# Trigonometry and Precalculus

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Credits: 1

Prerequisite: Geometry, Algebra 2

Recommended: 11th, 12th

Test Prep: CLEP exam

Course Description: This course offers a quarter (45 lessons) of trigonometry followed by a semester of precalculus. In trigonometry, students will not only learn the basic trigonometric functions and how to apply them to solve real-life problems, but will explore a number of topics from trigonometry including: triangle properties, radian, identities, solving complex equations, inverse functions, vectors, and the polar coordinate system. Students will study and write proofs and learn about the Law of Sines and Cosines and their applications. Functions are the focus of the pre-calculus including: linear, polynomial, rational, logarithmic, and exponential functions. Students will graph functions, combine functions, interpret roots and find the maxima and minima of functions. Students will apply their knowledge to model and to solve real-world applications.

Students will be using Khan Academy and Yay Math! (trigonometry) and OpenTextbook (pre-calculus).

Materials:

You will need a calculator. You can use one online. On Lesson 7 you will receive some instruction on how to use a calculator to solve trigonometric functions. You can learn about other calculator options (handheld, mobile, etc.) on this page under “Tips/Suggestions”.

Print out some graph paper to have on hand. Regular Polar (for unit 6)

Scoring:

You may give yourself half credit on a question done correctly with one small “typo” type error.

Testing:

There are quizzes and assignments, but the finals will have their questions all come from previous work in the course.

Portfolio:

Work in a single spiral notebook, or keep all loose-leaf paper in a single binder for the course. Hold onto your written notes and exercises. Use them to study and as a record of what you’ve done.

Lesson 1(*)

1. If you didn’t get here through My EP. Please make an account to track your progress in the course. It’s free to create an account.
2. The first quarter of this course is on trigonometry, though it will come back in the second part of the course, which is pre-calculus.
3. Go through these readings and videos on triangles. It will move you through the lesson. Keep clicking on the button to continue to the next piece. The last thing is the exercise. It will say “Up Next: Lesson 2” when you are done. Stop clicking. I think it only gives you that “next” button if you are logged in. You can use the menu to navigate or log in.
• When you do the reading, make sure you do the practice questions.
• When you watch a video, grab your notebook and do the problems along with him.
• There will be quizzes and tests.
4. (*)Print out your first quarter grading sheet, or use the excel version.

Lesson 2

1. Learn the introduction to the trigonometric ratios.
2. Do the four activities. Continue through the whole thing.

Lesson 3

1. Take the quiz. You’ll always need to pay attention to your score.
2. Record your score out of 5.
3. Learn about solving for a side in a right triangle using the trigonometric ratios: Right triangles & trigonometry.
4. Complete the lesson through the practice exercise. I don’t know what it looks like on a mobile device, but on a computer, there is a menu on the left that shows you all the parts to a lesson. Sometimes we’ll split up a long lesson, but mostly, we’ll complete a whole lesson.

Lesson 4

1. Learn about solving for an angle in a right triangle using the trigonometric ratios.
2. Complete the lesson.
3. Choose a way to mark questions you got wrong or lesson you had trouble with. On a review day, go back and try again. You can make a list in the back of your notebook, keep a list on your computer, highlight problems with red in your notebook.

Lesson 5

1. Learn about sine and cosine of complementary angles.
2. Complete the lesson.

Lesson 6

1. Learn about modeling with right triangles.
2. Complete the lesson.
3. Take the quiz.
4. Record your score out of 5.

Lesson 7

1. Learn about the reciprocal trigonometric ratios.
2. Complete the lesson.

Lesson 8

1. You can take some time to review. Your test should take around 20 minutes.
2. Take the unit test.
3. Record your score out of 9.

Lesson 9(*)

1. We’re going to switch it up for a few days.
2. (*)Print the worksheet and follow along with the lesson (or do a good job writing down what he’s doing.
3. Watch the video.

Lesson 10(*)

1. (*)Print the worksheet and follow along with the lesson (or do a good job writing down what he’s doing.
2. Watch the video.
3. Take the quiz. You are NOT emailing to anyone. Record your score out of 10.
4. Take another quiz.
5. Record your score out of 12.

Lesson 11 (Materials: scientific calculator)

1. He’s going to talk about using a calculator.
2. Get out a notebook and calculator and work along with him.
3. Watch the video.

