Welcome! Lesson details for each day are described below. I will do my best to not only stay updated, but also provide extra links and resources for you to use and explore. * My Channel for Precalculus*

Units match the corresponding chapter in our book. It should be noted that this course will follow the course content and outcomes listed for Math 111 and Math 112. You can glance over these to see the content that will be covered as well as some of the strategies for learning the material.

Math 111: Course Content and Outcomes

Math 112: Course Content and Outcomes

**Need a tutor? Mr. Laiche offers Advanced Math Tutoring! He was my substitute for a few days in October and did an outstanding job. His e-mail is mrLaiche@gmail.com His website is MrLaiche.com**

# Final Exam:

Review: PC and PCN 2nd Semester Study Guide 2016-17

ANSWER KEY: FinalReviewAnswerKey (Missing part of #23… but I have it in class for you)

# Seniors:

FINAL REVIEW: PC and PCN 2nd Semester Study Guide 2016-17

ANWER KEY: FinalReviewAnswerKey

**Combinatorics/Binomial Theorem: **

**Juniors:** PCN9-4A Sequence Practice #1 and PCN9-4B Sequence Practice #2 and PCN9-4C Sequence Practice #3

*Monday May 15th – Monday May 22nd : SBAC Testing for Juniors*

*Juniors will be taking the Smarter Balanced Computer Adaptive Test (CAT) with me. They should report directly to room C-8 for class. All non-Juniors or Juniors who have opted out should report to the assigned room. *

*Period 1: Report to Ms. Andrews room (C-32). Seniors have a take-home test, and everyone else not testing can review/finish the Binomial Theorem Packet. *

*Period 3: Report to Room C-8!!. Seniors have a take-home test, and everyone else not testing can review/finish the Binomial Theorem Packet. *

*Period 7: Everyone report to the normal room C-30. Seniors have a take-home test, and everyone else not testing can review/finish the Binomial Theorem Packet. *

**Lesson 2: ** Students will use Pascal’s Triangle to expand binomials raised to a power. **Assignment: **PCN9-3 Binomial Theorem Packet

**Lesson 1: ** Students will examine combinatorics. **Watch these videos!!! They are helpful!!** Khan Academy Packet:** PCN9-1 Combinatorics Packet**

**Unit 9: Polar Graphs and Equations**

Lesson 3: April 26th/27th. **Objective: **Students will use parametric equations in applied mathematics problems. **Assignment:** Last page of the Parametric Equations Packet from last class. **Homework:** Quiz Review

Lesson 2: April 24th/25th. **Objective: **Students will explore parametric equations. **Assignment: ****Parametric Equations Packet (Another Ewing creation!). Homework: **Finish the first two pages (front and back) of the packet, as well as: p. 736 #’s 1, 5, 13, 19 just graph and table only.

Lesson 1: April 20th/21st. **Objective: **Students will explore graphs of polar equations and make conclusions on the parameters that change them. **Assignment: (A Ewing creation!): ****PC9-1 Polar Graphing Homework: **-Finish Packet from today’s assignment. Also: p.619 #’s 1-15 odd and #’s 17-24 All.

# Unit 7: **Vectors**

**Although I do like to make my own videos, I often find ones online that are much better than mine. Here is one I liked: **ProfRobBob

**CHAPTER REVIEW:** PC8-Review

Day 4: April 12th/13th. **Objective: **Students will graph polar coordinates and convert between polar and rectangular coordinates. **Notes: ****PC 8-4Notes Homework: **p. 600 #’s 1-9 odd, #’s 13-17 odd, #’s 25-31 odd, #’s 41-45 odd, # 49 and #51.

Day 3: April 10th/11th. **Objective: **Students will use the dot product to find the angle between vectors. **Notes/Classwork: **PC8-3 Notes/Assignment **Homework:** p 650 #’s 1-9 odd, #19, and #23

Day 2: April 5th/6th. **Objective: **Students will find unit vectors, and apply concepts of vectors to real world problems. **Notes/Practice: ****PC8-2Notes ****Application Problems: **PC8-2Application **Homework: ** p 641/642 #’s 33, 37, 39, 41, 43, 49 and 51.

Day 1: April 3rd/4th. **Objective: **Students will determine if vectors are equivalent by calculating their magnitude and direction. **Assignment/Homework: ****PC8-1 Notes/Homework Note: ** Khan Academy has a lot of great videos on this topic.

