City of Angels School Student



City of Angels School

Independent Study

Los Angeles Unified School District

Course Title: Math Analysis / Trigonometry A

Student’s Instructional Guide

Text: Larson, Hostetler, and Edwards, Precalculus with Limits, 5th ed., Brooks-Cole/Cengage Learning, 2008

Prerequisite: Grade of “C” or better in Algebra 2B

Student ________________________

Teacher ________________________

Beginning Date _______________

Ending Date ___________________

Final Mark _______ Credits _5_

Course Description

The purpose of this course is to develop a firm background in, and to extend the understanding of pre-calculus topics and concepts. This discipline combines many of the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus. The most significant new concept is that of limits. Math Analysis AB meets the UC/CSU admission requirement C.

Content

Material covered in this course is in line with California state content standards for mathematics.

Websites



The Khan Academy is a not-for-profit educational organization created by Salman Khan. With the stated mission "of providing a high quality education to anyone, anywhere", the Academy supplies a free online collection of just under 2,000 videos on mathematics, history, finance, physics, chemistry, astronomy, and economics. Recently featured on CNN, ABC, and the PBS Newshour. No password is required.



This site walks students through a step-by-step solution for every odd-numbered problem in their textbook. Login password: angels123

Homework

• Students should expect to work two hours a day, five days a week on assignments for this course.

• Label your homework with student name, chapter and section number.

• Please write down the problem, show all necessary work and check your answers using the answer key at the back of the book.

• Remember that all Quizzes, Chapter Tests, and Periodic Assessments will be taken at the site.

Grades

Final grades will be based on the following matrix:

|Homework |40% |

|Chapter Tests |30% |

|Final Exam |10% |

Weekly Assignments will be graded based on the following standard breakdown for work complete/correct:

|A |90-100% |

|B |80-89% |

|C |70-79% |

|D |60-69% |

|F |0-59% |

|Assignment for Week # 1 |Date Assigned |Date Due |

|Chapter 1: Functions and Their Graphs | | |

|(Sections 1.1 – 1.3) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|1.1 Lines in the Plane | |(1) |

| | | |

|Study Examples 1-7. | |Lines in the Plane |

|View any or all of the videos to the right. | |37:53 |

|Homework: pgs. 11-12, Exercises # 7, 9, 19, 21, 25, 29, 31, 45, 47, 57, 59, 61 | | |

| | | |

|1.2 Functions |Domain of Function |(1) |

| | | |

|Study Examples 1-9. |Domain and Range of Function |Functions 31:58 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 24-29, Exercises # 5, 7, 19, 21, 29, 31, 37, 41, 59-65 (odd), |Testing Function | |

|74-77 (all), 87, 89 | | |

| | | |

|1.3 Graphs of Functions |Maxima and Minima |(1) |

| | | |

|Study Examples 1-10. | |Graphs of Function 32:36 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 38-40, Exercises # 1-7 (odd), 15-21 (odd), 43, 47, 59-65 (odd) | | |

|Assignment for Week # 2 |Date Assigned |Date Due |

|Chapter 1: Functions and Their Graphs | | |

|(Sections 1.4 – 1.6) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|1.4 Shifting, Reflecting, and Stretching Graphs |Shifting Quadratic Graph |(1) |

| | | |

|Study Examples 1-6. | |Shifting, Reflecting, and |

|View any or all of the videos to the right. | |Stretching Graphs 29:52 |

|Homework: pg. 49, Exercises # 15-37 (odd) | | |

| | | |

|1.5 Combinations of Functions | |(1) |

| | | |

|Study Examples 1-11. | |Combinations of Functions 9:07 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 58-59, Exercises # 7, 11, 35, 37, 39, 41, 49, 51, 65, 69 | | |

| | | |

|1.6 Inverse Functions |Inverse Function 1 |(1) |

| | | |

|Study Examples 1-9. |Inverse Function 2 |Inverse Functions 27:02 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 69-70, Exercises # 1-7 (odd), 15-19 (odd), 25-33 (odd), 49, 55, | | |

|59-67 (odd) | | |

| | | |

|Study for Chapter 1 Test | | |

|Assignment for Week # 3 |Date Assigned |Date Due |

|Chapter 2: Polynomial and Rational Functions | | |

|(Sections 2.1 – 2.3) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|2.1 Quadratic Functions |Quadratic Funtion |(2) |