Lesson 12

2. Complete the lesson.

Lesson 13

2. Complete the lesson.

Lesson 14

1. Learn about the Pythagorean theorem.
2. Complete the lesson.

Lesson 15

2. Complete the lesson.
3. Make sure you are keeping track of lessons you need to practice and/or individual questions you got wrong that you should retry.

Lesson 16

1. Learn about trigonometric values on the unit circle.
2. Complete the lesson.
3. Take the quiz.
4. Record your score out of 7.

Lesson 17

1. Learn about the graphs of sin(x), cos(x), and tan(x).
2. Complete the lesson.
3. There is no exercise. Take notes. Draw graphs.

Lesson 18

1. Learn about amplitude, midline, and period.
2. Complete the lesson.

Lesson 19

1. Learn about graphing sinusoidal functions.
2. Learn about transforming sinusoidal graphs.

Lesson 20

1. Go through the example of transforming sinusoidal graphs.
2. Try the questions.

Lesson 21

2. Complete the lesson.
3. Make sure you are keeping track of what lessons gave you trouble or individual problems you got wrong and could try again on a practice day.

Lesson 22

1. Take the quiz.
2. Record your score out of 6.
3. Take the quiz.
4. Record your score out of 4. (room for extra credit)
5. Take the unit test.
6. Record your score out of 10. (room for extra credit)

Lesson 23

1. Learn about the law of sines.
2. Complete the lesson.

Lesson 24

1. Learn about the law of cosines.
2. Complete the lesson.

Lesson 25

1. Learn about solving general triangles.
2. Complete the lesson.
3. Take the unit test. (10-20 minutes)
4. Record your score out of 9.

Lesson 26

1. Learn about inverse trigonometric functions.
2. Complete the lesson. This is a longer one. Keep moving.

Lesson 27

2. Complete the lesson.

Lesson 28

2. Complete the lesson.
3. Take the quiz.
4. Record your score out of 5.

Lesson 29

2. Complete the lesson.

Lesson 30

1. Learn about using trigonometric identities.
2. Complete the lesson.
3. Take the quiz.
4. Record your score out of 5.

Lesson 31

1. Try the challenging trigonometric questions!
2. How many can you get?

Lesson 32

1. Review. This unit starts with inverse trigonometric functions.
2. Take the unit test. (20 minutes)
3. Record your score out of 9.

Lesson 33

1. Take the challenge. (30-45 minutes)
2. Record your score out of 30.

Lesson 34(**)

1. Let’s break it up with some Yay Math!
2. This is review. You should be pretty good at this. By the time we go through it again now, you’ll really have this.
3. (*)Print the worksheet or get out your notebook and copy down what he’s doing.
4. Watch the video on the trig functions.
5. Take the quiz.
6. Record your score out of 17.
7. (*)Print the worksheet or write down the problems as he does them.
8. Watch the video on trigonometric functions with right triangles.
9. Take the quiz.
10. Record your score out of 4 points.

Lesson 35(*)

1. (*)Print the worksheet or write down the problems as he does them.
2. Watch the lesson on trig function with general angles.
3. Take the quiz.
4. Record your score out of  29 points.

Lesson 36(**)

1. (*)Print the worksheet and work along with the video or write down the problems as he does them and work along.
2. Watch the lesson on the law of sines. You can stop when he finishes the problem around 20:20.
3. Take the quiz.
4. Record your score out of 9.
5. (*)Print the worksheet or write the problems down as he does them.
6. Watch the video on the law of cosines.
7. Take the quiz.
8. Record your score out of 7.

Lesson 37(**)

1. (*)Print the worksheet and work along with the video or write down the problems as he does them.
2. Watch the lesson on circular functions and the unit circle.
3. Take the quiz.
4. Record your score out of 23.
5. (*)Print out the worksheet or use your notebook.
6. Watch the lesson on graphing sine and cosine.

Lesson 38(**)

1. (*)Print the worksheet and work along with the video or write down the problems as he does them.
2. Watch the lesson on graphing CSC and SEC.
3. Take the quiz.
4. Record your score out of 21.
5. (*)Print out the worksheet or use your notebook.
6. Watch the lesson on graphing TAN and COT.

