". The matrix inverse method for solving a 2x2 system is described on pp 939-940. * p117 #1-12: solve by the matrix inverse method. * Check your answers by matrix multiplication, as * shown in class. Also check odd-numbered answers in the text. 30:4/17 4/19 Cramers' and Matrix inverse methods (2x2) * p124 ALL #13,14,15,16: (a) solve each by Cramer's method (determinants). (b) solve each by the matrix inversion method. 31:4/22 4/26 Inverse of a 3x3 matrix. * work through the example on p940-941 (inverse of a 3x3 matrix) (in your HW notebook, or on other paper). * p943 #31,#33. (in your HW notebook, or on other paper). NOTE: HW#31 is now due on 4/26 32:4/26 4/29 Using factoring in combining fractions Read p364-367. * p368 ODD #3-25 33:4/29 5/1 Simplifying radical expressions Learn "Simple Radical Form" (bocx, p419) Read examples #1-4, p 417-420. (especially ex.#4) [I CORRECTED THIS SO YOU ONLY NEED TO DO THE ODD PROBLEMS, EXCEPT #12,#30]. Thanks, Dario! * p420-421 ODD #1-37,#12,#30 THERE IS NO NEW HW DUE on 5/3/2013. 34:5/6 5/8 Simplifying radical expressions, again Please re-study HW#32 and HW#33; Prepare for a re-test on this topic. NO ADDITIONAL WRITTEN WORK. BEGIN TO REVIEW THE CLASS. Go over all of your old HWs.