| | | |

|Study Examples 1-7. | |Quadratic Functions 31:09 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 99-101, Exercises # 1-4 (all), 5-19 (odd), 29, 31, 55 | | |

| | | |

|2.2 Polynomial Functions of Higher Degree |Coefficient and Exponents in |(2) |

| |Polynomial | |

|Study Examples 1-9. | |Polynomial Functions of Higher |

|View any or all of the videos to the right. | |degree 30:48 |

|Homework: pgs. 112-113, Exercises # 9, 15, 21-29 (odd), 33, 35, 53, 55, 71, 73 | | |

| | | |

|2.3 Real Zeros of Polynomial Functions |Polynomial Division with Monomial |(2) |

| | | |

|Study Examples 1-11. | |Real Zeros of Polynomial Functions |

|View any or all of the videos to the right. | |37:19 |

|Homework: pgs. 127-129, Exercises # 1, 3, 7, 9, 15, 20, 35, 37, 45-55 (odd), 65,| | |

|75 | | |

|Assignment for Week # 4 |Date Assigned |Date Due |

|Chapter 2: Polynomial and Rational Functions | | |

|(Sections 2.4 – 2.5) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|2.4 Complex Numbers |Intro to Imaginary Number |(2) |

| | | |

|Study Examples 1-6. |Multiplying Complex Number |Complex Numbers 22:58 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 137-138, Exercises # 9, 11, 17 19, 21, 29, 33, 35, 37, 43, 47, |Complex Number 2 | |

|49, 53, 57, 71, 73 | | |

| |Conjugates | |

| | | |

|2.5 The Fundamental Theorem of Algebra | |(2) |

| | | |

|Study Examples 1-6. | |The Fundamental Theorem of Algebra |

|View any or all of the videos to the right. | |19:15 |

|Homework: pgs. 144-145, Exercises # 1, 3, 25, 27, 37, 39, 43, 45, 47, 51, 53, 55| | |

|Assignment for Week # 5 |Date Assigned |Date Due |

|Chapter 2: Polynomial and Rational Functions | | |

|(Sections 2.6 – 2.7) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|2.6 Rational Functions and Asymptotes |Asymptotes of Rational Function |(2) |

| | | |

|Study Examples 1-7. | |Rational Functions and Asymptotes |

|View any or all of the videos to the right. | |10:42 |

|Homework: pgs. 152-153, Exercises # 1, 13-25 (odd), 31-37 (odd) | | |

| | | |

|2.7 Graphs of Rational Functions | |(2) |

| | | |

|Study Examples 1-6. | |Graphs of Rational Functions 23:45 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 161-163, Exercises # 9-25 (odd), 43, 45, 79 | | |

| | | |

|Study for Chapter 2 Test | | |

|Assignment for Week # 6s O |Date Assigned |Date Due |

|Chapter 3: Exponential and Logarithmic Functions | | |

|(Sections 3.1 – 3.3) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|3.1 Exponential Functions and Their Graphs |Graphing Expoential Function |(3) |

| | | |

|Study Examples 1-11. | |Exponential Functions and Their |

|View any or all of the videos to the right. | |Graphs 28:12 |

|Homework: pgs. 193-195, Exercises # 1-11 (odd), 17, 21, 23, 25, 41, 43, 53, 55, | | |

|67, 69 | | |

| | | |

|3.2 Logarithmic Functions and Their Graphs |Graphing Logarithmic Function |(3) |

| | | |

|Study Examples 1-10. |Graphing Natural Logarithmic Function |Logarithmic Functions and Their |

|View any or all of the videos to the right. | |Graphs 34:47 |

|Homework: pgs. 203-204, Exercises # 1-41 (every other odd), 43, 47, 51, 57, | | |

|61-73 (odd), 79 | | |

| | | |

|3.3 Properties of Logarithms | |(3) |

| | | |

|Study Examples 1-7. | |Properties of Logarithms 26:19 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 211-212, Exercises # 1-21 (every other odd), 31-75 (every other | | |