Lesson 39(**)

1. (*)Print the worksheet and work along with the video or write down the problems as he does them.
2. Watch the lesson on the inverse trig function.
3. Take the quiz.
4. Record your score out of 10.
5. (*)Print out the worksheet or use your notebook.
6. Watch the rest of the lesson.

Lesson 40(*)

1. Take these quizzes we skipped over and record your scores. There is potential for extra credit.
2. (*)Print the worksheet and work along with the video or write down the problems as he does them.
3. Watch the lesson on trig identities.

Lesson 41(*)

1. (*)Print the worksheet and work along with the video or write down the problems as he does them.
2. Watch the lesson on trig identities.
3. Take the quiz.
4. Record your score out of 12.
5. Take the quiz.
6. Record your score out of 8.

Lesson 42(*)

1. (*)Print out the worksheet or use your notebook.
2. Watch the lesson on verifying trig identities.
3. Take the quiz.
4. Record your score out of 10.

Lesson 43(*)

1. (*)Print out the worksheet or use your notebook.
2. Watch the lesson on the sum and differences of angles.
3. Take the quiz.
4. Record your score out of 8.

Lesson 44(**)

1. (*)Print out the worksheet or use your notebook.
2. Watch the lesson on the double angle formula.
3. Take the quiz.
4. Record your score out of 5.
5. (*)Print out the worksheet or use your notebook.
6. Watch the lesson on half-angle formula.
7. Take the quiz.
8. Record your score out of 8.

Lesson 45(*)

1. (*)Print out the worksheet or use your notebook.
2. Watch the lesson on solving trigonometric equations.
3. Take the quiz.
4. Record your score out of 8.
5. If you want to improve your score on the course challenge from lesson 33, you can take it again and change your score if you improved. 🙂

STOP

Compute your grade for the first quarter. Hold onto your written work for studying and as a record of what you did for this course.

Lesson 46(*)

1. (*)Print out your second quarter grading sheet or use the Excel version.
2. Today we begin a new course, Pre-Calculus. I’m going to be linking to each chapter of the online textbook individually for using online, but if you’d like to download the whole text now for offline use, you can use the link found here. It also has a link to the answers for the whole book and links to buy the book.
4. We will also be doing some SAT practice and review. Make sure you are still keeping track of what you need to practice.
5. Read this introduction from Saylor.org. “This subunit launches the course by introducing an important basic concept of mathematics – the function. Functions are dependable – if you know the output for a particular input, you will always get that same output for that particular input. It’s an easy idea but it can be difficult to explain.
Suppose you have a company building a particular toy car that has three wheels. You could write a function for wheels based on how many cars you produced. If you make one car, you need three wheels. If you make two cars, you need six wheels. If you make 300 cars, you need 900 wheels. The output depends upon the input and any one input will ALWAYS yield the same output.”
6. Read pages one and two. As you go, answer the “Try It Now” questions. (Answers are on page 12.)

Lesson 47

1. Watch the video on function notation.
2. Evaluate the functions.
3. Read pages two through four in the online textbook. Do the “Try It Now” question 3 at the top of page 5. (Answers are on page 12.)

Lesson 48

1. Read page five in the textbook. Do the TIN question 4. Answers are on page 12.
2. Watch the video on evaluating a function. Here’s an example to watch as well.

Lesson 49

1. Practice evaluating expressions with function notation.
2. Watch this short video on the vertical line test.
3. Read through pages 5-7 in the online textbook. As before, always work through examples on paper.
4. Do the TIN question 5 on page 7. Answers are on page 12.

Lesson 50

1. Let’s mix it up.
2. We’ll call these review days.
3. Options:
• Go back and redo any questions you got wrong this week. Try them from scratch. You can also try a question from each lesson that wasn’t assigned. Make sure you can still do them without having the examples right in front of you and fresh in your mind.
• Practice for the SATs. You can do this a little at a time. After you have done your practice review and fixing mistakes work, you can do one or two of these.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final, not to mention calculus maybe in your future. Make sure you know the material. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 51

1. Read this introductory material from Saylor.org. “Think of it: If you know the diameter of a circle, you can find the circumference. It is a function because one particular diameter will ALWAYS yield one particular circumference – it won’t change. This subunit looks at relations and how to rewrite them to clarify the functional relation. For example: if x + y = 5, you can rearrange the algebra to write y = 5 – x. This would identify a function we might call g, and the algebraic description would be g(x) = 5 – x. “
2. Read through pages 7-10 in the online textbook. As before, always work through examples on paper. Complete the TIN question on page 10. Check your answer on page 12.

