Calculus

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Credit: 1

Prerequisites: Trigonometry/Pre-Calculus

Test Prep: CLEP, AP Calculus BC Note: If you are planning on taking the AP exam, please realize that it will cover things at the very end of the course. Plan your timing so that you will know that material before you take the test.

Course Description: This introductory calculus course covers differentiation and integration of functions of one variable, with applications. It is built from MIT’s Open Courseware Calculus course. Students will be using a traditional textbook for this course along with a study guide. There are optional video lectures for students who prefer to learn by listening. There is a midterm and final, but the goal that is emphasized is the daily understanding of the information in the given lesson. Students are rewarded for going back and figuring out any problems they got wrong in any given assignment. For a complete list of topics covered see lessons 1.1 through 10.4.

Notes: You will be able to use a graphing calculator in this course. On the AP exam you are able to use a calculator on part of the exam as well. If you don’t have one, here’s a free online graphing calculator you can use. When you need graph paper, you can print graph paper from here. In your assignments, if a problem you need to do refers to another problem, you will have to do that as well. When you are checking your answers sometimes an answer will vary; you will count your answer as correct if you found an answer. If you are stuck, here’s a site that might be able to help you solve an equation.

Recommendation: Hold onto your work. Do your daily work in a spiral notebook or on paper in a binder. Label each page at the top with the lesson number and chapter portion. Keep it together and organized. For your midterm and final, write out all of your work.

Lesson 1 (*) (Note that an asterisk * indicates that there is a worksheet in this lesson.)
Welcome to your first day of school! I wanted to give you one important reminder before you begin. Many of your lessons below have an internet link for you to click on. When you go to the different internet pages for your lessons, please DO NOT click on anything else on that page except what the directions tell you to. DO NOT click on any advertisements or games. DO NOT click on anything that takes you to a different website. Just stay focused on your lesson and then close that window and you should be right back here for the next lesson. Okay?
  1. If you didn’t get here through My EP Assignments, I suggest you go there and create an account.
  2. Scroll up to read your learning outcomes and all the notes on this course.
  3. (*) Print out the first quarter or use the Excel version.
  4. Read Chapter 1, Section 1.1, Velocity & Distance. There’s an outline of the lesson right under where it says “Exercises 1.1.” Every section has this. Try to fill in the blanks from the reading.
  5. Here’s the answer key.
  6. This is the end of your work for this course for your first day. You are allowed to move at your own pace (this is homeschooling), but it’s intended you complete one lesson a day.

Lesson 2

  1. Use section 1.1 again and answer questions in Exercises 1.1 (every 3rd question, up to #45). Chapter 1.1 – 1.4
  2. Check your answers for the exercises and for the chapter outline with the blanks filled in. That info is the most important “take away” for each chapter. Work to understand that section each time.

Lesson 3

  1. Use section 1.1 to check all of your answers. Chapter 1.1 – 1.4
  2. Figure out your mistakes and work on other problems and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to. (This is always referring to the problems you did in the lesson before and then worked on again if necessary.)

Lesson 4

  1. Read section 1.2, Calculus without Limits. Chapter 1.1 – 1.4
  2. Use the study guide for chapter 1 along with the reading.
  3. There’s an outline of the lesson right under where it says “Exercises 1.2.” Try to fill in the blanks from the reading.

Lesson 5

  1. Use section 1.2 again and answer the questions (the multiples of 3 up to 45). Chapter 1.1 – 1.4
  2. Check your answers for the chapter outline with the blanks filled in.

Lesson 6

  1. Use section 1.2 to check your answers. Chapter 1.1 – 1.4
  2. Figure out your mistakes and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 7

  1. Read section 1.3, Velocity and Distance. Chapter 1.1 – 1.4
  2. Use the study guide for chapter 1 along with the reading.
  3. Complete the “Read-Through Questions” at the end of the section. Fill in the blanks from the reading.

Lesson 8

  1. Use section 1.3 again and answer questions (the multiples of 3 up to 27). There’s a link to print graph paper at the top of the course in the “Notes” section. Chapter 1.1 – 1.4
  2. Check your answers for the chapter outline.

Lesson 9

  1. Use section 1.3 to check all of your answers. Chapter 1.1 – 1.4
  2. Figure out your mistakes and work on other problems and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 10

  1. Read section 1.4, Circular Motion. Chapter 1.1 – 1.4
  2. Use the study guide for chapter 1 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 11

  1. Use section 1.4 again and answer the questions (the multiples of 3 up to 39). Chapter 1.1 – 1.4
  2. Check your answers for the chapter outline.

