MATH 1051 -- Changes

Fri Mar 26 10:50:18 2010

Effective Term: New:  1109 - Fall 2010
Old:  1089 - Fall 2008
Catalog
Description:
New:  Graphs of equations and functions, transformations of graphs; linear, quadratic, polynomial, and rational functions, with applications; zeroes of polynomials; inverses and composition of functions; exponential and logarithmic functions, with applications; coverage beyond that found in the usual 3 years of high school math.
Old:  Algebra, analytic geometry, exponentials, logarithms, beyond usual coverage found in three-year high school mathematics program.
Course
Prerequisites
for Catalog:
New:  3 years of high school mathematics or satisfactory score on placement test or grade of at least C- in [PSTL 731 or PSTL 732]
Old:  Satisfactory score on placement test or grade of at least C- in [PSTL 731 or PSTL 732]
Course
Equivalency:
New:  Math 1031, 1151, 1155
Old:  No course equivalencies
Editor Comments: New:  <no text provided>
Old:  In last update, line in prerequisite concerning not granting
credit if certain courses already taken was left out by
mistake.
[added to PS note field, course notes sequence nbr 3:]Credit will not be granted if credit has been received for:  
1031, 1151, 1155
Proposal Changes: New:  Submitted for Lib Ed Mathematical Thinking requirement, plus minor fixes.  Essentially the same course as before.
Old:  only change in prerequisites-- line added.
Faculty
Sponsor Name:
New:  Lawrence Gray (Director of Undergrad Studies)
Old:  David Frank
Faculty
Sponsor E-mail Address:
New:  gray@math.umn.edu
Old:  
Student Learning Outcomes: * Student in the course:

- Can identify, define, and solve problems

New:

Please explain briefly how this outcome will be addressed in the course. Give brief examples of class work related to the outcome.

Problem solving is at the heart of any mathematics course. In this course some problems would involve purely mathematical issues, like finding the roots of a polynomial or determining the features of the graph of a rational functions. Other problems involve taking a real world situation like predicting the trajectory of a projectile or analyzing population growth and decline, requiring students to first identify the mathematically relevant aspects, then define appropriate mathematical variables and relations, and finally solve the resulting mathematics problem.

How will you assess the students' learning related to this outcome? Give brief examples of how class work related to the outcome will be evaluated.

Practically every homework assignment, quiz and examination consists of problems to be solved. Students will be challenged to develop their problem-solving skills, and they will get ample feedback about their progress during the semester.

Old: unselected


Requirement
this course fulfills:
New:  MATH - MATH Mathematical Thinking
Old:  
Criteria for
Core Courses:
Describe how the course meets the specific bullet points for the proposed core requirement. Give concrete and detailed examples for the course syllabus, detailed outline, laboratory material, student projects, or other instructional materials or method.

Core courses must meet the following requirements:

  • They explicitly help students understand what liberal education is, how the content and the substance of this course enhance a liberal education, and what this means for them as students and as citizens
  • They employ teaching and learning strategies that engage students with doing the work of the field, not just reading about it.
  • They include small group experiences (such as discussion sections or labs) and use writing as appropriate to the discipline to help students learn and reflect on their learning.
  • They do not (except in rare and clearly justified cases) have prerequisites beyond the University´┐Żs entrance requirements.
  • They are offered on a regular schedule.
  • They are taught by regular faculty or under exceptional circumstances by instructors on continuing appointments. Departments proposing instructors other than regular faculty must provide documentation of how such instructors will be trained and supervised to ensure consistency and continuity in courses.

New:
Precalculus I (Math 1051) covers topics in algebra that are of intrinsic mathematical interest, have important applications in science and everyday life, and needed for a full understanding of calculus.   Although the course does not require previous mathematical background beyond high school, it develops in the students a real understanding of the symbolic language of mathematics and gives them ample opportunity to see how mathematics is done by mathematicians as the students solve problems for themselves, communicate their results, and learn how abstract mathematical concepts can find applications in the real world.  In the TA discussion sessions, students have opportunities to engage in problem solving with their peers.

An important component of a liberal education is an appreciation of mathematics as a body of thought which has been developed over the millennia both for aesthetic reasons and to solve concrete problems.  At the heart of much of modern mathematics is the algebra of equations and functions.  The first symbolic approach to equations began in the Arab world during the 9th century AD, and the concept of function was first introduced in the 14th century.  But it was the advent of calculus that made the algebra of equations and functions central to so many applications of mathematics.  That is why Math 1051, Precalculus I, focuses on using algebra to solve equations and analyze some basic families of functions.  It helps prepare students for the kind of mathematical thinking that is central to calculus, and hence to much of modern mathematics.  

Math 1051 is taught every semester, by a combination of regular faculty and adjunct faculty with ongoing appointments.  Occasionally, the lectures are also taught by experienced graduate students or postdocs, under close supervision by regular faculty.  The final exam is a departmental common exam, in order to ensure a consistent level of expectations.  