Lesson 52

1. Read through pages 10-12 in the online textbook. As before, always work through examples on paper. Pay attention to the shapes of the functions.
2. Make a chart of these toolkit functions and keep it in a handy place to refer to during the course.

Lesson 53

1. Complete the odd problems in pages 13 – 16 in the online textbook.

Lesson 54

1. Complete the odd problems on pages 17 – 19 in the online textbook.
2. Check your answers, 1.1. Understand your mistakes. Your final exam will be made up of questions from the exercises you will be completing during the course.
3. Record your score out of 24.

Lesson 55

1. Watch the video on set builder notation.
2. Read through pages 21-24 in the online textbook.
3. Do the TIN questions as you come to them.

Lesson 56

1. Watch the video on finding domain and range of a function using a graph.
2. Read through pages 24-27 in the online textbook. As always, complete the TIN question when you come to it.

Lesson 57

1. Watch the video on piecewise functions.
2. Read through pages 28-30 in the online textbook. As always, complete the TIN question when you come to it.

Lesson 58

1. Complete the odd problems numbers 1-35 on pages 31 through 33 in the online textbook.
2. Check your answers, 1.2. Score up to 2 points each.
3. Record your score out of 30. (potential for extra credit)

Lesson 59

1. Watch the video on rate of change. (YouTube)
2. Read through pages 34-37 in the online textbook. As always, complete the TIN questions when you come to them.

Lesson 60

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Recommended if you are planning on taking the SAT: Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 61

1. Read through pages 38-43 in the online textbook. As always, complete the TIN questions when you come to them.

Lesson 62

1. Complete the odd problems from pages 46 to 48 in the online textbook.
2. Check your answers, 1.3. (up to 2 points each)
3. Record your score out of 40. (potential for extra credit)

Lesson 63

1. Watch this short video on the composition of functions.
2. Read pages 49-51 of the chapter on the composition of functions. As always, answer any TIN questions as you come to them.

Lesson 64

1. Watch the video on the composition of functions.
2. Read from page 51 to 55 of the chapter on the composition of functions. As always, answer any TIN questions as you come to them.

Lesson 65

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Recommended if you are planning on taking the SAT: Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 66

1. Do the odd-numbered exercises for chapter 1.4, numbers 1-43.
2. Check your answers, 1.4. (Score up to 2 points for each problem.)
3. Record your score out of 40. (potential for extra credit)

Lesson 67

1. Read the section on shifts in the online textbook, pages 61-67. Stop at “Reflections.”
2. Remember to work through examples and do the TIN questions.

Lesson 68

1. Read the section in your online textbook on reflections, pages 67-70.
2. Check the answers to the TIN question on page 81.
3. Watch the video on odd/even functions.

Lesson 69

1. Work through the page on graphs and functions transformations.
2. Read pages 71-76 through the TIN question on 76.

Lesson 70

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Recommended if you are planning on taking the SAT: Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 71

1. Watch this lesson on transformations in combination.
2. Work through pages 76-80.

Lesson 72

1. Do every fourth problem – 1, 5, 9, 13, 17,… from problems 1-99 starting on page 82.
2. Do problem 99 for up to 6 points of extra credit!
3. Check your answers, 1.5. (up to 2 points each)
4. Record your score out of 48.

Lesson 73

1. Watch the video on function inverses.
2. Work through pages 90-95.

Lesson 74

1. Starting on page 96, complete the odd problems.
2. Check your answers, 1.6. (up to 2 points each)
3. Record your score out of 24.

Lesson 75

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Recommended if you are planning on taking the SAT: Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 76

1. Here is chapter two of our online textbook. Today read pages 99-101. As always, work through the examples on paper and complete any “Try It Now” (or now, “Flashback”) questions. Today, complete the TIN question at the top of 102.

Lesson 77

1. Today read pages 102-106 in your online textbook. As always work through the examples on paper and complete any “Try It Now” (or now, “Flashback”) questions.
3. Watch the video on average rate of change. (youtube)

Lesson 78

1. Today complete the odd-numbered questions, #1-49, beginning on page 107 in your online textbook.
2. Check your answers, 2.1. Score up to 2 points per problem.
3. Record your score out of 50.