Lesson 12

  1. Use section 1.4 to check your answers. Chapter 1.1 – 1.4
  2. Figure out your mistakes and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 13

  1. Read section 1.5, Circular Motion. Chapter 1.5 – 1.7
  2. Use the study guide for chapter 1 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 14

  1. Use section 1.5 again and answer the questions (the multiples of 3 up to 36). Chapter 1.5 – 1.7
  2. Check your answers for the chapter outline.

Lesson 15

  1. Use section 1.5 to check your answers. Chapter 1.5 – 1.7
  2. Do question 37. Figure out your mistakes from Lesson 14 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 16

  1. Read sections 1.6 and 1.7. Chapter 1.5 – 1.7

Lesson 17

  1. Practice with your graphing calculator or with an online option. See “Notes” at the top of the page.

Lesson 18

  1. Read section 2.1, The Derivative of a Function. Chapter 2.1 – 2.4
  2. Use the study guide for chapter 2 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 19

  1. Use section 2.1 again and answer the questions (the multiples of 3 up to 39). Chapter 2.1 – 2.4
  2. Check your answers for the chapter outline.

Lesson 20

  1. Use section 2.1 to check your answers. Chapter 2.1 – 2.4
  2. Figure out your mistakes from Lesson 19 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 21

  1. Read section 2.2, Powers and Polynomials. Chapter 2.1 – 2.4
  2. Use the study guide for chapter 2 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 22

  1. Use section 2.2 again and answer the questions (the multiples of 3 up to 42). Chapter 2.1 – 2.4
  2. Check your answers for the chapter outline.

Lesson 23

  1. Use section 2.2 to check your answers. Chapter 2.1 – 2.4
  2. Do number 49. Check your answer.
  3. Figure out your mistakes from Lesson 22 and work on other questions and check your answers. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 24

  1. Read section 2.3, The Slope and the Tangent Line. Chapter 2.1 – 2.4
  2. Use the study guide for chapter 2 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 25

  1. Use section 2.3 again and answer the questions (the multiples of 3 up to 39). Chapter 2.1 – 2.4
  2. Check your answers for the chapter outline.

Lesson 26

  1. Use section 2.3 to check your answers. Chapter 2.1 – 2.4
  2. Do number 45. Check your answer.
  3. Figure out your mistakes from Lesson 25 and work on other questions and check your answers. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 27

  1. Here’s something different today. Watch this calculus class given at MIT.
  2. Decide if you want to watch more of these lectures. Decide if it’s profitable to you. Do you learn more easily when you hear it and see it explained, instead of reading it?
  3. I don’t have the time to put these classes on a separate day. I will link to them though, and you can use them if they are helpful to you.

Lesson 28

  1. Read section 2.4, Derivative of the Sine and Cosine. Chapter 2.1 – 2.4
  2. Use the study guide for chapter 2 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 29

  1. Use section 2.4 again and answer the questions (the multiples of 3 up to 30). Chapter 2.1 – 2.4
  2. Check your answers for the chapter outline.

Lesson 30

  1. Use section 2.4 to check your answers. Chapter 2.1 – 2.4
  2. Do number 33.
  3. Figure out your mistakes from Lesson 29 and work on other questions and check your answers. Spend 40 minutes working. (If you find it more helpful, you could use the video of lecture 3 instead for today’s lesson .)
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 31

  1. Read section 2.5, The Product and Quotient and Power Rules. Chapter 2.5 – 2.7
  2. Use the study guide for chapter 2 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 32

  1. Use section 2.5 again and answer the questions (the multiples of 3 up to 45). Chapter 2.5 – 2.7
  2. Check your answers for the chapter outline.

Lesson 33

  1. Use section 2.5 to check your answers. Chapter 2.5 – 2.7
  2. Figure out your mistakes from Lesson 32 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 34

  1. Read section 2.6, Limits. Chapter 2.5 – 2.7
  2. Use the study guide for chapter 2 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 35

  1. Use section 2.6 again and answer the questions (the multiples of 3 up to 42). Chapter 2.5 – 2.7
  2. Check your answers for the chapter outline.