Old:
<no text provided>
Provisional
Syllabus:
Please provide a provisional syllabus for new courses and courses in which changes in content and/or description and/or credits are proposed that include the following information: course goals and description; format/structure of the course (proposed number of instructor contact hours per week, student workload effort per week, etc.); topics to be covered; scope and nature of assigned readings (texts, authors, frequency, amount per week); required course assignments; nature of any student projects; and how students will be evaluated.

The University policy on credits is found under Section 4A of "Standards for Semester Conversion" at http://www.fpd.finop.umn.edu/groups/senate/documents/policy/semestercon.html . Provisional course syllabus information will be retained in this system until new syllabus information is entered with the next major course modification, This provisional course syllabus information may not correspond to the course as offered in a particular semester.

New:  (Actual syllabus from a recent semester, modified to include Lib Ed statement and to make it somewhat shorter)

Math 1051 Precalculus I Syllabus for Spring 2010

LEC section 10 meets with Professor Robertson MWF, 2;30 to 3:20 in Tate Lab of Physics 131

DIS section 11 meets 2:30 to 3:20 in Vincent Hall 209 on Tuesdays with Graduate Teaching Assistant (GTA) Guoyi Xu and on Thursdays with PAL facilitator Lauren Sawallisch.

DIS section 12 meets 2:30 to 3:20 in Vincent Hall 364 on Tuesdays with Graduate Teaching Assistant (GTA) Ning Wei and on Thursdays with PAL facilitator Rhonda Younker.

DIS section 13 meets 3:35 to 4:25 in Vincent Hall 364 on Tuesdays with Graduate Teaching Assistant (GTA) Ji Hee Kim and on Thursdays with PAL facilitator Lauren Sawallisch.

       
       
Course: This School of Mathematics course is the first in a two-course sequence that covers the content of a standard precalculus course. We begin with a quick review of high school algebra and then move on to examine the behavior of functions in some depth including inverses, transformations, and compositions; we pay particular attention to linear, quadratic, polynomial, rational, exponential, and logarithmic functions and their graphs. There is no trigonometry in Precalculus I┐that is covered in Math 1151 Precalculus II. For students who wish to move at a faster pace, Precalculus I & II are combined into a single course, Math 1155 Intensive Precalculus.


Liberal Education:  This course satisfies the Mathematical Thinking Core portion of the Liberal Education requirements at the University of Minnesota.  An important component of a liberal education is an appreciation of mathematics as a body of thought which has been developed over the millennia both for aesthetic reasons and to solve concrete problems.  At the heart of much of modern mathematics is the algebra of equations and functions.  The first symbolic approach to equations began in the Arab world during the 9th century AD, and the concept of function was first introduced in the 14th century.  But it was the advent of calculus that made the algebra of equations and functions central to so many applications of mathematics.  That is why Math 1051, Precalculus I, focuses on using algebra to solve equations and analyze some basic families of functions.  It helps prepare students for the kind of mathematical thinking that is central to calculus, and hence to much of modern mathematics.

Learning to solve problems is also a part of a liberal education, and problem solving is a crucial component of this course.  Developing your ability to translate real world problems into the language and symbols of mathematics, solve them using the mathematical techniques described in the course, and communicate your results is an important goal.

Lecturer: Professor Robertson, 211D Burton Hall (in the Knoll Area between the river and University Avenue), droberts@umn.edu, 612-625-1075.

Course Prerequisites: To be successful in this course you should have completed at least three years of high school math, or PsTL 0732 here at the U, with a grade of at least C and you still remember all the material! Information on the kinds of things you should know before taking Math 1051 can be found at http://www.tc.umn.edu/~droberts/MathPlacementHO.pdf

       

┐        Textbook:         Sullivan, Michael, Precalculus, eighth edition, Prentice Hall, 2008. This comes bundled with the Student Solutions Manual, which has the solutions to all the odd-numbered problems and Chapter Tests. You will use this textbook for both Math 1051 Precalculus I and Math 1151 Precalculus II.

MWF Lectures: The primary source of new material in this course will be the Monday-Wednesday-Friday large classroom lectures. I will explain the mathematics, provide worked examples, and have you work some problems in class. Attending the lectures is very important┐students who skip the lectures tend to fail the course. I will also collect some of the assigned homework on most Fridays and Exam days.

Tuesday Discussion Sessions: Each Tuesday, you will attend a discussion session that is lead by a mathematics graduate teaching assistant (GTA). The GTA will do some sample problems that will be similar to those that will appear on the exams, and answer any questions you have on the material or the homework. Your GTA will also return your graded homework.

Thursday PAL Sessions: Each Thursday, you will attend a Peer Assisted Learning (PAL) session. These are small classes where you will work with a PAL facilitator (who is an undergraduate student with a good mathematics background) and your fellow students to actively solve problems using a structured approach. Most of the problems you work on will be similar to exam problems in both content and level of difficulty. This is not a homework question and answer session but a guided work session to help you internalize the processes involved in solving mathematics problems. Some of your classwork will be collected and be graded as a homework assignment.