Lesson 79

1. Today work through pages 111-117 in your online textbook. You can stop at Parallel and Perpendicular Lines.

Lesson 80

1. NOTE: If you are honestly doing well and don’t have missed problems you need to redo and you are doing all your work thoroughly each day and are being successful at the SAT practice, then you can move on to the next day whenever you know you don’t need the practice or review. Even if you do this sometimes, you should still sometimes take the day to go back and do older problems and make sure you can still do them. Try some SAT problems again and see if you are doing okay still.
• On My EP, click on Did More? on the Settings page near the top, and you’ll be able to have the next lesson pop up for you once you mark this one complete.
2. Catch up – Review day
3. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Recommended if you are planning on taking the SAT: Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 81

1. Today work through pages 117-121 in your online textbook.
3. There were six sets of exercises in chapter 1. Do two odd problems from the first set of exercises. You may use the online textbook to review how to do problems if you need to, but you may not use the solutions! (We’ll record the score for this on Lesson 93.)

Lesson 82

1. Today complete the odd-numbered questions, #1-51, beginning on page 122 in your online textbook.
2. Check your answers, 2.2. Score up to 2 points per problem.
3. Record your score out of 50. (potential for extra credit)

Lesson 83

1. Today work through pages 126-133 in your online textbook.
2. There were six sets of exercises in chapter 1. Do two odd problems from the second set of exercises. You may use the online textbook to review how to do problems if you need to, but you may not use the solutions! (Hold onto your cumulative scores.)

Lesson 84

1. Today complete the odd-numbered questions, #1-21, beginning on page 134 in your online textbook.
2. Check your answers, 2.3. Score up to 2 points per problem.
3. Record your score out of 20. (potential for extra credit)

Lesson 85

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 86

1. Go through this introduction on trend lines and answer the questions. Scroll down for answers.
2. Work through pages 138-139. Remember to answer Flashback questions as you would TIN questions.
3. Answers are on page 143.
4. Complete this matching activity.
5. There were six sets of exercises in chapter 1. Do two odd problems from the third set of exercises. You may use the online textbook to review how to do problems if you need to, but you may not use the solutions! (Hold onto your score from these problems, along with those from the first two sets.)

Lesson 87

1. Play with correlation. After you guess, the top number is the actual correlation coefficient. What observations can you make about the correlation coefficient?
2. Work through pages 139-143.
3. Answers are on page 143.
4. There were six sets of exercises in chapter 1. Do two odd problems from the fourth set of exercises. You may use the online textbook to review how to do problems if you need to, but you may not use the solutions! (Hold onto your score.)

Lesson 88

1. Today complete the odd questions, #1-13, beginning on page 144 in your online textbook.
2. Check your answers, 2.4. Score up to 4 points per problem.
3. Record your score out of 28.

Lesson 89

1. Work through pages 146-149.
2. Answers are on page 152.
3. There were six sets of exercises in chapter 1. Do two odd problems from the fifth set of exercises. You may use the online textbook to review how to do problems if you need to, but you may not use the solutions! Hold onto your score.

Lesson 90

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

STOP

Compute your grade for the second quarter. You have one last quarter to raise your grade or to keep it up. Finish strong. Hold onto your written work for studying and as a record of what you did for this course.

Lesson 91(*)

1. (*) Print out your third quarter grading sheet or use the Excel version.
2. Watch the video on the connection between distance and absolute value.
3. Work through pages 149-152.
4. Answers are on page 152.
5. There were six sets of exercises in chapter 1. Do two odd problems from the sixth set of exercises. You may use the online textbook to review how to do problems if you need to, but you may not use the solutions! (Add up all your scores from the twelve problems and hold onto it.)

