Math 2 – Precalculus

Fall 2009

Instructor: Gail Edinger

Office: MC 59

Phone: (310) 434-3972 (voicemail)

Email:

**Important note: Due to problems with email from unknown senders, put the following in the subject section of all emails: Your full name – Math 2. If you do not have this in the subject section I will not read your email.******

Office Hours: Monday & Wednesday 8:45 a.m. – 9:15 a.m., Tuesday 6:15 – 7:15 p.m. and Thursday 10 a.m. – 11 a.m. Other times by appointment.

Description: An intensive preparation for calculus. Review and extend important concepts in algebra including the study of functions (polynomial, rational, exponential, logarithmic, and trigonometric including graphs and inverses; learn the basic definitions and identities of trigonometry; develop computational skills, including applications of log and trig functions; solve systems of equations and inequalities. We will also study properties of sequences and series; proof by induction and develop the topics involving conic sections.

Prerequisites: Math 20 and Math 32

Transfer information: UC, CSU IGETC Area 2

Textbook: Stewart, Redlin, and Watson; Precalculus: Mathematics for Calculus, 5th edition, Thomson Brooks/Cole, 2007.

Calculator: Any scientific calculator for homework, calculators may not be used on exams.

Outline: There is a class schedule and outline attached. Please note that there could be changes to this schedule.

Attendance: Attendance is expected and encouraged. I will take attendance at every class. If you are absent for all or part of more than 3 classes, you may be withdrawn for nonattendance, regardless of current grade in the class.

If you intend to drop the class, do not just stop coming. It is your responsibility to do the paperwork.

If you are absent, you are still responsible for all material covered. You will be expected to complete and turn in all assignments on time. You may call me, email me or contact a classmate to find out what you have missed so that you can complete the material. You are also responsible for any changes to the syllabus, including changes in exam dates and assignment dates.

Homework: You are expected to do homework after every class. The homework is not collected, but is considered due at the beginning of the next class. It is an important part of this class and crucial to your success. An initial assignment list is attached. There will be a short time at the beginning of each class (approx. 5 minutes) to answer short questions on the homework from the previous class. I will generally not have time to work out long problems in class, these questions should be taken care of in office hours. If you have many questions, please see me during office hours or go to the math lab. I will only answer questions from the previous homework assignment during class. If you fall behind on the assignments, I will be glad to answer those questions during office hours, but we will not take class time away from the students who have kept up to answer questions for those that have fallen behind in the assignments.

Exams: There are 5 exams scheduled, each is worth 100 points. (See outline for dates) These will be closed book exams, scheduled for the entire class time. You are expected to take the exams on the scheduled date. NO MAKE-UP EXAMS WILL BE GIVEN FOR ANY REASON. If you miss one exam the grade from the final will be substituted for that exam. If you miss more than one exam, you will receive a grade of 0% for any further exams missed. If you have taken all of the scheduled in class exams you may substitute the grade on the final for your lowest exam grade. Exams will be closed book, note and generally taken without a calculator.

There will be a comprehensive final. The date is noted on the outline.

Quizzes: There will be a short quiz at the end of class every Thursday. These quizzes will be heavily based on the homework and the material covered will usually be announced on Tuesday. If you are up to date on the homework, they should be no problem. At the end of the semester, the lowest two quiz grades will be dropped. NO MAKE-UP QUIZZES WILL BE GIVEN FOR ANY REASON. If you miss a quiz that will have to be one of the ones dropped, if you miss more than 2, a grade of 0 will be recorded for all following missed exams. This grade cannot be made up in any way.

The quiz time will always be the end of class and will not be changed. Please do not ask me to give you the quiz at a different time from the rest of the class for any reason.

Grading: The final grades will be assigned according to final averages as follows:

90 – 100 = A, 80 – 89 = B, 70 – 79 = C, 60 – 69 = D, below 60 = F

using the following formula:

60% = exam scores

10% = Quiz scores

30% = Comprehensive final

If you have taken all of the in class exams and your final exam grade is greater than ONE of your in class exam grades, that low exam grade will be dropped and the final exam score will take its place. I will not deviate from this system for any reason; please do not ask me to. The grades will not be curved other than the possible replacement of the lowest by the final as outlined above. I will not make deals or take your personal situation into account when assigning grades. This includes, but is not limited to your transfer status, GPA, graduation status or any other personal reason you can think of. There will be no extra credit in this class.