Attendance: You are expected to show up on time for every lecture, discussion, and PAL session and to stay until the class is over. If your schedule or personal habits do not permit this, switch to a section that fits your schedule, take the course through Online and Distance Learning (http://www.cce.umn.edu/creditcourses/distance/), or drop the course. If you can do the work without attending class, you are in the wrong course and you are wasting your time and money; see me or your adviser about switching to a higher level course such as  Math 1151 Precalculus II, Math 1155 Intensive Precalculus, or Math 1271 Calculus I.

Expectations: To be successful you must take an active role in your own instruction. You will be responsible for learning the material and for getting help when you have questions. While in class you will be expected to make a good faith effort to learn the course material, follow directions, and exhibit behaviors that will improve your chances for success. These behaviors include:

┐        Showing up for every class on time and prepared.

┐        Completing all assigned homework on time and with complete worked-out solutions.

┐        Asking questions when you don't understand something.

┐        Getting help outside of class from the free tutors (see below).

┐        Studying and working on math outside of class every day, seven days a week.

Course Difficulty: Although you may have had a course called "Precalculus" in high school, the difficulty, level of abstraction, and expectations usually are much higher at the U. Math 1051 has a 35% non-completion (withdrawals and failures) rate for several reasons:

1.        Some students enter the course without a solid knowledge of high school algebra, either because they never learned it well or because they have forgotten large chunks of it. We begin with a two-week review of high school algebra but that goes very fast and is intended as a quick reminder of what you should already know rather than an in-depth treatment of the material. If you think your algebra background is not strong enough to do well in this course talk to me about switching to a lower level course, such as PsTL 0732 Intermediate Algebra.

2.        Many students are not prepared for the large amount of work it will take to learn all the material. It is important for you to memorize many formulas and procedures, but even more importantly you must spend enough time doing mathematics so that you understand the ideas and concepts that form the basis for the formulas and procedures. Understanding what you are doing, and why, takes a commitment that goes far beyond memorizing┐we want you to develop a feel for the material in much the same way a pianist develops a feel for her music or an athlete develops a feel for his sport.

3.        The course material is difficult and gets more difficult as the semester progresses. If you start off having difficulties things will only get worse because you must know and understand the beginning material in order to learn the subsequent material. You are taking this course to prepare yourself for calculus which will, in turn, prepare you for higher mathematics, science, and engineering. Like any other language, mathematics requires that you build upon your early work as the ideas and concepts become more complicated.

Credits and Workload Expectations: At the U, each class hour is designed to correspond to an average of 3 hours of learning effort per week necessary for an average student to achieve a C in the course. So, an average student shooting for a C (which is way too low a goal for a serious student) taking Precalculus I, which meets 5 hours per week, should expect to spend an additional 10 hours per week on coursework outside the classroom. If math is a difficult subject for you or if you want to get a grade higher than a C then you will have to spend more hours on it. Knowing the material in this course will be crucial to your success in Precalculus II and Calculus. The time you spend on this course will have a great payoff later on.



Homework Problems: Practicing the skills you learn in this course is of utmost importance. In order to be able to use mathematics you must become automatic at doing symbolic manipulation, such as simplifying expressions, solving equations, and working with functions. Like learning to dance, to play the piano, or to read, learning mathematics involves lots of memorization of what people before you have discovered and then your practicing it until it becomes second nature to you. As the problems become more difficult you will have to perform basic operations and manipulations without thinking about them┐they must be automatic. Homework is designed to get you to practice the skills and to help you figure out what you need to spend more time on.

       

Homework Grading: To receive full credit for homework and exam problems, you must show the mathematical steps necessary to solve the problems. Your written work is meant to ┐communicate┐ to us what you know about math, not just the answers, so your work must be neat, organized, and complete. Each homework assignment will be worth a maximum of 5 points.

Exams: The four 50-minute midterm exams are closed book and notes. They will be done during a regular lecture class on the dates indicated on the schedule handed out in class. Keys for the exams will be posted on the Web after the exams are given. Because of the time constraint for the in-class exams, you must be very well prepared in order to work the problems in the time allotted. If you feel that you have a learning disability that would prevent you from doing your best within that time frame you should immediately contact the Office for Students with Disabilities to see if they can authorize accommodations for you. Information is available on their web site at http://ds.umn.edu/, by calling 612-626-1333 (for both voice and TTY), or by sending an email to ds@umn.edu.

        The final exam will be on common final exam day from 1:30 to 4:30 in a room to be announced in lecture and posted on my web site. The room will most likely NOT be our regular lecture room. If you don┐t know where to go on final exam day call the School of Mathematics at 612-625-4848.

        There will be no make-up exams. If you miss an exam you will be given a score of 0 until you take the final exam. At that time, your score on the final exam will be substituted for the 0. If you miss more than one exam you will get a score of 0 for the additional missed exams.

Final Course Grade: The final grade for this course will be computed as follows:

        Homework        10%        Handed in at the start of lecture on the days specified on the schedule.