Lesson 92

1. Today complete the odd questions, #1-25, beginning on page 153 in your online textbook.
2. Check your answers, 2.5. Score up to 2 points per problem. (ANSWER CORRECTION: #3 should be: f(x)= -3|x-3|+3)
3. Record your score out of 25. (potential for one point extra credit)

Lesson 93

1. I had to change the order of some exercises, which is why this score got spread out to exercises over the last couple of weeks. Good news! Each correct answer is worth up to 4 points. You can record it now. I hope that served as a good review of the first chapter.
2. Record your score out of 48.
3. Do two SAT questions.
4. Read the introduction from Saylor.org.  Unit 2 planted seeds of ideas that are extended in Unit 3 to more complex functions. A linear function is a simple, special case of a polynomial function. In a polynomial function, the unknowns will have whole number exponents. We began with linear functions because they offered a simple model with which to explore the basic concepts of function and representations of functions. Linear functions, however, can often be solved with simple arithmetic. Unit 3 extends the function ideas to the more complex functions called polynomial and rational that are more easily solved with an algebraic approach.A rational function involves an algebraic fraction made with a polynomial numerator and a polynomial denominator. Their graphs are more complex than polynomial functions, and the solution process is more intricate than the functions in the previous chapter.Here you will explore concepts of functions and models as the course presents symbolic and graphical ways to investigate a number of situations. The unit begins with power and polynomial functions with special attention to quadratic functions. The middle of the unit presents graphs of polynomial functions. After that you will address rational functions and their graphs. The unit closes with the inverses of polynomial functions, which are called radical functions.This is a power-packed unit with complex concepts, so take a deep breath and be ready to think powerfully and work hard. Let’s get going!
5. Work through pages 155 to 157 in chapter 3. Stop at Polynomials. As usual, answer the “Try It Now” questions when you come to them.

Lesson 94

1. Work through pages 157 to 161 in chapter 3. As usual, answer the “Try It Now” questions when you come to them.
2. Watch the video on the “End Behavior or Long Run Behavior of Functions.”

Lesson 95

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 96

1. Do the odd questions on page 162, #1-33.
2. Check your answers, 3.1. Score up to 2 points per problem.
3. Record your score out of 30. (potential for extra credit)

Lesson 97

1. Watch the video on graphing quadratic functions.
2. Work through pages 163 through to the end of 165. As usual, answer the “Try It Now” questions when you come to them.

Lesson 98

1. Work through pages 166 to 168. As usual, answer the “Try It Now” questions when you come to them. Stop at “Short Run Behavior.”
3. Watch this video on the “Vertex and Root of Parabola.”

Lesson 99

2. Work through pages 168 to 171. As usual, answer the “Try It Now” questions when you come to them.

Lesson 100

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 101

1. Do the odd questions #1-39 starting on page 172. (Skip #9)
2. Check your answers, 3.2. Score up to 2 points for each question. Give yourself the 2 points for #9!
3. Record your score out of 40.

Lesson 102

1. Find the roots of the polynomial functions. Here is a second example.
2. Work through pages 176 and 177, stopping after the TIN question.
3. Answers are on page 184.
4. If you found today’s lesson short, take your extra time to review your trig!

Lesson 103

1. Read this introduction to the next section from Saylor.org.
• A polynomial function has only one vertical intercept, because otherwise it would not be a function. It can, however, have multiple horizontal intercepts. At a horizontal intercept, the function may change sign or loop back into the same vertical half of the coordinate grid. Mathematicians, scientists, businesspeople, and others develop functions to model real-world behavior, such as the trajectory of a meteor, the growth of income in a company, the intensity of earthquakes, and climate change. A function model makes it possible to study phenomena and to better predict future outcomes.
2. Watch this video on “Graphs of Polynomial – End Behavior, Zeros, Multiplicity.”
3. Work through pages 177 to 179. Stop at Solving Polynomial Equations.
4. Answers are on page 184.

Lesson 104

1. Watch the video on Solving a Polynomial Inequality.
2. Work through pages 179 to the end of the section on 181.
3. Answers are on page 184.

Lesson 105

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 106

1. Work through pages 181 to 184.
2. Answers are on page 184.

Lesson 107

1. Do the odd problems from pages 185-187, #1-49.
2. Do number 51 for extra credit.
3. Check your answers, 3.3. Score up to 2 points for each problem.
4. Record your score out of 50.

Lesson 108

1. Read this intro to the next section from Saylor.org.
• Rational Functions look like fractions, and their graphs are complex. Brushing up on your earlier fraction skills will help enormously in this subunit because algebraic fractions work in a parallel way – like when you need a common denominator. This subunit begins by defining a rational function and identifying its characteristics. It continues by exploring graphs of rational functions and helps you determine asymptotes and intercepts.
2. Watch the video on the Asymptotes of Rational Functions.
3. Work through pages 188-191 until the next section begins. As always, do the TIN questions as you come to them.

