M130. Homeworks assigned. Dr. Leisinger, Fall 2012. Updated 12/11/2012, 1:34 pm. Name of this file: http://math.umb.edu/~aleising/M130/Homeworks.txt ======================== EXTRA M130 Sessions with Tutor: ==== See: Tutoring.txt for tutoring hours and information ============================================================= HW#, Date Date Assignment Assigned Due 0:9/5 9/7 Read math.umb.edu/~aleising/General_Information.txt and follow the directions there 1:9/5 9/7 Graph lines (handout) WORK IS TO BE DONE ON THE GRAPH PAPER HANDED OUT! 2:9/5 9/7 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 index on sides 1,2,3,4. (M130-03: I haven't explained the index yet, just wait) 3: 9/5 9/7 Takehome "Where you are" quiz (NOT GRADED). (see H3_WhereYouAre.pdf) Do NOT use a calculator. Do NOT spend more than 45 minutes on this quiz. I am using it just to see where you are at this point. Do this quiz on the paper handout. (M130-03: you will need to print this from the website) 4: 9/7 9/10 See HW4_graphLines.pdf This is the first assignment to do in your HW book. Please start it on page 5. Remember to put the HW # on every sheet at the top. 5: 9/12 9/14 Equations of lines from their graphs Read pp 118-126. in HW notebook: * p 127 ODD-NUMBERED PROBLEMS #3-15;27,35,37 [In this file, "*" means "written work") 6: 9/12 9/14 Circles Read from the middle of p294 to the middle of p296. * Write an equation of each circle below; then sketch its graph. 1. Center at the origin, radius 5 2. Center at the origin, radius 3.2 3. Center at (2,-5), radius 1/2 4. Center at (-3,2), radius 2.1 5. Center at (5,0), radius 17 6. Center at (-3,-1), radius 104 7: 9/14 9/17 Circles, continued Completing the square to find C,r of a circle from its equation * In your HW notebook, work problems 1-21 from the file: HW7_Circles.pdf Note that for the equation (for example) (x+1)^2+(y-3)^2 < 25, the graph of the solutions contains ALL points INSIDE and NOT ON the circle of radius 25 centered at (-1,3). If the inequality sign were ">" , then all points OUTSIDE the circle would be on the graph. NEWS FLASH: EXTRA TUTORING AVAILABLE FOR Math-130: Please read Tutoring.txt on this website. 8: 9/17 9/19 Number Systems. Field Properties The REAL numbers, the Rational numbers, and the COMPLEX numbers are fields. The number systems N,W,Z are not fields. (Why?) For most of this class, we work in the field of REAL numbers. But when we are FACTORING polynomials, we normally work in the set of integers (Z). In the file "May29.pdf": Read pp 7-11 (p7 is the first page, and it has no page number) Learn the names of the Field Axioms. In your HW notebook: * on p15 in this file: * do problems Q7,Q8,Q9,Q10 and ODD-numbered problems #1-35 On Wednesday, 9/19, I will collect your HW notebooks. ` 9: 9/19 9/21 Factoring (not to be handed in yet) Read and intently study the "Factoring Anything" handout. On a scrap sheet of paper, not to be turned in, work the following problems on page 2 of the handout: #1-10; #15-17; #28,30. Don't start the trinomials yet. 9(continued) due 9/24 Finish the "factoring anything" handout. Turn it in on 9/24 10: 9/21 9/26 More factoring MoreFactoringProblems.pdf (see website) DO THIS ON THE WORKSHEET FOUND ON THE WEBSITE: (you may use extra paper, labeling each problem as required for the HW notebook; but put the answers on the worksheet) This assignment is due on 9/26; but I strongly suggest you do as much as you can by Monday 9/24. Advice: check your factoring answers by multiplication. Advice#2: check your multiplication by SPECIALIZATION: example: to check (x+3)(x+2) = (x^2+5x+6), try substituting x=2. You will get: ((2)+3)((2)+2) =? ((2)^2+5(2)+6), (5) (4) =? (4 +10 +6), 20 = (20) Yes, it checks. 11: 9/24 9/26 Real numbers (a) Learn and understand the proof that sqrt(2) is irrational (see book, p.5) (b) Read examples 1,2 on p. 6. * p.6 #1-6 (all) (c) Learn and understand boxes, pp 11,12,13. * p. 15 ODD #5-13; ODD #21-29 * p. 26 ODD #7-11, ODD #31-39 12:9/24 9/26 (a)Review quiz 2C, and make sure you can do all of the problems. Study for a retest of quiz 2C. Do this in your HW notebook: (b) Read the box "Domain not specified" on p37. Carefully read pp 37-38, examples 6,7,8. * book p42 ALL #45-50 (c) * 1.Explain the definition of a relation (as I gave it in class) 2.Explain the definition of a function (as I gave it in class) 3.Is every function a relation? If not, give a counterexample. 4.Is every relation a function? If not, give a counterexample. 