        Exam #1        10%        In-class exam covering Appendix sections A.2, A.3, A.5, A.6, A.8, and A.10.

        Exam #2        20%         In-class exam covering Chapters 1 and 2.

        Exam #3        20%        In-class exam covering Chapters 3 and 4.

        Exam #4        10%        In-class exam covering Chapter 5.

        Final exam        30%        Exam covering the entire course. It will be on common exam day from 1:30 to 4:30 in a room to be announced in lecture and posted on the Web. The room will most likely NOT be our regular lecture room. If you don┐t know where to go on exam day call the School of Mathematics at 612-625-4848.

        Letter grades will most likely be assigned as follows:

Grade        Total Points

        A        = 4.00        100 ┐ 96        &#61660;        Represents achievement that is outstanding relative

        A┐        = 3.67        95 ┐ 90        to the level necessary to meet course requirements.

        B+        = 3.33        89 ┐ 86

        B        = 3.00        85 ┐ 82        &#61660;        Represents achievement that is significantly above

        B┐        = 2.67        81 ┐ 80        the level necessary to meet course requirements.

        C+        = 2.33        79 ┐ 76

        C        = 2.00        75 ┐ 73        &#61660;        Represents achievement that meets the course

        C┐        = 1.67        72 ┐ 70        requirements in every respect.

        D+        = 1.33        69 ┐ 68

        D        = 1.00        67 ┐ 65        &#61660;        Represents achievement that is worthy of credit even

        though it fails to meet fully the course requirements.

        S        none        100 ┐ 73        &#61660;        Represents achievement that is satisfactory, i.e., is equivalent to         a 2.00.

        F        = 0.0        under 65        &#61660;        Represents a failure to meet course requirements.

        N        = 0.0        under 73        &#61660;        Represents a failure to meet course requirements.

        You may get your grades or transcript by going to One Stop:

http://onestop.umn.edu/onestop/grades.html

Incompletes: Grades of I are normally not given in this course. However, they may be permitted due to extenuating circumstances for students who have completed most of the course and who are passing. In those cases a well-documented petition is required and the grade of I is subject to the approval of the Director of Undergraduate Studies of the School of Mathematics.

Withdrawal: If you need to withdraw from the course, be aware of the following:

        You may drop the course without permission before the end of the eighth week of the semester. After that date you cannot drop without permission of the instructor and the Director of Undergraduate Studies of the School of Mathematics.

        If you drop before the end of the second week of the semester no mention of the course will appear on your transcript; if you drop later, a W will appear on your transcript.

        Grades of W are subject to the conditions of your college and cannot be given if you take the final exam. If you find that you need to withdraw from the course contact me and your adviser immediately, don┐t just stop coming to class!

Disability Accommodations: Reasonable accommodations will be provided for students with disabilities on an individualized and flexible basis. The staff at Disability Services will determine appropriate accommodations through consultation with the student. Information is available on their web site at http://ds.umn.edu/, by calling 612-626-1333 (for both voice and TTY), or by sending an email to ds@umn.edu.

Harassment: The University of Minnesota is committed to providing a safe climate for all students, faculty, and staff. All persons shall have equal access to its programs, facilities, and employment without regard to race, color, creed, religion, national origin, sex, age, marital status, disability, public assistance status, veteran status, or sexual orientation. Reports of harassment are taken seriously, and there are individuals and offices available for help. Contact the Office of Equal Opportunity and Affirmative Action (http://www.eoaffact.umn.edu/), 419 Morrill Hall, 612-624-9547.

Complaints Regarding Teaching/Grading: Students with complaints about teaching or grading should first try to resolve the problem with the instructor involved. If no satisfactory resolution can be reached, students may then discuss the matter with the Director of Undergraduate Studies of the School of Mathematics, 115 Vincent Hall, who will attempt to mediate. Failing an informal resolution, the student may file a formal complaint.

Student Conduct: The University of Minnesota Student Conduct Code governs all activities in the University, including this course. Students who engage in behavior that disrupts the learning environment for others may be subject to disciplinary action under the Code. This includes any behavior that substantially or repeatedly interrupts either the instructor's ability to teach or student learning. The classroom extends to any setting where a student is engaged in work toward academic credit or satisfaction of program-based requirements or related activities. Students responsible for such behavior may be asked to cancel their registration (or have their registration canceled). For more information see http://www1.umn.edu/oscai/conduct/student/procedure.html

Scholastic Dishonesty: This includes plagiarizing, cheating on assignments or exams, using a graphing calculator while taking an exam, engaging in unauthorized collaboration on academic work, and taking, acquiring, or using exam materials without faculty permission. Scholastic dishonesty in any portion of the academic work for a course shall be grounds for awarding a grade of F or N for the entire course. For more information contact the Office for Student Conduct and Academic Integrity, 211 Appleby Hall, 612-624-6073, http://www1.umn.edu/oscai/.