Lesson 109

1. Work through pages 191-195.
2. Answers are on page 200.
3. Watch the video on Determining Vertical and Horizontal Asymptotes.

Lesson 110

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 111

1. Work through pages 195-199.
2. Answers are on page 200.

Lesson 112

1. Do the odd-numbered problems #1-43 starting on page 201. SKIP number 31.
2. Do number 40 for up to 4 points extra credit.
3. Check your answers, 3.4. Score up to 2 points per problem.
4. Record your score out of 42.

Lesson 113

1. Work through pages 206-211.
2. Answers are on page 211.

Lesson 114

1. Do the odd-numbered problems #1-23 starting on page 212.
2. Check your answers, 3.5. Score up to 2 points per problem.
3. Record your score out of 24.

Lesson 115

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• This is a good habit I am teaching you. When you are in college, you will only have classes a few times a week. It’s a great practice to do your homework on the day that it is assigned. Try to complete it. Then when you have an extra day, you can go back to anything you got wrong and make sure you have it figured out.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble. Hopefully, you listened to me and have a list. Are you still keeping a list?
• Binge watch with notebook and pencil in hand of course!

Lesson 116

1. There were five sets of exercises in chapter 2. Do four odd problems from each set of exercises. It’s better for you to choose each one from a different section to get more review. You may use the textbook review, but not the solutions!
2. Check your answers. (up to 2 points each)
3. Record your score out of 40.

Lesson 117

1. Review exponent rules. (If you need to review this, you can use these links.)
2. Work through pages 215-219 (until the start of the next section.) As usual, complete the TIN questions as you come to them.
3. Answers are on page 227.

Lesson 118

1. Watch the video on Exponential Growth Functions. (youtube)
2. Work through pages 219-221. As usual, complete the TIN questions as you come to them.
3. Answers are on page 227.

Lesson 119

1. Watch the video introduction to compound interest. (youtube)
2. Work through pages 222-224 (to the start of the next section). As usual, complete the TIN questions as you come to them.
3. Answers are on page 227.

Lesson 120

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble.

Lesson 121

1. Finish the unit working through pages 224-227. As usual, complete the TIN questions as you come to them.
2. Answers are on page 227.
3. Do problem 37 on page 231.
5. Record your score out of 4. (potential for one point extra credit)

Lesson 122

1. Do the odd-numbered questions 1-35, starting on page 228.
2. Check your answers, 4.1. Score up to 2 points per question.
3. Record your score out of 35. (potential for one point extra credit)

Lesson 123

1. Watch the video on graphing exponential functions. (youtube)
2. Work through pages 232-235 (to the start of the next section). As usual, complete the TIN questions as you come to them.
3. Answers are on page 239.

Lesson 124

1. Watch the video on transformations of graphs. Take notes. Pause and draw graphs.
2. Work through pages 235-239 (to the start of the next section). As usual, complete the TIN questions as you come to them.
3. Answers are on page 239.

Lesson 125

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble.

Lesson 126

1. Do the odd-numbered questions 1-35, starting on page 240.
2. Check your answers, 4.2. Score up to 2 points per question.
3. Record your score out of 35. (potential for one point extra credit)

Lesson 127

1. Work through pages 242-244. As usual, complete the TIN questions as you come to them.
2. Answers are on page 250.
3. Check your understanding of logarithms with these problems. (This is a Shockwave Flash file. If you can’t use it, you could do the first four example problems on this page.) You could also use that second link if you want to hear someone else explain logarithms to you. They do have a point! They make some complicated equations easier to deal with.

Lesson 128

1. Work through pages 244-245. As usual, complete the TIN questions as you come to them.
2. Answers are on page 250.
3. Watch the video on calculators for natural logarithms. (YouTube)

Lesson 129

1. Work through pages 245-247. As usual, complete the TIN questions as you come to them.
2. Answers are on page 250.
3. Watch the video on change of base rules.

Lesson 130

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble.

Lesson 131

1. Work through pages 247-250. As usual, complete the TIN questions as you come to them.
2. Answers are on page 250.
3. Watch the video on solving exponential equations.