**Unit 6: **Trigonometry (part 2)

**Review: **PC6-Review * Make sure to rationalize the denominators when simplifying!*

**Day 7: **March 15th/16th. **Objective: **Students will write algebraic proofs. **Assignment(s): ****PC6-6A and PC6-6B. Video: **Example Problem

**NEW VIDEO UPLOAD!!**

Check out the new videos I uploaded if you are stuck on one of the recent assignments. Examples are from the assignments in class. * YouTube*

**Day 6: **March 9th/10th. **Objective: **Students will apply half angle formulas. **Homework: **PC6-5A

**Day 5: **March 7th/8th. **Objective: **Students will apply the double angle formulas for sine, cosine, and tangent. **Homework: **PC6-4B.

**Day 4: **March 3rd/6th. **Objective: **Students will use the sum and difference formulas as well as double angle formulas to evaluate trigonometric expressions. **Homework: **PC 6-3 B and PC 6-4 A.

**Day 3:** March 1st/2nd. **Objective: **Students will use the sum and difference formulas to evaluate trigonometric expressions. **Homework: **PC 6-3A

**Day 2: **February 23rd/24th. **Objective: **Students will solve trigonometric equations **Assignment: **PC6-2A and PC6-2B. **Homework**: Finish the assignment documents. **Here is how to do the “new” stuff: **Solving Trig Equations

**Special help on last night’s homework: **

Video: Simplifying Trig Expressions **HW Scans: **HW Scan 1 of 2 and HW Scan 2 of 2

**Day 6-1**: February 21st/22nd. **Objective:** Students will use trigonometric identities to simplify expressions. **Assignment: PC 6-1 ****Homework: **Finish the assignment (1 stamp) Complete problems on page 479 #’s 1-11 odd for another stamp.

# Unit 5: Trigonometry (part 1)

**TEST DAY!!!! – **February 16th/17th. **Homework: **Review the next chapter by writing down all the theorems that appear in the first section of the book.

**Review Day/Group Test: **February 14th/15th. I’ve compiled all of your quizzes from this entire unit and put them in a PDF. Here they are: PC 5 – Quizzes Use them to study!! Remember, you need to have memorized the unit circle.

**Day 5-7**: February 10th/ 13th. Objective: Students will find the values of inverse trigonometric functions. **Assignment: ** p. 467 #’s 2-26 even. (worth a stamp)** Homework: **Memorize the unit circle. Review each quiz starting with PC 5-1. Go back to each homework assignment from PC-1 through PC 5-7 and choose one **even** problem to complete. You will have 7 problems from 7 sections when you are finished. (Due next class)

**Day 5-6** February 8th/9th. Objective: Students will find the values of inverse trigonometric functions. **Assignment: ****Inverse Practice Review: **p. 467 #’s 1-45 odd. Guess what? I did the homework! A few answers should be simplified further by rationalizing the denominator. Here is my scanned copy: HOMEWORK KEY.

**Day 5-5**. February 6th/7th. Objective: Students will find the zeros of a trigonometric function by graphing. **Assignment: ** PC 4-8 **Homework: **p. 450 #’s 1-19 odd, 21-30 all, 31-51 odd. (Due next class)

# Unit 5: Trigonometry (part 1)

**Day 5-4**: January 23rd/24th. Objective: Students will graph basic trigonometric functions and transformations of basic trigonometric functions. **Homework: **PC 5-4 and start studying for the final exam. Look at old reviews, quizzes, homework, and notes.

**Day 5-3:** January 19th/20th. Objective: Students will find the relationship between acute angles and the six trigonometric functions. **Homework: **p. 429 #’s 1-61 odd. **Helpful Video: Reference Triangles. **

**Snow-Day #6…..** I hope you all are checking this website for some updates. I’m slowly losing my mind with all of this snow out here. In order to combat it, I’m doing some math! The next section in our book starts on page 420. The example problems follow on page 429. The book explains a few properties and makes important mention of the sine and cosine values in each quadrant (p.424 at the bottom). This will work as an aid as you attempt to complete some problems. Specifically **p429 #’s 1-47 odd.** Also, I made a video that might help here: **Reference Triangles**

Section 5.4 covers some basic right triangle trigonometry which should be a review from geometry. Starting in section 5.5 we have graphs of trigonometric functions. I made a video on some of this stuff here: **UnitCircle(2) **Try graphing sin(x) and cos(x)!