Lesson 36

  1. Use section 2.6 to check your answers. Chapter 2.5 – 2.7
  2. Do number 45. Check your answer.
  3. Figure out your mistakes from Lesson 35 and work on other questions and check your answers. Spend 40 minutes working.
    1. Or, you can watch lecture 2.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 37

  1. Read section 2.7, Continuous Functions. Chapter 2.5 – 2.7
  2. Use the study guide for chapter 2 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 38

  1. Use section 2.7 again and answer the questions (the multiples of 3 up to 39). Chapter 2.5 – 2.7
  2. Check your answers for the chapter outline.

Lesson 39

  1. Use section 2.7 to check your answers. Chapter 2.5 – 2.7
  2. Do number 42. Check your answer.
  3. Figure out your mistakes from Lesson 38 and work on other questions and check your answers. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 40

  1. Read section 3.1, Linear Approximation. Chapter 3.1 – 3.4
  2. Use the study guide for chapter 3 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 41

  1. Use section 3.1 again and answer the questions (the multiples of 3 up to 24, and 29-31). Chapter 3.1 – 3.4
  2. Check your answers for the chapter outline.

Lesson 42

  1. Use section 3.1 to check your answers. Chapter 3.1 – 3.4
  2. Figure out your mistakes from Lesson 41 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 43

  1. Read section 3.2, Maximum and Minimum Problems. Chapter 3.1 – 3.4
  2. Use the study guide for chapter 3 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 44

  1. Use section 3.2 again and answer the questions (the multiples of 3 up to 60). Chapter 3.1 – 3.4
  2. Check your answers for the chapter outline.

Lesson 45

  1. Use section 3.2 to check your answers. Chapter 3.1 – 3.4
  2. Figure out your mistakes from Lesson 44 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.
  4. Calculate your grade for this quarter. Save your work.

Lesson 46 (*)

  1. (*)Print out your second quarter grading sheet or use the Excel version.
  2. Read section 3.3, Second Derivatives: Minimum vs. Maximum. Chapter 3.1 – 3.4
  3. Use the study guide for chapter 3 along with the reading.
  4. Fill in the blanks in the “Read-Through Questions” section.

Lesson 47

  1. Use section 3.3 again and answer the questions (the multiples of 3 up to 42). Chapter 3.1 – 3.4
  2. Check your answers for the chapter outline.

Lesson 48

  1. Use section 3.3 to check your answers. Chapter 3.1 – 3.4
  2. Figure out your mistakes from Lesson 47 and work on other questions and check your answers. Spend 40 minutes working. You could choose to spend your time today watching lecture 4.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 49

  1. Read section 3.4, Graphs. Chapter 3.1 – 3.4
  2. Use the study guide for chapter 3 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 50

  1. Use section 3.4 again and answer the questions (the multiples of 3 up to 51). Chapter 3.1 – 3.4
  2. Check your answers for the chapter outline.

Lesson 51

  1. Use section 3.4 to check your answers. Chapter 3.1 – 3.4
  2. Figure out your mistakes from Lesson 50 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 52

  1. Read section 3.5, Ellipses, Parabolas, and Hyperbolas. Chapter 3.5 – 3.8
  2. Use the study guide for chapter 3 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 53

  1. Use section 3.5 again and answer the questions (the multiples of 3 up to 42). Chapter 3.5 – 3.8
  2. Check your answers for the chapter outline.

Lesson 54

  1. Use section 3.5 to check your answers. Chapter 3.5 – 3.8
  2. Figure out your mistakes from Lesson 53 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 55

  1. Read section 3.6, Iterations x[n+1] = F(x[n]). Chapter 3.5 – 3.8
  2. Use the study guide for chapter 3 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 56

  1. Use section 3.6 again and answer the questions (the multiples of 3 up to 36). Chapter 3.5 – 3.8
  2. Check your answers for the chapter outline.

Lesson 57

  1. Use section 3.6 to check your answers. Chapter 3.5 – 3.8
  2. Do number 42 and check your answer.
  3. Figure out your mistakes from Lesson 56 and work on other questions and check your answers. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 58

  1. Read section 3.7, Newton’s Method and Chaos. Chapter 3.5 – 3.8
  2. Use the study guide for chapter 3 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 59

  1. Use section 3.7 again and answer the questions (the multiples of 3 up to 42). Chapter 3.5 – 3.8
  2. Check your answers for the chapter outline.

Lesson 60

  1. Use section 3.7 to check your answers. Chapter 3.5 – 3.8
  2. Do number 45 and check your answer.
  3. Figure out your mistakes from Lesson 59 and work on other questions and check your answers. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to (as always, from the original problem set only).