Lesson 132

1. Do the odd-numbered questions 1-35, starting on page 251.
2. Check your answers, 4.3. Score up to 2 points per question.
3. Record your score out of 35. (potential for one point extra credit)

Lesson 133

1. Do the odd-numbered questions 37-71, starting on page 251.
2. Check your answers, 4.3. Score up to 2 points per question.
3. Record your score out of 35. (potential for one point extra credit)

Lesson 134

1. Work through pages 253-254. As usual, complete the TIN questions as you come to them and work through examples.
2. Answers are on page 259.

Lesson 135

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble.

Lesson 136

1. Read the page on understanding logarithms. Watch the video at the bottom of the page on logarithm properties. (youtube)
2. Practice logs.

Lesson 137

1. Work through pages 255-256. As usual, complete the TIN questions as you come to them and work through examples.
2. Answers are on page 259.
3. Watch the video on solving logarithmic equations.

Lesson 138

1. Watch another video on solving logarithmic equations.
2. Work through pages 256-259.

Lesson 139

1. Do the odd-numbered questions 1-25, on page 260.
2. Check your answers, 4.4. Score up to 2 points per question.
3. Record your score out of 25. (potential for one point extra credit)

Lesson 140

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble.

Lesson 141

1. Do the odd-numbered questions 27-47, on page 261.
2. Check your answers, 4.4. Score up to 2 points per question.
3. Record your score out of 22.

Lesson 142

1. Watch the video on graphing natural logarithms. (YouTube)
2. Watch the video on graphing logarithmic functions. (YouTube)
3. Work through pages 262 and 263 in the online textbook.
4. Answers are on page 267.

Lesson 143

1. Watch the video on transformations of logarithmic functions.
2. Work through pages 262 and 263 in the online textbook.

Lesson 144

1. Do the odd-numbered questions 1-23, on page 268.
2. Check your answers, 4.5. Score up to 2 points per question.
3. Record your score out of 24.

Lesson 145

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble.

Lesson 146

1. Work through pages 270 – 274 in the online textbook.
2. Answers are on Lesson 282.
3. Your final for Pre-Calculus is on Lesson 180. All problems will be from the test/exercises you’ve been doing.

Lesson 147

1. Work through pages 274 – 276 in the online textbook.
2. Answers are on Lesson 282.

Lesson 148

1. Work through pages 276 – 282 in the online textbook.

Lesson 149

1. Do the odd-numbered questions 1-39, on page 283.
2. Check your answers, 4.6. Score up to 2 points per question.
• Answer Note: I’m getting different answers for number 11, close, but not the same. 24,000 and 15,084 (or 15,119). You can count them as correct answers.
3. Record your score out of 40.

Lesson 150

1. Catch up – Review day
2. Options:
• Go back to this past week’s lessons and redo any you got wrong. Try them from scratch. You can also try a question from each section that wasn’t assigned. Make sure you can still do them without having the examples right in front of you.
• Practice for the SATs.
• Here are ACT practice questions. This is more limited in what’s offered.
• There will be a final. You need to know these things. Go back and redo lessons/questions that gave you trouble.

Lesson 151

1. Look at, and understand, the four graphs, linear and logarithmic.
2. Work through pages 289 – 292 in the online textbook.
3. Answers are on page 294.

Lesson 152

1. Work through pages 292 – 294 in the online textbook.

Lesson 153

1. Do the odd-numbered questions 1-15, on page 295.
2. Check your answers, 4.7. Score up to 2 points per question.
3. Record your score out of 16.

Lesson 154

1. Your final exams are on Lesson 159 and 160, trigonometry and precalculus.
2. Review your work from the year.

Lesson 155

1. Review for the final. You’ve been doing review throughout the year. You should be good at this. Are there things you need to go over?
2. A good idea is to take one question from each unit and try it to see if you can do it without the examples.

Lesson 156

1. Review for the finals, trig on Lesson 159 and precalculus on Lesson 160.

Lesson 157

1. Review for the finals, trig on Lesson 159 and precalculus on Lesson 160.

Lesson 158

1. Review for the finals, trig on Lesson 159 and precalculus on Lesson 160.

Lesson 159

1. Take the Trig final.
2. Record your score out of 30.

Lesson 160

1. Take your final.