13:9/26 9/28 Solving inequalities Carefully read section 0.3, pp 18-26. * Section 0.3 pp26-27, ODD #1,7-19, 25-29. 14:9/26 9/28 Functions Carefully read p52-54, examples 4,5,6. * Section 1.2, pp54-5, ODD#1-7,11-23,31, and 32 * Section 1-2, p55, problems 45,46,47 15:9/28 10/1 Function Transformations Read Section 1.3 pp 62-69; stop just before even/odd functions (We didn't go over vertical or horizontal stretching; you may leave such problems to be done by 10/3.) * Section 1.3 Ex. ODD pp71-72 # 1-45. 16:9/28 10/1 Exponents and introduction to Logarithms Completely learn section 3.1 box p231, "Algebraic Properties of exponennts" * Section 3.1 Exercises p232 ALL #1-8 * Section 3.2 Exercises p243 ODD #1-7, 13-27. 17:10/1 10/3 Exponents and introduction to Logarithms Do the worksheet "Graphing Exponential Functions" ON THE SHEET If you didn't get the handout, it is on the website. (see GraphingExponentialFunctions.pdf ) 18:10/1 10/3 Mirroring functions Take the practice quiz found on the website: Functions_Shift_Mirror_Domain.pdf Be ready to turn it in on Wednesday, 10/3 at the start of class. 19:10/3 10/5 Logarithm properties. Book section 3.2, 3.3 For M130-03: we haven't gone over this in class yet! But please do as much as you can Carefully study the blue box p.241, Inverse Properties of Logs Also, section 3.3 p248-252, blue boxes: Log of a product: log(xy) = log(x) + log(y) Log of a quotient: log(x/y) = log(x) - log(y) Log of a mult. inverse: log(1/y) = - log(y) Log of a power: log(x^m) = m log(x) (where "x^m" means "x to the m-th power") We aren't doing "change of base for logarithms" yet. * Section 3.2 p244 #29. * Section 3.2 p244 ODD #31-35. Use a calculator. DO NOT ROUND OFF! * Section 3.2 p244 PROBLEMS #71,73,75,77,78 (Problems are harder than exercises) Do your best! These are a bit of a challenge. * Section 3.3 p252 ODD #1-17 and #18.i Use a calculator only where indicated. * Section 3.3 p253 ODD #19-26. I won't collect this on 10/5 but you should do all you can. Be sure it is finished by 10/10. 20:10/7 10/10 More logarithm properties. Learn the Change of Base property (Section 3.2, boxes, p. 242) * Section 3.2 p244 Ex. ALL #63-70 (use change of base formula) * Section 3.3 p253 Ex. ALL #27-32 * Section 3.3 p254 Problems. ALL #57-60 21:10/11 10/15 Graphing logarithmic functions * See GraphLogs.pdf . Turn in on the worksheet. I know this HW has been posted late. Try to finish it by 10/15. I will accept it up until 10/17. 22:10/15 10/19 Logarithmic and exponential equations * See Exponential&LogEquations.pdf Turn in this on the worksheet. 23:10/20 10/24 Applications of exponential and logarithmic equations Note: this assignment is due on Wednesday 10/23. It would be a good idea to do as much of it as you can now, since there will be another assignment also due on 10/24 Read Section 3.4. Study examples #1-8 * Section 3.4 p269 Exercises #1,3, 5-8, 15-18,23,25 Read Section 3.5. These four examples are important: Radioactive decay; Richter Scale; Decibels * Section 3.5 p282 All #1-5,7-8,9-12,17,23,24 The quiz on 10/22 will be similar to quiz 4.5; but it will have a few questions on solving exponential and logarithmic equations. 24:10/23 10/24 Graphing quadratics Read GraphingQuadraticFunctions.doc (also available as GraphingQuadraticFunctions.pdf ) * Do the exercises on page 3. Do these on the page as printed. If you need more space, do the extra work in your HW notebook. Turn in the 3rd page, plus graphs. 25:10/24 10/26 Completing the square. In your HW notebook: * find the roots of each equation in HW24, by using the method of completing the square. Check each answer against your HW#24 result, which you obtained by either factoring or using the Quadratic Formula. Expect a quiz on 10/26 on graphing quadratics. There will be perhaps 4 or 5 problems like HW#24, and maybe one completing-the-square problem. 26:10/26 10/29 Worksheet: Unit Circle HW26_UnitCircle.pdf 27:10/31 11/2 Begin Trigonometry. Special triangles. Definition of sin() and cos() functions. Determination of sin() and cos() for special angles. Definition of radian. Conversion between radians and degrees. Worksheet: * H27_ChangeToVertexForm&Trig.pdf 28:11/4 11/5 * HW28_GraphCosine.pdf 29:11/5 11/7 Using a calculator to find cos(x) To the points you found on HW28, add all points with x-value 0.0, 0.1, 0.2, 0.3, .... , 6.3 Use your calculator to find the cosine of each: cos(0.1) = ___, cos(0.2) = ___ Then, plot those points on the SAME GRAPH you used for #28. 