Lesson 61

  1. Read section 3.8, The Mean Value Theorem and l’Hopital’s Rule. Chapter 3.5 – 3.8
  2. Use the study guide for chapter 3 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 62

  1. Use section 3.8 again and answer the questions (the multiples of 3 up to 36). Chapter 3.5 – 3.8
  2. Check your answers for the chapter outline.

Lesson 63

  1. Use section 3.8 to check your answers. Chapter 3.5 – 3.8
  2. Figure out your mistakes from Lesson 62 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 64

  1. Read section 4.1, Derivatives by the Chain Rule. Chapter 4.1 – 4.2
  2. Use the study guide for chapter 4 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 65

  1. Use section 4.1 again and answer the questions (the multiples of 3 from 1 to 30 and 42 – 57). Chapter 4.1 – 4.2
  2. Check your answers for the chapter outline.

Lesson 66

  1. Use section 4.1 to check your answers. Chapter 4.1 – 4.2
  2. Do numbers 36 and 39 and check your answers.
  3. Figure out your mistakes from Lesson 65 and work on other questions and check your answers. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to. (This, as always, refers only to the first set of problems you did, the ones from Lesson 65.)

Lesson 67

  1. Read section 4.2, Implicit Differentiation and Related Rates. Chapter 4.1 – 4.2
  2. Use the study guide for chapter 4 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 68

  1. Use section 4.2 again and answer the questions (the multiples of 3 from 1 to 27). Chapter 4.1 – 4.2
  2. Check your answers for the chapter outline.

Lesson 69

  1. Use section 4.2 to check your answers. Chapter 4.1 – 4.2
  2. Figure out your mistakes from Lesson 68 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 70

  1. Read section 4.3, Inverse Functions and Their Derivatives. Chapter 4.3-4.4
  2. Use the study guide for chapter 4 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 71

  1. Use section 4.3 again and answer the questions (the multiples of 3 to 42, and do number 48). Chapter 4.3-4.4
  2. Check your answers for the chapter outline.

Lesson 72

  1. Use section 4.3 to check your answers. Chapter 4.3-4.4
  2. Do number 59 and check your answers.
  3. Figure out your mistakes from Lesson 71 and work on other questions and check your answers. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 73

  1. Read section 4.4, Inverses of Trigonometric Functions. Chapter 4.3-4.4
  2. Use the study guide for chapter 4 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 74

  1. Use section 4.4 again and answer the questions (the multiples of 3 to 45, and do number 50). Chapter 4.3-4.4
  2. Check your answers for the chapter outline.

Lesson 75

  1. Use section 4.4 to check your answers. Chapter 4.3-4.4
  2. Figure out your mistakes from Lesson 74 and work on other questions and check your answers. Spend 40 minutes working. You could decide it would be better to watch the lecture on inverses, lecture 5.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.
  4. On Lesson 91 you will have a midterm exam on questions you have been assigned from the beginning up through section 5.4. The test will be made up of only problems you have already been assigned.

Lesson 76

  1. Read section 5.1, The Idea of an Integral. Chapter 5.1 – 5.4
  2. Use the study guide for chapter 5 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 77

  1. Use section 5.1 again and answer the questions (the multiples of 3 to 24). Chapter 5.1 – 5.4
  2. Check your answers for the chapter outline.

Lesson 78

  1. Use section 5.1 to check your answers. Chapter 5.1 – 5.4
  2. Figure out your mistakes from Lesson 77 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 79

  1. Read section 5.2, Antiderivatives. Chapter 5.1 – 5.4
  2. Use the study guide for chapter 5 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 80

  1. Use section 5.2 again and answer the questions (the multiples of 3 to 33). Chapter 5.1 – 5.4
  2. Check your answers for the chapter outline.

Lesson 81

  1. Use section 5.2 to check your answers. Chapter 5.1 – 5.4
  2. Figure out your mistakes from Lesson 80 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 82

  1. Read section 5.3, Summation vs. Integration. Chapter 5.1 – 5.4
  2. Use the study guide for chapter 5 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 83

  1. Use section 5.3 again and answer the questions (the multiples of 3 to 30). Chapter 5.1-5.4
  2. Check your answers for the chapter outline.