Mental Health Issues: Sometimes, coping with the stress of attending the University and dealing with your personal, family, and work life can be overwhelming. We each battle stress in different ways and most of the time we can make it through the tough spots without professional help. However, if you or a friend are having mental health issues that you cannot handle, you might want to take advantage of the services offered by the University through it's mental health web site, www.mentalhealth.umn.edu. This site is designed for students, parents, faculty, and staff who are looking for student mental health information and related resources at the University of Minnesota, Twin Cities campus.

       

Schedule of Topics and Assigned Homework

Day        Section Topic and Sub-topics
        No Class: MLK Holiday
1        "Introduction, syllabus, do Diagnostic Pretest of high school algebra in class and hand in
to your GTA"
        After class, read the syllabus
2        "Before class, read text pages xxvi (To Student) & pages  A14 - A19 (in Appendix A at
the back of the textbook)"
        At start of class, pickup handout with Diagnostic Test key and homework problems
        Lecture on Geometry Essentials, which includes:
        Pythagorean Theorem
        Geometry formulas (area, perimeter, volume)
        Congruent and similar triangles
        After class, do the 18 problems on Diagnostic Test Key handed out today in class
        After class, on page A19 do odd # problems 13, 15, 21-37, 38 (ans: 4 - &#960;), 41-53
3        Problem solving session on section A.2
4        Before class, read text pages A22-A29 (Appendix A)
        At start of class, hand in HW2 (your solutions to the 18 problems on the Diagnostic Test Key handed out in lecture)
        At start of class, hand in HW3 on sec A.2
        Lecture on Polynomials, which includes:
        Definitions
        Factor using FOIL (First, Outer, Inner, Last)
        "Special product formulas (difference of squares, square of binomial, sum and
difference of cubes)"
        Divide polynomials using long division
        Factor polynomials
5        Before class, review lecture notes from last class.
        Lecture on Problem Solving: Interest, Mixture, Motion Applications, concluded
        "After class, on page A29 do odd # problems 21, 23, 25, 31-43, 49, 51, 53, 57-63, 67,
71-97, 111, 113, 115"
6        Discuss sections A.2, A.3
7        Before class, read text pages A35-A41 (Appendix A)
        Lecture on Rational Expressions, which includes:
        Reduce
        Multiply and divide
        Add and subtract
        Complex rational expressions
        After class, on page A41 do odd # problems 5-33
8        Problem solving session on sections A.3, A.5
9        Before class, read text pages A43-A51 (Appendix A)
        At start of class, hand in HW5 on sec A.3
        At start of class, hand in HW6 on sec A.5
        Lecture on Solving Equations, which includes:
        Linear
        Quadratic and higher order
        Absolute value
        Complete the square
        Quadratic formula
        After class, on page A52 do odd # problems 25-51, 59-67, 75, 85-99, 101
10        Before class, read text pages A62-A68 (Appendix A)
        Lecture on Problem Solving: Interest, Mixture, Motion Applications which includes:
        Translate Verbal Descriptions into Mathematical Expressions
        Simple Interest Problems
        Mixture Problems
        Uniform Motion Problems
        Constant Rate Job Problems
11        Discuss sections A.5, A.6, A.8
12        Before class, review lecture notes from last class.
        Lecture on Problem Solving: Interest, Mixture, Motion Applications, concluded
        After class, on page A69 do problems 15, 17, 21, 23, 25, 27, 29, 33, 35, 41, 45, 55
13        Problem solving session on sections A.6, A.8
14        Before class, read text pages A81-A87 (Appendix A)
        At start of class, hand in HW8 on sec A.6
        At start of class, hand in HW9 on sec A.8
        Lecture on nth Roots; Rational Exponents; Radical Equations, which includes:
        Simplify radicals
        Add and subtract radicals
        Rationalize denominators of radicals
        Solve radical equations
        Rational exponents
        After class, on page A87 do odd # problems 7-21, 27-35, 41-51, 55-77, 87, 97
15        Review for Exam 1 on A.2 to A.10
        After class, review the diagnostic test homework problems (HW2) and the textbook homework that was assigned. Be sure you know the formulas and how to solve those types of problems.
        After class, do the practice exam on my web site.
16        Discuss sections A.2 to A.10 in review for the exam
17        Before class, study formulas and review homework
        In class, before exam begins, hand in HW11 on sec A10
        "In class, before exam begins, hand in HW12, which is the practice exam
from my web site - RE1"
        Exam 1 on A.2 to A.10
        After class, take a well-deserved break!
18        Problem solving session on logic-based situations
19        Before class, read text pages 1-6 and 9-17
        Lecture on Rectangular coordinates; Distance & Midpoint Formulas, which includes:
        Rectangular (x-y) coordinates
        Distance formula
