El Camino College

Mathematics

Pre-Calculus
Alice Martinez

Math 180

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penguins

Math 180 Information:             Syllabus           Tentative Schedule


 Spring '18 Section 0830  Room: MBA 309  Time:  MTWTh 11:30am-12:40pm

 

Announcements/Info:         TI instructions   

 Quiz:  Ch 7.1, 5.6, 5.5:  Be able to solve problems with inverse trig functions, including understanding the domain and range of the inverse functions.  Trig identities to simplify expressions.  Representing harmonic motion with sine and cosine curves with specified amplitude and period. 

Quiz: Ch 8.1 & 8.4:  Conversion between rectangular and polar form for coordinates and equations; Parametric equations.

Final Exam Info:  (Calculators allowed.  Two, one-sided, page of notes allowed for each part.  You may re-use the same pages or use different ones for day 2. If you need a unit circle be sure it is included on ONE of these one-sided pages of notes.)

Part I: [Ch 2, 3, 4, 10]

Functions (includes evaluating, graphing, etc.): Piecewise defined, logs, exponential, inverses, Domain/Range, polynomial, rational 

Systems of Equations (3x3 or larger)

Part II:  [Ch 2, 10, 12, 5, 6, 7, 8]

Rate of change, increasing/decreasing intervals, Inductive Proof, partial fractions,

Trig, trig equations, parametric equations, complex numbers, polar form, Linear and angular velocity, harmonic motion, trig proof

 

Grades are based on a points: (See syllabus for more details)

Homework = 40 points each      Quizzes = 20 points each
Exams = 300 points each          Final Exam = 500 points 
Must earn 65% on final exam along with sufficient points in the course in order to pass.
Grades will be rounded up if Final exam is the higher of the two grades AND 80% of HW and CA have been completed.    
 
Tentative Schedule:

May      M    21         7.17.3           Trig Identities        

            T     22         7.4 / 7.5            Trig Equations

            W    23         8.1                    Polar Form                                 Quiz:  Ch 7.1, 5.6, 5.5

            Th    24         8.4                    Parametric Equations                                                   

             M    28         HOLIDAY

            T    29         8.3                    Complex numbers in polar form                        

            W   30         11.1/11.2           Parabolas & Ellipses                             Quiz: Ch 8.1 & 8.4  

           Th    31         11.2/11.3           Ellipses & Hyperbolas                          

June     M     4          Review

             T      5          Final Exam Part 1   Ch 2, 3, 4, 10, 11

             W     6          Review             HW Packet 5 Due

             Th         7          Final Exam Part 2  Ch 2, 10, 12, 5, 6, 7, 8           

  

    

 

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Assignments:

Instructions for video portions of the assignments:  Take notes while watching the videos.  Be sure to write the TITLE of each video above EACH of your video notes and write the definition/description of the main concepts. Turn this in with your HW.  

Instructions for Vocabulary: Make a list of pertinent vocabulary for EVERY section of HW that you turn in, even though it will not list this on the daily HW assignment. Do this for each NEW section covered in the HW.  Be sure to label what section EACH vocabulary is from.  (You do not need to redo vocabulary for sections already covered on previous HW.) 

General HW instructions Be sure to read the general HW instructions to avoid losing points.

HW Packet 1 ; HW Packet #2; HW Packet 3Packet 4:

 

Packet 5

 

5/17

Video:  harmonic motion example;  

5.3   37, 49, 51

5.5   3, 7, 33, 37 (inverse trig functions)

5.6    5, 13,  41ac only  (harmonic motion)

Ch 6 Test (pg 532):  13, 14

Ch 2 Review (pg 231-234)  54

3.1  #53

 

5/21 

Videos: (These are worth the time to go over.  It is ok to fast forward if you can go faster than her, but be sure to listed to her explanations of the incorrect proofs.)