Lesson 84

  1. Use section 5.3 to check your answers. Chapter 5.1 – 5.4
  2. Do number 33 and check your answer.
  3. Figure out your mistakes from Lesson 83 and work on other questions and check your answers. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 85

  1. Read section 5.4, Indefinite Integrals and Substitutions. Chapter 5.1 – 5.4
  2. Use the study guide for chapter 5 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 86

  1. Use section 5.4 again and answer the questions (the multiples of 3 to 36). Chapter 5.1 – 5.4
  2. Check your answers for the chapter outline.

Lesson 87

  1. Use section 5.4 to check your answers. Chapter 5.1 – 5.4
  2. Figure out your mistakes from Lesson 86 and work on other questions and check your answers. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.
  4. On Lesson 91 you will be tested on problems you have been assigned up to this point. (All of the questions will be from your normally assigned work, not from any extra problems given you.) You need to keep moving on your coursework, but you can also take some time to look over your work to prepare.

Lesson 88

  1. Read section 5.5, The Definite Integral. Chapter 5.5 – 5.8
  2. Use the study guide for chapter 5 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 89

  1. Use section 5.5 again and answer the questions (the multiples of 3 to 33). Chapter 5.5 – 5.8
  2. Check your answers for the chapter outline.

Lesson 90

  1. Use section 5.5 to check your answers. Chapter 5.5 – 5.8
  2. Figure out your mistakes from Lesson 89 and go over your assigned work from the course to prepare for your midterm. You could do a problem from each section for practice.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.
  4. Lesson 91 is a midterm on Chapters 1 through 5.4.
  5. Calculate your grade for this quarter.

Lesson 91 (*)

  1. (*)Print out your third quarter grading sheet or use the Excel version.
  2. Take your Calculus Midterm.
  3. Check your answers. You may award partial credit. Add 1 to your score and record it.

Lesson 92

  1. Read section 5.6, Properties of the Integral and the Average Value. Chapter 5.5 – 5.8
  2. Use the study guide for chapter 5 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 93

  1. Use section 5.6 again and answer the questions (the multiples of 3 to 36). Chapter 5.5 – 5.8
  2. Check your answers for the chapter outline.

Lesson 94

  1. Use section 5.6 to check your answers. Chapter 5.5 – 5.8
  2. Start the one minute timer and do number 39.
  3. Figure out your mistakes from Lesson 93 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 95

  1. Read section 5.7, The Fundamental Theorem and Its Consequences. Chapter 5.5 – 5.8
  2. Use the study guide for chapter 5 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 96

  1. Use section 5.7 again and answer the questions (the multiples of 3 to 36). Chapter 5.5 – 5.8
  2. Check your answers for the chapter outline.

Lesson 97

  1. Use section 5.7 to check your answers. Chapter 5.5 – 5.8
  2. Figure out your mistakes from Lesson 96 and work on other problems from the section for practice. Keep checking your answers as you go.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 98

  1. Read section 5.8, Numerical Integration. Chapter 5.5 – 5.8
  2. Use the study guide for chapter 5 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 99

  1. Use section 5.8 again and answer the questions (the multiples of 3 to 27). Chapter 5.5 – 5.8
  2. Check your answers for the chapter outline.

Lesson 100

  1. Use section 5.8 to check your answers. Chapter 5.5 – 5.8
  2. Figure out your mistakes from Lesson 99 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 101

  1. Read section 6.1, An Overview. Chapter 6.1 – 6.4
  2. Use the study guide for chapter 6 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 102

  1. Use section 6.1 again and answer the questions (the multiples of 3 to 27). Chapter 6.1 – 6.4
  2. Check your answers for the chapter outline.

Lesson 103

  1. Use section 6.1 to check your answers. Chapter 6.1 – 6.4
  2. Figure out your mistakes from Lesson 102 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 104

  1. Read section 6.2, The Exponential e^x. Chapter 6.1 – 6.4
  2. Use the study guide for chapter 6 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 105

  1. Use section 6.2 again and answer the questions (the multiples of 3 to 48). Chapter 6.1 – 6.4
  2. Check your answers for the chapter outline.

Lesson 106

  1. Use section 6.2 to check your answers. Chapter 6.1 – 6.4
  2. Figure out your mistakes from Lesson 105 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 107

  1. Read section 6.3, The Exponential e^x. Chapter 6.1 – 6.4
  2. Use the study guide for chapter 6 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 108

  1. Use section 6.3 again and answer the questions (the multiples of 3 to 51). Chapter 6.1 – 6.4
  2. Check your answers for the chapter outline.