30:11/7 11/9 Graphing sinusoidal functions. Use the box method taught in class. Do on the sheet and graph paper provided: * HW30_Sinusoids 31:11/13 11/14 The six trigonometric functions Things to know: a. Learn the definitions of sin,cos,tan,cot,sec,csc tan = sin/cos ; cot = 1/tan; sec = 1/cos; csc = 1/sin b. Understand that the SIGN of each of these functions depends on the QUADRANT in which the arc x is found. c. Be able to calculate the six trig. functions for every angle with a REFERENCE ANGLE of pi/2,pi/4,pi/6,pi/3 d. Be able to graph the sinusoid y-C = A cos(B (x-D) ) e. Know the three Pythagorean relationships: sin^2 + cos^2 = 1; tan^2 + 1 = sec^2; cot^2 + 1 = csc^2 f. Know the three reciprocal relationships: tan = 1 / cot; sec = 1/cos ; csc = 1/sin g. Read Chapter 5 sections 1-4, looking for things to learn. See boxes p 388 (first Pythagorean relationship) See boxes p 400 (Domain & Range of Tangent), p. 401 Things to write: * ODD PROBLEMS:p365 #1-9;p378 #1-17,23,25;p391 #1-11;p402 #1-11 ====>>> NOTE: Quiz on Friday, 11/14 finding sin() and cos() of angles (no calculator) Graphing sinusoids. Graphing quadratics. 32:11/14 11/19 Write sinusoidal equations from their graphs Read "Al's Box Method_2.docx" on the website. * See HW32_WriteSinusoidalEquations.pdf * Put answers on: HW32_AnswerSheet.pdf to turn in. [ added 11/16 ] NOTE: the first several problems have x-values given in degrees. You have two choices. Either: (a) keep the value of D and p in degrees; or (b) Change the value of D and p to radian measure In either case, the value of B will be a dimensionless constant. e.g. if p = 60 degrees, then [(2 pi)/p] is equal to 360 degrees / 60 degrees = 6; or if you change p to radians, then p = pi/3, and B = 2 pi/p and therefore B = (2 pi)/(pi/3) = 6. Either way, B=6. 33:11/23 11/26 Cosine of a sum formula; sine of a sum formula a. Learn very well these two formulae: cos(x+y) = cos(x) cos(y) - sin(x) sin(y) sin(x+y) = cos(x) sin(y) + sin(x) cos(y) b. Read, understand, and study well, the proof: Proof_CosOfSumFormula.pdf NOTE added 11/26/2012 9:30 am: I have updated the file Proof_CosOfSumFormula.pdf to correct three typos. c. recall that: an EVEN function f(x) is one for which f(-x) = f(x) an ODD function g(x) is one for which g(-x) = -g(x) * Use the fact that sin(x) is an odd function and cos(x) is an even function to verify the formulae: cos(u-v) = cos(u) cos(v) + sin(u) sin(v) and sin(u-v) = sin(u) cos(v) - cos(u) sin(v) (see boxes pp 498,499). You shouldn't try to memorize these two formulae. You can derive them when needed. 34:11/23 11/28 Cosine of a sum formula; sine of a sum formula [exercises and problems using HW33 #(a) and (c) above: * Section 6.4 p 501-2: ALL exercises #1-4,#13-20,#29-32 [ note correction: do not do problem #43 ; Nov 24, 2012] * Section 6.4 p 502-3: ALL problems #37-42. Hints for problem #39: square both sides. NOTE added 11/26/2012 9:30 am: I have updated the file Proof_CosOfSumFormula.pdf to correct three typos. Note: Proof_LawOfCosines.pdf is now available. 35:11/27 11/30 Using sum and difference formulae; Law of Cosines *Section 6.4 p501 #21-24. (note: find tan(x),tan(y) etc,first.) Using the Law of Cosines: Read Section 6.2 examples 4,5. *Section 6.2 p475,#9a,10a,11a,12a.Problem 20(use Law of Cosines) 36:12/1 12/3 Area of a triangle Section 6.1 p462 #1,3,5,7,11,15 37:12/1 12/3 More sum & difference formulae *Section 6.2 p475, (all parts) #1,3,5,7,9,11,13. [remember you did parts of #9 and #11 as HW#35] 38:12/1 12/3 More sum & difference formulae * Section 6.3; p489 #11-22 all For practice: (you don't have to turn in the following p501 problems.) * Section 6.4: p501 #25,27,29,31 << added 12/11; for practice 39:12/4 12/5 Difference Quotient Read carefully the handout DifferenceQuotient_B.pdf * Work the problems in your HW notebook. REVIEW SESSIONS FOR THE FINAL EXAM: Thursday, December 13, 10am-12noon: Dr. Leisinger (Room TBA) Thursday, December 13, 12:30pm-3pm: Prof. Kovitz (Room TBA) =============================================================== Study materials for the final exam. In: http://www.math.umb.edu/courses/undergraduate/math130/ m130_topics.txt topics covered in the course math130_2012_Problems.pdf A repository of 109 problems that you should be able to solve, in order to be prepared for Math-140 (Calculus I) math130_2012_Index.pdf an index of problems in the problem repository that are most relevant to the 2012 Fall final m130_2011-SampleFinal.pdf A sample final exam (used in December 2011) ================================================================