Academic Honesty: The academic honesty policy of Santa MonicaCollege will be strictly enforced. If there is any evidence of academic dishonesty on any exam or graded work, all parties involved will receive a grade of 0% for the entire exam or graded assignment, regardless of who did the original work and how much of the exam or assignment was involved. This 0% cannot be the exam grade dropped. It will count toward your final average. A report of Academic Dishonesty will be filed with the school.

Disabilities: Working with the disabled student center, I will make accommodations for disability related needs.

Reaching me: Drop by during office hours. If you have a question outside office hours, the best way to find me is via email. I check my email daily, Monday - Friday and will be glad to answer any questions on the homework. I will do my best to check email on the weekends, but if I cannot get to it on Sat. or Sun. I will definitely respond on the following Monday.

Withdrawl Policies: The SMC withdrawl dates are listed below. Please read them carefully. They will be strictly followed.

WITHDRAWAL DEADLINES

Last day to withdraw in Fall Semester (16-week session)

To receive enrollment fee and tuition refund

By phone/web – Sun, Sept 13, 2009, 10 p.m.

To avoid a W on permanent record

By phone/web – Mon, Sept 21, 2009, 10 p.m.

To receive a guaranteed W

By phone/web – Mon, Oct 26, 2009, 10 p.m.

To receive a W with faculty approval of extenuating circumstances (NO grade check required)

(instructor must drop you online) Mon, Nov 23, 2009 –you must have spoken with me in person (Not via email) regarding this by the end of office hours on this date.

Please note: “extenuating circumstances” mean that there is some verifiable and unforeseeable emergency which precludes your completing your semester at SMC. This does NOT include avoiding a low grade, the effect of this class on your GPA, your transfer status or any other such circumstance. You will have until Oct. 26 to drop for these reasons, after that you are in the class for a grade. If you want discuss “extenuating circumstances” to invoke this option of withdrawing after Oct. 26 you will probably be in a situation which requires that you withdraw from ALL of your SMC classes not just this one. Therefore all students should consider October 26 as the last day to drop the class. It is very unlikely you will be withdrawn after this date.

Comments:

  1. Get to know each other
  2. Ask questions. If you do not understand something, ask as soon as possible. I welcome questions during class. You may also ask for help before class and during the break.
  3. Make frequent use of the math lab. This is a useful way to get questions answered. It is FREE!
  4. Keep up. I cannot stress this enough. The material is cumulative and if you fall behind, it is very difficult to catch up. You should expect to do 1 – 2 hours of homework for every hour spent in class.
  5. You are expected to turn off your cell phone, pager, watch or any other noise making device before class starts. If your device goes off in class you will be asked to turn it off immediately. Please do not take this as an opportunity to check your message. If your device goes off during an exam or quiz, your exam or quiz will be considered finished, the work will be collected and you will be asked to leave. No additional time will be given.

Mathematics Skills Associated With This Course

Entry Level Skills

Skills the instructor assumes you know prior to enrollment in this course

  • Simplify advanced numerical and algebraic expressions involving multiple operations.
  • Perform operations on polynomials.
  • Solve literal equations for a designated variable.
  • Solve and graph inequalities involving absolute value.
  • Solve polynomial equations by factoring.
  • Solve quadratic equations by using quadratic formula and completing the square.
  • Complete the square.
  • Solve rational and radical equations.
  • Use interval notation to express the solution to a linear, quadratic or rational inequality.
  • Solve application problems using equations.
  • Find the domain and range of linear, quadratic and absolute value relations.
  • Find domain of rational and square root functions.
  • Perform operations on functions including composition of functions.
  • Determine the inverse of a function
  • Perform operations on complex numbers.
  • Convert between exponential and logarithmic forms.
  • Evaluate and graph exponential and logarithmic functions.
  • Solve elementary logarithmic and exponential equations.
  • Graph parabolas and circles by completing the square.
  • Solve systems of linear equations in three variables by elimination and matrices.
  • Graph systems of linear and quadratic inequalities.
  • Evaluate simple expressions involving sigma notation.
  • Graph simple functions by vertical and horizontal translation.
  • Define basic geometric terms.
  • Distinguish between hypothesis and conclusion.
  • Describe the relationship between a theorem and its converse, inverse and contrapositive.
  • Set up and complete simple direct and indirect proofs.
  • Perform basic geometric constructions.
  • Apply geometric theorems involving similar and congruent triangle; parallel lines; parallelograms and their properties; lines and circles and their properties; lines and circles and their relationships; right triangles (Pythagorean theorem).