Lesson 109

  1. Use section 6.3 to check your answers. Chapter 6.1 – 6.4
  2. Do number 66 and check your answer.
  3. Figure out your mistakes from Lesson 108 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 110

  1. Read section 6.4, Logarithms. Chapter 6.1 – 6.4
  2. Use the study guide for chapter 6 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 111

  1. Use section 6.4 again and answer the questions (the multiples of 3 to 66). Chapter 6.1 – 6.4
  2. Check your answers for the chapter outline.

Lesson 112

  1. Use section 6.4 to check your answers. Chapter 6.1 – 6.4
  2. Figure out your mistakes from Lesson 111 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 113

  1. Read section 6.5, Separable Equations Including the Logistic Equation. Chapter 6.5 – 6.7
  2. Use the study guide for chapter 6 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 114

  1. Use section 6.5 again and answer the questions (the multiples of 3 to 33). Chapter 6.5 – 6.7
  2. Check your answers for the chapter outline.

Lesson 115

  1. Use section 6.5 to check your answers. Chapter 6.5 – 6.7
  2. Figure out your mistakes from Lesson 114 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 116

  1. Read section 6.6, Powers Instead of Exponentials. Chapter 6.5 – 6.7
  2. Use the study guide for chapter 6 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 117

  1. Use section 6.6 again and answer the questions (the multiples of 3 to 39). Chapter 6.5 – 6.7
  2. Check your answers for the chapter outline.

Lesson 118

  1. Use section 6.6 to check your answers. Chapter 6.5 – 6.7
  2. Figure out your mistakes from Lesson 117 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 119

  1. Read section 6.7, Hyperbolic Functions. Chapter 6.5 – 6.7
  2. Use the study guide for chapter 6 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 120

  1. Use section 6.7 again and answer the questions (the multiples of 3 to 54). Chapter 6.5 – 6.7
  2. Check your answers for the chapter outline.

Lesson 121

  1. Use section 6.7 to check your answers. Chapter 6.5 – 6.7
  2. Figure out your mistakes from Lesson 120 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working. Or, you might want to watch lecture 6.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 122

  1. Read section 7.1, Integration by Parts. Chapter 7.1 – 7.3
  2. Use the study guide for chapter 7 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 123

  1. Use section 7.1 again and answer the questions (the multiples of 3 to 54). Chapter 7.1 – 7.3
  2. Check your answers for the chapter outline.

Lesson 124

  1. Use section 7.1 to check your answers. Chapter 7.1 – 7.3
  2. Figure out your mistakes from Lesson 123 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 125

  1. Read section 7.2, Trigonometric Integrals. Chapter 7.1 – 7.3
  2. Use the study guide for chapter 7 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 126

  1. Use section 7.2 again and answer the questions (the multiples of 3 to 54). Chapter 7.1 – 7.3
  2. Check your answers for the chapter outline.

Lesson 127

  1. Use section 7.2 to check your answers. Chapter 7.1 – 7.3
  2. Figure out your mistakes from Lesson 126 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 128

  1. Read section 7.3, Trigonometric Substitutions. Chapter 7.1 – 7.3
  2. Use the study guide for chapter 7 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 129

  1. Use section 7.3 again and answer the questions (the multiples of 3 to 48). Chapter 7.1 – 7.3
  2. Check your answers for the chapter outline.

Lesson 130

  1. Use section 7.3 to check your answers. Chapter 7.1 – 7.3
  2. Do number 54 and check your answer.
  3. Figure out your mistakes from Lesson 129 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 131

  1. Read section 7.4, Partial Fractions. Chapter 7.4 – 7.5
  2. Use the study guide for chapter 7 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 132

  1. Use section 7.4 again and answer the questions (the multiples of 3 to 27). Chapter 7.4- 7.5
  2. Check your answers for the chapter outline.

Lesson 133

  1. Use section 7.4 to check your answers. Chapter 7.4 – 7.5
  2. Figure out your mistakes from Lesson 132 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working. Or, you might decide to watch video lecture 29 on partial fractions.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 134

  1. Read section 7.5, Improper Integrals. Chapter 7.4 – 7.5
  2. Use the study guide for chapter 7 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 135

  1. Use section 7.5 again and answer the questions (the multiples of 3 to 27, and do number 29). Chapter 7.4 – 7.5
  2. Check your answers for the chapter outline.
  3. Calculate your grade for this quarter. Save your work.