7.1  11, 15, 17, 19

7.2  3, 15, 25, 29

5.3  35

5.6   19, 29, 33, 43 

pg 320 #20, 81

 

5/22 

7.3  3, 5, 29a

7.4  5, 11, 27

5.5  35, 36, 39, 41

5.6  15

7.1  9, 37, 49

 

5/23 (pending)

8.1  5, 11, 17, 19, 25, 27. 51, 53

7.4   19, 39, 41

3.6  74

2.1  33 

Ch 2 Review (pg 232): 13

 

5/24  (pending)

8.1  29, 41, 55, 59, 

8.4   3, 5, 13

Videos:    Intro to the history of complex numbers and the fundamental theorem of Algebra(part 1); Complex numbers (part 5)complex plane - (part 6);  polar form (part 7);  These videos provide a quick review of complex numbers along with their interesting history.  (I skipped parts 2, 3 & 4 for times sake but you can watch those also if you want.)  What is really useful about these videos is that he shows how the complex numbers  come from the fundamental theorem of Algebra and how they work naturally in polar form, which is what we will be working with this week.  Take the time to watch these four videos.  

1.6    21, 29  (complex number practice.... if you need more review, try a few more of the problems.)

7.2  7

7.4   33, 47

Ch 2 Review (pg 232-4): 53, 96. 97 

Ch 3 Review:  81, 85

 

5/29 (pending)

7.2  17, 27

5.6  17

8.1  31

8.4  9, 16

 

5/30 (pending)

8.4  37

5.6  1, 3

 

OTHER VIDEOS for further study:

Ch 2

2.6 Great quick video about reflections, compressions and stretches of graphs

Ch 3

Longhand division of polynomials  video 1, video 2, video 3

Videos:  Synthetic division of polynomials

Graphing polynomial functions

Finding Zeros and their multiplicity

How to think through finding zeros of polynomials

End behavior of polynomial graphs

Domain and Range from a Graph

Rational Zero Theorem

Finding all zeros of polynomial

Descartes' Rule of signs

Secondary Descartes' rules of signs video

Upper and lower bounds for zeros of polynomials

Ch 4

 Finding equation of exponential using the graph

Graphing basic logarithmic Equations 

 4.3 Graphing Logs with asymptotes, transformations (5:53)

Basic Concept of logarithms

Fundamental properties of logs

Sum and Product rules of logs

Change of base formula

Understanding log in "real world:

4.7  Richter Scale; 4.7 Ph-Scale

Ch 5

Simple harmonic motion explained on unit circle;  

harmonic motion example;  harmonic motion example;  

Ch 6

 law of cosines finding a side,  finding an angle

Ch 7

Ch 8

Videos:    Intro to the history of complex numbers and the fundamental theorem of Algebra(part 1); Complex numbers (part 5)complex plane - (part 6);  polar form (part 7)These videos provide a quick review of complex numbers along with their interesting history.  (I skipped parts 2, 3 & 4 for times sake but you can watch those also if you want.)  What is really useful about these videos is that he shows how the complex numbers  come from the fundamental theorem of Algebra and how they work naturally in polar form.

Intro to Complex numbers and their uses(part 1)

Ch 10

Evaluating 2x2 determinant

Intro to Gaussian Elimination

10.7 - Partial Fractions

partial fractions in 5 min

partial fractions as used for calculus (in class)

Quadratic factors

repeated linear factors

identifying types of partial fractions

cover-up rule for quick partial fractions

 

Other possible videos:

Video:  complex numbers in the trig form (24 minutes)

rectangular to trig form,.

trig to rectangular form

 

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Course Material:

*Precalculus-Mathematics for Calculus, 7th Edition, Stewart/Redlin/Watson, 2016, Brooks/Cole (Cengage) 

*TI-84 Plus (TI 86 and TI 89 not allowed. There will be no sharing of calculators during exams, nor substitution via other types of calculators, your calculator must ONLY be a calculator and have no internet access options. You must have this calculator to perform operations in class and to practice the work at home to become proficient. See me if you need help getting a calculator).

*Three-ring binder to keep track of  Class Activity Work and handouts.

Optional materials:  TI-84 user help: http://mathbits.com/mathbits/TISection/Openpage.htm.

 Calculator Help:

Class Lecture 2017: 

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Online Resources:

 Videos:

 2x2 augmented Matricies

Evaluating piecewise defined functions

How to graph piecewise defined functions on TI 84

Finding inverse of function (lesson with one-to-one intro, 12:52)

Finding inverse function (Khan, 7:01)

Finding inverse (quick version, 2:32)

Documentaries: 

 

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El Camino College, 16007 Crenshaw Blvd., Torrance, California 90506
Phone: 310-532-3760 Toll Free: 1-866-ELCAMINO (1-866-352-2646)

 

 

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