Course Objectives

Skills to be learned during this course

  • Determine domain, range, symmetry and inverse, if it exists, of a relation.
  • Analyze and graph a given function, including but not limited to piecewise defined, polynomial, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
  • Use transformation techniques including vertical and horizontal shifts, compression, stretching, and reflection over the x- or y-axis to sketch the graph of a function.
  • Use the language and standard mathematical notation of the algebra of functions.
  • Determine algebraic combinations and compositions of functions and state their domains.
  • State and apply the unit-circle and right-triangle definitions of trigonometric functions and their inverses.
  • State and apply fundamental trigonometric identities and the sum, difference, double-angle and half-angle identities.
  • Factor polynomials using rational and complex zeros.
  • Solve polynomial, rational, exponential, logarithmic, trigonometric and inverse trigonometric equations.
  • Write algebraic and trigonometric relationships to solve application problems, including solution of triangles.
  • Prove trigonometric identities.
  • Classify, analyze and graph conic sections given any quadratic equation in two variables. (Excludes rotation)
  • Solve systems of nonlinear equations.
  • Prove statements using mathematical induction.
  • Apply the binomial theorem to expand a binomial and find required intermediate term.
  • Use the language and notation of sequences and series. Determine any term in a sequence.
  • Evaluate, manipulate and interpret summation notation.
  • Solve problems involving work and other applications of vectors (if time permits).

Math 2 – Outline of topic and assignments

*Note that this schedule is approximate and there may

Be changes as we move through the semestser.