Lesson 136 (*)

  1. (*) Print out your fourth quarter grading sheet or use the Excel version.
  2. Use section 7.5 to check your answers. Chapter 7.4 – 7.5
  3. Figure out your mistakes from Lesson 135 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working. Or, you might want to watch a video lecture on integration.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 137

  1. Read section 8.1, Areas and Volumes by Slices. Chapter 8.1 – 8.3
  2. Use the study guide for Chapter 8 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 138

  1. Use section 8.1 again and answer the questions (the multiples of 3 to 57). Chapter 8.1 – 8.3
  2. Check your answers for the chapter outline.

Lesson 139

  1. Use section 8.1 to check your answers. Chapter 8.1 – 8.3
  2. Do number 69 and check your answer.
  3. Figure out your mistakes from Lesson 138 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 140

  1. Read section 8.2, Length of a Plane Curve. Chapter 8.1 – 8.3
  2. Use the study guide for Chapter 8 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 141

  1. Use section 8.2 again and answer the questions (the multiples of 3 to 30). Chapter 8.1 – 8.3
  2. Check your answers for the chapter outline.

Lesson 142

  1. Use section 8.2 to check your answers. Chapter 8.1 – 8.3
  2. Figure out your mistakes from Lesson 141 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working. Or you might want to watch video lecture 31.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 143

  1. Read section 8.3, Area of a Surface of Revolution. Chapter 8.1 – 8.3
  2. Use the study guide for Chapter 8 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 144

  1. Use section 8.3 again and answer the questions (the multiples of 3 to 24). Chapter 8.1 – 8.3
  2. Check your answers for the chapter outline.

Lesson 145

  1. Use section 8.3 to check your answers. Chapter 8.1 – 8.3
  2. Figure out your mistakes from Lesson 144 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer.

Lesson 146

  1. Read section 8.4, Probability and Calculus. Chapter 8.4 – 8.6
  2. Use the study guide for Chapter 8 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 147

  1. Use section 8.4 again and answer the questions (the multiples of 3 to 33). Chapter 8.4 – 8.6
  2. Check your answers for the chapter outline.

Lesson 148

  1. Use section 8.4 to check your answers. Chapter 8.4 – 8.6
  2. Figure out your mistakes from Lesson 147 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 149

  1. Read section 8.5, Masses and Moments. Chapter 8.4 – 8.6
  2. Use the study guide for Chapter 8 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 150

  1. Use section 8.5 again and answer the questions (the multiples of 3 to 36). Chapter 8.4 – 8.6
  2. Check your answers for the chapter outline.

Lesson 151

  1. Use section 8.5 to check your answers. Chapter 8.4 – 8.6
  2. Do number 42 and check your answer.
  3. Figure out your mistakes from Lesson 150 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 152

  1. Read section 8.6, Force, Work, and Energy. Chapter 8.4 – 8.6
  2. Use the study guide for Chapter 8 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 153

  1. Use section 8.6 again and answer the questions (the multiples of 3 to 21). Chapter 8.4 – 8.6
  2. Check your answers for the chapter outline.

Lesson 154

  1. Use section 8.6 to check your answers. Chapter 8.4 – 8.6
  2. Do numbers 23 and 24 and check your answers.
  3. Figure out your mistakes from Lesson 153 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 155

  1. Read section 9.1, Polar Coordinates. Chapter 9.1 – 9.2
  2. Use the study guide for chapter 9 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 156

  1. Use section 9.1 again and answer the questions (the multiples of 3 to 27). Chapter 9.1 – 9.2
  2. Check your answers for the chapter outline.

Lesson 157

  1. Use section 9.1 to check your answers. Chapter 9.1 – 9.2
  2. Figure out your mistakes from Lesson 156 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working. Or, you might want to watch the video lecture on polar coordinates.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 158

  1. Read section 9.2, Polar Equations and Graphs. Chapter 9.1 – 9.2
  2. Use the study guide for chapter 9 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 159

  1. Use section 9.2 again and answer the questions (the multiples of 3 to 32). Chapter 9.1 – 9.2
  2. Check your answers for the chapter outline.

Lesson 160

  1. Use section 9.2 to check your answers. Chapter 9.1 – 9.2
  2. Figure out your mistakes from Lesson 159 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 161

  1. Read section 9.3, Slope, Length, and Area for Polar Curves. Chapter 9.3 – 9.4
  2. Use the study guide for chapter 9 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 162

  1. Use section 9.3 again and answer the questions (the multiples of 3 to 35). Chapter 9.3 – 9.4
  2. Check your answers for the chapter outline.