        Midpoint formula
        Lecture on Graphs of Equations in Two Variables, which includes:
        Graph equation by plotting points
        Intercepts of a graph
        Test for symmetry with respect to x-axis, y-axis, and origin
        Graph y = x^3, x = y^2, and y = 1/x
        "After class, on page 7 do odd # problems 11-19, 27, 35, 37, 43, 45, 49, 55, 63
Graph paper is available at www.tc.umn.edu/~droberts"
        After class, on page 17 do odd # problems 19-23, 29, 31, 37-45, 51-63, 67, 69, 75, 77, 81
20        Before class, read text pages 19-31
        Lecture on Lines, which includes:
        Calculate and interpret the slope of a line
        Graph lines given a point and the slope
        Equation of vertical and horizontal lines
        Point-slope form of a line
        Find equation of a line given two points
        Slope-intercept form of a line
        Identify slope and y-intercept of a line given its equation
        General form of a line
        Parallel and Perpendicular lines
        "After class, on page 31 do odd # problems 17, 19, 23-29, 37-71, 77-85, 91, 93,
103, 105, 115, 117"
21        Discuss sections 1.1, 1.2, 1.3
22        Before class, read text pages 35-39
        Lecture on Circles, which includes:
        Standard form
        Graph a circle
        General form and completing the square
        After class, on page 39 do odd # problems 13, 17, 21-41, 47, 49
23        Problem solving session on sections 1.1, 1.2, 1.3, 1.4
24        Before class, read text pages 48-59, 62-66
        At start of class, hand in HW14 on sec 1.1
        At start of class, hand in HW15 on sec 1.2
        At start of class, hand in HW16 on sec 1.3
        At start of class, hand in HW17 on sec 1.4
        Lecture on Functions, which includes:
        Relations
        Value of a function, Implicit form of a function, Domain of a function
        Sums, differences, products, and quotients of functions
        Identify the graph of a function
        Obtain information from the graph of a function
        After class, on page 59 do odd problems 15-21, 27-39, 47-65, 71, 73, 81, 87-91, 95
        After class, on page 67 do odd # problems 11-25, 29a, 29b, 29d, 35, 41
25        Before class, read text pages 71-78
        Lecture on Properties of Functions, which includes:
        Determine even and odd functions from a graph
        Identify even and odd functions from the equation
        Use a graph to determine where a function is increasing, decreasing, or constant
        Local maxima and local minima
        Average rate of change of a function
        Secant line
        After class, on page 79 do odd # problems 21-43, 53, 57-61, 64a (ans is x^2 + 40/x)
26        Discuss sections 1.4, 2.1, 2.2, 2.3
27        Before class, read text pages 82-88
        Lecture on Library of Functions & Piecewise-defined Functions, which includes:
        Square root, cube root, absolute value, square, cube, reciprocal, greatest integer
        Piecewise-defined functions
        After class, on page 89 do odd # problems 9-47, 51
28        Problem solving session on sections 2.1, 2.2, 2.3, 2.4
29        Before class, read text pages 92-100
        At start of class, hand in HW19 on sec 2.1
        At start of class, hand in HW20 on sec 2.2
        At start of class, hand in HW21 on sec 2.3
        At start of class, hand in HW22 on sec 2.4
        Lecture on Graphing Techniques & Transformations, which includes:
        Vertical shifts
        Horizontal shifts
        Compressions
        Stretches
        Reflections about x-axis and y-axis
        After class, on page 101 do odd # problems 7-35, 41, 53, 57
30        Before class, read text pages 104-107
        Lecture on Mathematical Models & Building Functions, which includes:
        Applications of building and analyzing functions
        "After class, on page 107 do odd # problems 1a only, 5, 7a&b only, 11a&b only,
13, 19a, 23"
31        Discuss sections 1.1 to 2.6 in review for the exam
32        Review for Exam 2 on Cpt 1 and Cpt 2
        After class, on page 43 do ALL these problems (not just odds): 3-6, 9-17, 19, 21, 23, 25, 27-37, 41, 47, 50. Exam problems from Chapter 1 will be like these and the other assigned homework problems from Chapter 1.
        After class, on pages 109-111, memorize graphs, formulas, and Things to Know
        After class, on page 111 do ALL these problems (not just odds): 1, 3, 9-13, 17, 25, 27, 29, 30, 34, 35, 43, 45, 55-64, 69, 70, 73, 74a. Exam problems from Chapter 2 will be like these and the other assigned homework problems from Chapter 2.
33        Problem solving session in review for Exam 2
34        Before class, study formulas and review homework
        In class, before exam begins, hand in HW24 on sec 2.5
        In class, before exam begins, hand in HW25 on sec 2.6
        In class, before exam begins, hand in HW26 on Cpt 1 Review for Exam 2 - R2a
        In class, before exam begins, hand in HW27 on Cpt 2 Review for Exam 2 - R2b
        Exam 2 on Chapter 1 and Chapter 2
        After class, take a well-deserved break!
35        Before class, read text pages 118-123
        Lecture on Linear Functions and Their Properties, which includes:
        Graph linear functions