Date / Sections Covered / Assignment
Aug. 31 / 1.1, 1.2, 1.3 / 1.1: 53, 63, 69
1.2: 9 – 69 EOO (every other odd), 85
1.3: 69, 70, 97, 97, 101, 103
Sept. 1 / 1.4, 1.5 / 1.4: 57, 61, 67, 69, 71
1.5: 63, 77, 79, 85, 89, 95, 97, 112
2 / 1.7 / 1.7: 33, 39 – 75 odd, 101
3 / 1.8, 1.10 / 1.8: 51 – 67 odd, 84, 89
1.10: 21 – 35 odd, 53, 55, 57
Chapt 1 Review: 43, 37, 61, 64, 91, 127
Sept. 7 / Labor Day – no class
8 / 2.1: Functions / 2.1: 15 – 57 odd
9 / 2.2: Graphs of Functions / 2.2: 3 – 75 EOO, 81
10 / 2.4: Transformations / 2.4: 3 – 47 EOO, 53, 57, 61 – 71 odd
Sept. 14 / 2.6: Modeling with Functions / 2.6: 1 – 17 odd, 31a
15 / 2.7: Combining Functions / 2.7: 1 – 9 odd, 17 – 53 odd, 57, 59
16 / Review
2.5 Quadratic Functions / Chapter 2 review: (concepts) 7, 13
Chapter 2 review: (exercises) 3, 11, 13, 31,47, 64, 66
17 / EXAM 1 – Ch. 1, Ch 2 / 2.5: 1 – 17 odd
Sept. 21 / 2.5 Quadratic Functions
2.6 Modeling / 2.5: 19 – 43 odd, 59
2.6: 19, 21, 23, 29
Ch 2 review exercises: 53, 61
22 / 3.1 Polynomial Functions / 3.1: 1, 3, 5 – 10 all, 11 – 45 odd, 71, 73, 79ab
23 / 3.2: Synthetic Division
3.3: Real Zeros of Polynomials / 3.2: 23 – 63 EOO
3.3: 3 – 9 odd, 13 – 37 EOO
24 / 3.3: Real Zeros of Polynomials / 3.3: 41 – 57 EOO, 59 – 81 odd
Sept. 28 / 3.4: Complex Numbers
3.5: Complex Zeros / 3.4: 11 – 19 EOO, 21 – 65 EOO
3.5: 1 – 37 EOO, 39 – 55 EOO, 57, 61
29 / 3.6: Rational Functions / 3.6: 5 – 49 odd
30 / 3.6: Rational Functions / 3.6: 51 – 63 odd, 75, 83
Oct. 1 / Review
2.8: One-to-One Functions… / Chapter 3 Review: 23 – 29 odd, 39, 47, 49, 67, 69, 75
Oct. 5 / EXAM 2 (Ch. 2.5, 2.6, 3) / 2.8: 1 – 19 odd
6 / 2.8 One-to-One Functions… / 2.8: 21 – 69 odd, 71 *skip #59
7 / 4.1 Exponential Functions / 4.1: 5 – 17 odd, 19 – 24 all, 25 – 43 odd, 65,67
8 / 4.2: Logarithmic Functions / 4.2: 3-39odd,41-46 all, 47-63odd, 75,77,79
Oct. 12 / 4.3: Laws of Logarithms / 4.3: 1-59odd, 60, 61
13 / 4.4: Exp & Log Equations / 4.4: 1 – 53 odd, 54, 77, 81
14 / 4.5: Applications of exp & log / 4.5: 1, 5, 9, 11, 15, 21, 23, 27
15 / Review
5.1: The Unit Circle / Chapter 4 Rev: 1 – 61 EOO, 77, 79
Oct. 19 / Exam 3 – Ch. 2.8 & 4 / 5.1: 1 – 11 odd
20 / 5.1: The Unit Circle
6.1: Angles and Radian Measure / 5.1: 13 – 49 odd, 51, 53
6.1: 1 – 65 odd
21 / 5.2: Trig Functions of Real numbers / 5.2: 1 – 77 odd
22 / 6.3 Trig functions of angles / 6.3: 7-59 odd, 61a, 68a
Oct. 26 / 5.3: Graphs of Sine and Cosine / 5.3: 1 – 39 odd
27 / 5.3: Graphs of Sine and Cosine
5.4: Graphs of other trig fns. / 5.3: 41-48 all, 73ab, 75
5.4: 1 – 6 all, 7 – 31 odd
28 / 5.4: Graphs of other trig fns. / 5.4: 33 – 53 odd
Chapt. 5 Rev: 3-27 EOO, 33,35,39,45,47,49 63ab
29 / 7.1: Proving Trig Identites / 7.1: 1 – 23 odd, 25-77 EOO, 83, 89,91, 93
Nov. 2 / 7.2: Addition and Subtraction formulas / 7.2: 1 – 39 odd
3 / 7.2: Addition & Sub formulas
7.3: Double & half-angle formula / 7.2: 47, 48, 49
7.3: 1 – 39 odd
4 / 7.3: Double & half-angle formulas / 7.3: 59 - 69 odd, 90,. 91
5 / 7.4: Inverse Trig Functions / 7.4: 1 – 47 odd, 53
Nov. 9 / 7.4: Inverse Trig Functions / Supplementary Problems
10 / 7.5: Solving Trig Equations / 7.5: 1 – 47 odd
11 / 7.5: Solving Trig Equations / 7.5: 57 – 67 odd
12 / Review / Chapt. 7 Review: 7, 11, 21,33,35, 39, 41, 43, 53, 55, 65, 69, 71, 73
Nov. 16 / Exam 4 – Ch. 5, 6.1, 6.3 & 7
17 / 6.2: Trigonometry of Right Triangle / 6.2: 1 – 35 odd, 39,43,45, 49,53,55,57,59
18 / 6.4: The Law of Sines / 6.4: 1 – 11 odd, 15, 17,21,23,25,27,31,33
19 / 6.5: The Law of Cosines / 6.5: 1 – 25 odd, 29,32,35-43 odd
Chapt. 6 Rev: 19,20,57,59,61,63,64
Nov. 23 / 11.1: Sequences and Summation Notation
11.2:Arithmetic Sequences / 11.1: 1 – 15 odd, 23 – 45 odd, 53-67 odd
11.2: 1 – 49 EOO
24 / 11.3: Geometric Sequences / 11.3: 1 – 53 EOO, 65, 70
25 / Mathematical Induction / 11.5: 3 – 13 odd, 17, 19, 23, 25
26 / Thanksgiving
Nov. 30 / 11.5: Mathematical Induction
11.6: Binomial Theorem / 11.5: supplementary problems
11.6: 1 – 33 odd
Dec. 1 / 11.6: Binomial Theorem / 11.6: 35 – 49 odd
Chapt. 11 Review: 5,9,19,21,33,43,47,53,
57, 61, 62, 67, 69
2 / 10.1 Parabolas
10.4: Shifted Parabolas / 10.1: 7 – 45 odd, 49, 51
10.4: 5, 7, 13, 20
3 / 10.2 Ellipses
10.4 Shifted Ellipses / 10.2: 5- 41 EOO, 39, 51
10.4: 9, 11, 17, 21, 25
Dec. 7 / 10.3 Hyperbolas
10.4 Shifted Hyperbolas / 10.3: 5 – 37 EOO
10.4: 9, 11, 17, 21, 25
8 / 9.1 Systems of non-linear equations / 9.1: 3 – 31 EOO
9 / Review
10 / EXAM 5 –Ch. 6, 10, 11
Dec. 14 / Review
Dec. 15 / Final Exam 12 – 3 p.m.