Lesson 163

  1. Use section 9.3 to check your answers. Chapter 9.3 – 9.4
  2. Figure out your mistakes from Lesson 162 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 164

  1. Read section 9.4, Complex Numbers. Chapter 9.3 – 9.4
  2. Use the study guide for chapter 9 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 165

  1. Use section 9.4 again and answer the questions (the multiples of 3 to 33). Chapter 9.3 – 9.4
  2. Check your answers for the chapter outline.

Lesson 166

  1. Use section 9.4 to check your answers. Chapter 9.3 – 9.4
  2. Figure out your mistakes from Lesson 165 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 167

  1. Read section 10.1, The Geometric Series. Chapter 10.1 – 10.3
  2. Use the study guide for chapter 10 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 168

  1. Use section 10.1 again and answer the questions (the multiples of 3 to 42). Chapter 10.1 – 10.3
  2. Check your answers for the chapter outline.

Lesson 169

  1. Use section 10.1 to check your answers. Chapter 10.1 – 10.3
  2. Do number 43 and check your answer.
  3. Figure out your mistakes from Lesson 168 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  4. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 170

  1. Read section 10.2, Convergence Tests: Positive Series. Chapter 10.1 – 10.3
  2. Use the study guide for chapter 10 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 171

  1. Use section 10.2 again and answer the questions (the multiples of 3 to 60). Chapter 10.1 – 10.3
  2. Check your answers for the chapter outline.

Lesson 172

  1. Use section 10.2 to check your answers. Chapter 10.1 – 10.3
  2. Figure out your mistakes from Lesson 171 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 173

  1. Read section 10.3, Convergence Tests: All Series. Chapter 10.1 – 10.3
  2. Use the study guide for chapter 10 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 174

  1. Use section 10.3 again and answer the questions (the multiples of 3 to 36). Chapter 10.1 – 10.3
  2. Check your answers for the chapter outline.

Lesson 175

  1. Use section 10.3 to check your answers. Chapter 10.1 – 10.3
  2. Figure out your mistakes from Lesson 174 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working. Or, you might want to watch this lecture on infinite series and convergence tests.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 176

  1. Read section 10.4, The Taylor Series for e^x, sin x, and cos x. Chapter 10.4 – 10.5
  2. Use the study guide for chapter 10 along with the reading.
  3. Fill in the blanks in the “Read-Through Questions” section.

Lesson 177

  1. Use section 10.4 again and answer the questions (the multiples of 3 to 48). Chapter 10.4 – 10.5
  2. Check your answers for the chapter outline.

Lesson 178

  1. Use section 10.4 to check your answers. Chapter 10.4 – 10.5
  2. Figure out your mistakes from Lesson 174 and work on other problems for practice. Keep checking your answers as you go. Spend 40 minutes working. Or, you might want to watch this video lecture on the Taylor Series.
  3. Record your score out of 10. Subtract one point for every problem you can’t figure out the right answer to.

Lesson 179

  1. On Lesson 180 you are having a final. There will be one question from each of the first four chapters and two questions from each of last six chapters. They will all be problems that you have been assigned.
  2. Here’s a review lecture from some things up through hyperbolic functions in 6.7.
  3. Here’s a review video from right after polar coordinates.

Lesson 180

  1. Take your calculus final. Read the directions below. Don’t lose points! There are 21 questions.
    • READ THE DIRECTIONS on the site.
    • Carefully type in your answers. It will accept variations for the answer, but better to just do it right to make sure.
    • Show your work to get all the points. Do your work on separate paper.
    • Finish in one seating (no getting up for any reason). In a school final there’s no getting up and walking around or getting a drink, not even going to the bathroom.
      • This is the grading scale. Start with 100 points. Subtract off 3 points for any wrong answer.
      • For any answer you skipped and have no work to show for, subtract off an additional 2 points.
  2. Record your total out of 100.
  3. Congratulations! If you are planning on taking the AP exam, practice. Here are practice exams.
  4. Save your work for your portfolio. Save your final. To figure out your final grade,  divide your total number of points for all four quarters into the total possible for all four quarters.
  5. Please complete the polls, and take them seriously to help other students choose their courses.

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This course is derived from: David Jerison. 18.01 Single Variable Calculus, Fall 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 29 Dec, 2015). License: Creative Commons BY-NC-SA