        Average rate of change
        Determine whether a linear function is increasing, decreasing, or constant
        Applications of linear functions (word probs)
        After class, on page 124 do odd # problems13, 21, 29-37, 41, 43, 45, 51
        Note that we are skipping sec 3.2: Before class, read text pages 133-141
        Lecture on Quadratic Functions and Their Properties, which includes:
        Define quadratic function
        Graph a quadratic function using transformations
        Vertex,  axis of symmetry, and intercepts of a quadratic function
        Maximum or minimum value of a quadratic function
        "After class, on page 142 do odd # problems 11-23, 27, 31, 35, 37, 41, 53-63, 67, 69,
81, 83"
36        Discuss sections 3.1, 3.3
37        Before class, read text pages 145-149 (up to 2 Use a Graphing Utility...)
        Lecture on Quadratic Models & Building Quadratic Functions, which includes:
        Applications of quadratic functions (word probs)
        After class, on page 150 do odd # problems 3, 5, 7, 9, 11a&b&c only, 13-19
38        Problem solving session on sections 3.1, 3.3, 3.4
        No Class
        No Class - Spring Break
        No Class - Spring Break
        No Class - Spring Break
        No Class - Spring Break
        No Class - Spring Break
39        Before class, read text pages 154-156
        Lecture on Inequalities Involving Quadratic Functions, which includes:
        Solve inequalities involving a quadratic function
        After class, on page 156 do odd # problems 3, 5, 7, 9, 19, 21, 25, 33, 35
40        Discuss sections 3.4, 3.5
41        Before class, read text pages 164-179
        Lecture on Polynomial Functions and Models, which includes:
        Degree
        Power functions
        Graph polynomial functions using transformations
        Identify real zeros of polynomial functions and their multiplicities
        Behavior near a zero
        Turning points and end behavior
        Analyze the graph of a polynomial function
        After class, on page 180 do odd # problems 23-35, 45-51, 67, 69, 77, 83
42        Problem solving session on sections 3.5, 4.1
43        Before class, read text pages 184-192
        At start of class, hand in HW29 on sec 3.1
        At start of class, hand in HW30 on sec 3.3
        At start of class, hand in HW31 on sec 3.4
        At start of class, hand in HW33 on sec 3.5
        At start of class, hand in HW34 on sec 4.1
        Lecture on Properties of Rational Functions, which includes:
        Domain
        Vertical asymptotes
        Horizontal or oblique asymptotes
        After class, on page 192 do odd # problems 11-17, 23, 25, 29, 33, 37-49
44        Before class, read text pages 195-206
        Lecture on Graph of a Rational Function, which includes:
        Analyze the graph of a rational function, including holes.
        Applications of rational functions (word probs)
45        Discuss sections 4.1, 4.2, and 4.3 start
46        Before class, read text pages 195-206
        Lecture on Graph of a Rational Function, concluded
        After class, on page 206 do odd # problems 7-15, 25, 33, 41, 53a, 55a
47        Problem solving session on sections 4.2, 4.3
48        Before class, read text pages 209-213
        At start of class, hand in HW36 on sec 4.2
        At start of class, hand in HW37 on sec 4.3
        Lecture on Polynomial and Rational Inequalities, which includes:
        Solve polynomial inequalities
        Solve rational inequalities
        After class, on page 213 do odd # problems 3-13, 17, 21, 23, 27, 29, 33, 41, 51
49        Review for Exam 3 on Chapters 3 and 4
        After class, on page 158, memorize Things to Know
        After class, on page 158 do ALL these problems (not just odds): 1, 3, 5, 9-15, 19, 25, 29, 31-34, 35, 37, 40, 44
        After class, on page 234, memorize Things to Know through Rational function
        After class, on page 236 do ALL these problems (not just odds): 5-9, 11, 19, 20, 23, 25, 29, 31, 35, 37, 39, 42, 89a, 89b, page 214 #35
50        Discuss sections 3.1 to 4.4 in review for the exam
51        Before class, study formulas and review homework
        In class, before exam begins, hand in HW39 on sec 4.4
        In class, before exam begins, hand in HW40 on Cpt 3 Review for Exam 3 - R3a
        In class, before exam begins, hand in HW41 on Cpt 4 Review for Exam 3 - R3b
        Exam 3 on Chapters 3 and 4
        After class, take a well-deserved break!
52        Problem solving session on Multiple Choice problems that are on the final exam
53        Before class, read text pages 242-246
        Lecture on Composite Functions, which includes:
        Form a composite function
        Domain of a composite function
        After class, on page 247 do odd # problems 7,11,13,19-29,33,35,41,53,55,61,65,69
54        Before class, read text pages 249-259
        Lecture on One-to-One Functions & Inverse Functions, which includes:
        Determine whether a function is one-to-one
        Inverse of a function by mapping
        Graph of the inverse of a function
        Inverse of a function given its equation
        After class, on page 259 do odd # problems 9-19, 31, 35, 49, 53, 59-65, 69, 73, 77, 89
55        Discuss sections 5.1 and 5.2