|odd), 81, 85, 89, 93 | | |

|Assignment for Week # 7 |Date Assigned |Date Due |

|Chapter 3: Exponential and Logarithmic Functions | | |

|(Sections 3.4 – 3.5) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|3.4 Solving Exponential and Logarithmic Equations |Solving Logarithmic Equations |(3) |

| | | |

|Study Examples 1-13. | |Solving Exponential and Logarithmic|

|View any or all of the videos to the right. | |Equations 33:27 |

|Homework: pgs. 221-223, Exercises # 17, 21, 27-43 (odd), 49, 55-61 (odd), 87, | | |

|89, 95, 103, 131, 137 | | |

| | | |

|3.5 Exponential and Logarithmic Models | |(3) |

| | | |

|Study Examples 1-7. | |Exponential and Logarithmic Models |

|View any or all of the videos to the right. | |48:26 |

|Homework: pgs. 232-233, Exercises # 7, 11, 19, 28, 29, 31, 32, 37, 39, 41 | | |

| | | |

|Study for Chapter 3 Test | | |

|Assignment for Week # 8s O |Date Assigned |Date Due |

|Chapter 8: Sequences, Series, and Probability | | |

|(Sections 8.1 – 8.3) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|8.1 Sequences and Series |Patterns In Sequences |(8) |

| | | |

|Study Examples 1-9. | |Exponential Functions and Their |

|View any or all of the videos to the right. | |Graphs 28:12 |

|Homework: pgs. 587-589, Exercises # 1, 11, 43-59 (odd), 65, 75, 79, 83, 89, 109,| | |

|113 | | |

| | | |

|8.2 Arithmetic Sequences and Partial Sums |Finding 100th Place in a Sequences |(8) |

| | | |

|Study Examples 1-8. | |Logarithmic Functions and Their |

|View any or all of the videos to the right. | |Graphs 34:47 |

|Homework: pgs. 598-599, Exercises # 1-25 (every other odd), 31, 39, 41, 53, 55, | | |

|61, 63, 65, 81, 83 | | |

| | | |

|8.3 Geometric Sequences and Partial Sums |Introduction To Geometric Sequence |(8) |

| | | |

|Study Examples 1-9. | |Geometric Sequence and Series |

|View any or all of the videos to the right. | |29:40 |

|Homework: pgs. 607-608, Exercises # 1-33 (every other odd), 31, 45, 47, 49, | | |

|63-71 (odd), 85 | | |

|Assignment for Week # 9 |Date Assigned |Date Due |

|Chapter 8: Sequences, Series, and Probability | | |

|(Sections 8.4 – 8.5) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|8.4 Mathematical Induction |Proof by Induction |(8) |

| | | |

|Study Examples 1-5. | |Mathematical Induction 24:25 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 617-618, Exercises # 5, 7, 9, 13, 17, 25, 51, 53 | | |

| | | |

|8.5 The Binomial Theorem |Binomial Theorem 1 |(8) |

| | | |

|Study Examples 1-7. |Binomial Theorem 2 |The Binomial Theorem 27:48 |

|View any or all of the videos to the right. | | |

|Homework: pg. 624-625, Exercises # 1-41 (every other odd), 49-69 (every other | | |

|odd), 77-93 (every other odd) | | |

|Assignment for Week # 10 |Date Assigned |Date Due |

|Chapter 8: Sequences, Series, and Probability | | |

|(Sections 8.6 – 8.7) | | |

| |Khan Academy |Larson’s DVD |

| | | |

|8.6 Counting Principles |Permutation and Combination |(8) |

| | | |

|Study Examples 1-10. |Permutation and Combination 2 |Counting Principles 23:49 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 634-636, Exercises # 1-8 (all), 9-39 (odd), 45-69 (odd) | | |

| | | |

|8.7 Probability |Probability Using Combination |(8) |

| | | |

|Study Examples 1-11. |Probability and Combination |Probability 29:13 |

|View any or all of the videos to the right. | | |

|Homework: pgs. 645-648, Exercises # 1, 7-31 (odd), 49, 51, 52, 53, 55 | | |

| | | |

|Study for Chapter 8 Test | | |

|Assignment for Week # 11 |Date Assigned |Date Due |

|Study for Final Exam | | |

| | | |

| | | |

|Complete the Final Exam for Math Analysis A. | | |

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