56        Before class, read text pages 263-272
        Lecture on Exponential Functions, which includes:
        Definition
        Graph exponential functions
        Define the number e
        Solve exponential equations
        After class, on page 273 do odd # problems 11, 17, 19, 29-39, 43, 57-77, 83
57        Problem solving session on sections 5.1, 5.2, 5.3
58        Before class, read text pages 277-285
        At start of class, hand in HW43 on sec 5.1
        At start of class, hand in HW44 on sec 5.2
        At start of class, hand in HW45 on sec 5.3
        Lecture on Logarithmic Functions, which includes:
        Change between log and exponential forms
        Evaluate logarithmic expressions
        Domain
        Graph logarithmic functions
        Solve logarithmic equations
        After class, on page 286 do odd # problems 9, 13, 17, 23, 29, 33, 37, 43, 49, 63-69, 87-93, 99-109, 119, 131, 133a, 133b, 133c, 133d
59        Before class, read text pages 290-296
        Lecture on Properties of Logarithms, which includes:
        Properties
        Rewrite logarithmic expressions using properties
        Change-of-base formula
        After class, on page 297 do odd # problems 7-21, 39, 41, 43, 51, 55, 61, 65, 81, 87, 95
60        Discuss sections 5.3, 5.4, and 5.5
61        Before class, read text pages 299-303
        Lecture on Logarithmic and Exponential Equations, which includes:
        Solve logarithmic equations
        Solve exponential equations
        "After class, on page 303 do odd # problems 7-15, 21, 23, 29, 31, 33, 35, 41, 45, 49-55,
75, 77, 81, 97"
62        Problem solving session on sections 5.4, 5.5, 5.6
63        Before class, read text pages 305-312
        At start of class, hand in HW47 on sec 5.4
        At start of class, hand in HW48 on sec 5.5
        At start of class, hand in HW49 on sec 5.6
        Lecture on Compound Interest, which includes:
        Determine future value of a lump sum of money
        Calculate effective rates of return
        Determine present value of a lump sum of money
        After class, on page 312 do odd # problems 3, 11, 13, 21, 23, 27, 29, 31, 39, 49, 53
64        Review for Exam 4 on Chapter 5
        After class, on page 334, memorize Things to Know  through Change-of-Base Formula
        After class, on page 336 do ALL these problems (not just odds): 1, 5, 7, 11, 17-21, 29, 33-42, 45, 47, 49, 51, 52, 56, 63-66, 69, 70, 71, 75, 77, 81, 90, and page 341 #22
65        Discuss sections 5.1 to 5.7 in review for the exam
66        Before class, study formulas and review homework
        In class, before exam begins, hand in HW51 on sec 5.7
        In class, before exam begins, hand in HW52 on Review for Exam 4 - RE4
        Exam 4 on sec 5.1 through 5.7
        After class, take a well-deserved break!
67        Problem solving session on review for final exam
68        Before class, review homework and procedures from Appendix A and Chapter 1
        Review for final exam focusing on Algebra Review and Chapter 1
        "After class, do ALL these problems (not just odds): pg A20 #19, 39, 42;
pg A30 #45, 55, 65, 78, 90, 94, 117; pg A41 #10, 18, 28;
pg A52 #28, 32, 41, 73, 103; pg A69 #24, 39, 54;
pg A87 #25, 37, 39, 48, 70, 76, 78"
        After class, do ALL these problems (not just odds): pg 44 #1-10
69        Before class, review homework and procedures from Chapters 2 and 3
        Review for final exam focusing on Chapters 2 and 3
        "After class, do ALL these problems (not just odds): pg 108 #14, 15, 22a, 24;
pg 114 #1-5, 7-10, 12; pg 115 #1-6, 16-19"
        After class, do ALL these problems (not just odds): pg 160 #1-9, pg 161 #4, 5, 6, 12
70        Discuss Review for Final on A.2 to 5.7
71        Before class, review homework and procedures from Chapters 4 and 5
        Review for final exam focusing on Chapters 4 and 5
        "After class, do ALL these problems (not just odds): pg 238 (Cpt Test) #1, 5, 6, 7, 11;
pg 238 (Cum Rev) #3, 8, 18, 19, 21, 22, 24"
        "After class, do ALL these problems (not just odds): pg 339 #91;
pg 340 #1-7, 10, 14-20; pg 341 #6, 8, 9, 12, 13"
        "After class, do the course evaluation at www.eval.umn.edu. On a piece of paper, write
""I did the course evaluation."" and turn in the paper as part of your homework at the final exam."
72        Problem solving session on review for final exam
        No class - Study on your own
73        Before class, review homework and procedures from all sections covered
        In class, before exam begins, hand in HW54, review of Appendix
        In class, before exam begins, hand in HW55, review of Cpt 1
        In class, before exam begins, hand in HW56, review of Cpt 2
        In class, before exam begins, hand in HW57, review of Cpt 3
        In class, before exam begins, hand in HW58, review of Cpt 4
        In class, before exam begins, hand in HW59, review of Cpt 5
        In class, before exam begins, hand in HW60, course evaluation
        "Exam (final) 1:30 to 4:30 in a room to be announced. If you don┐t know the room call
612-625-4848 or check www.tc.umn.edu/~droberts"
        After class, have a nice semester break and best wishes in Precalculus II



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