**Day 5-2: **January 6th/9th. Objective: Students will begin learning the unit circle. **Homework: ** p. 417 #’s 1, 3, 7. #s 11-19 odd. #’s 31-39 odd. #’s 47-57 odd. **Helpful Video**: Unit Circle

**Day 5-1:** January 4th/5th. Objective: Students will convert from degrees to radians, radians to degrees, and calculate the arc length given a radius and angle. **In Class Notes: ****PC5-1 Notes Homework: **p 404 #’s 1-39 odd, 43-67 every other odd, #69 and #75.

**Unit 4: Logarithms and Exponential Functions**

**Helpful Link: **Khan Academy – Introducing Logs and Exponential Functions

**SNOW DAY! ** Clearly we have had our fair share of breaks this year. B-day classes will take their individual test on the first day back from break. It’s a bummer I know, but maybe you’ll take some of that time during winter break to study. E-mail me questions/comments if you have them. As far as the A-day students go, I would assume that everyone has already taken the test. Those that haven’t will need to when we return. Let me know via e-mail and we can figure it out. **Individual Test Day!** December 12/December 13th. Objective: Students will prove their knowledge of unit concepts by completing an individual test.

**Group Test Day! **December 8th/December 9th. Objective: Students will complete a group test based on the unit.

**Review Day!** December 6th/December 7th. Objective: Students will summarize concepts from the unit by completing a review. **Review Document: ****PC-4 Review Answer Key: PC-4 Review Answer Key** **Problem #****13: Missing Problem #13 (corrected version)** ** ****Homework: ** Study for the test!

**Day 4-6** December 2nd/December 5th. Objective: Students will use logarithms to solve applied mathematics problems involving earthquakes and the loudness of sound. **Notes: ** PC 4-6 (Notes) **Homework: **p 386 #’s 1-10 (all of them)

**Day 4-Mid Unit Review** November 30th/December 1st. Objective: Students will summarize unit objectives and re-create similar problems **Homework: **Your book has 4 worked out examples starting on page 383. They need to be copied, showing all work. You also need to think of three questions that you can bring to class (right them down).

**Day 4-5** November 28th/29th. Objective: Students will model growth with exponential and logistic equations. **Assignment:** PC 4-5 and **Glue In**: PC 4-5GlueIn. **Homework: **p. 367 #’s 1-9 odd. #’s 13, 16, 21, 25. Read section 4.9 in your textbook. It starts on page 383, and continues until page 386.

**Day 4-4** November 21st/22nd. Objective: Students will solve problems involving interest. **Assignment: **PC 4-4 Assignment **Homework: **p. 357 #’s 1-10 odd, 11, 13, 25, 27, 31, 33, 53, 54. (due next class)

**Day 4-3** November 17th/18th. Objective: Students will use properties of logarithms to solve equations. **Notes:** PC 4-3 Glue-In **Assignment: **PC 4-3.1 and PC 4-3.2 **Homework: **finish both of the worksheet assignments. (due next class)

**Day 4-2** November 15th/16th. Objective: Students will solve exponential and logarithmic equations. Students will find the domain of logarithmic functions. **Assignment: ****PC 4-2 Homework: **p. 330 #’s 1-23 (odd), #’s 37, 39, 77, and 78. (due next class)

**Day 4-1: **November 8th/14th. Objective: Students will graph exponential and logarithmic functions and identify their properties. **Assignment: ****PC 4-1 **** Homework**: p 320 # 37 – 42, and try #’s 59, 61, and 62. (Due next class) Also: Watch this: graphing logs. and this one on population growth

# Unit 3: Polynomials and Rational Functions

**Helpful Link: **Khan Academy – Intro to Polynomials

**Day 3-10: ****November 3rd/7th. **Objective: Students will prove their knowledge of polynomials and rational functions by completing an individual test.

**Day 3-9: ****November 1st/2nd. **Objective: Students will prove their knowledge of polynomials and rational functions by completing a group test. **Homework: **Study for individual test next class. Use the chapter review and other documents for practice problems. Ask all questions prior to test day. (Due next class) **Group Test: **PC 3-Group Test (hidden for now)

**Day 3-8: ****October 28th/31st. **Review Day. Objective: Students will summarize polynomials and rational functions unit through a group review. **Homework/Practice Problems: **p 290 # 1-5 (True/False). p. 291 #’s 5, 7, 17, 23, 30, graph #35, 41, 43, find all roots of #45. Optional Portion: #69, find all roots on #89, and complete #117. **HW Scan: **pc3-reviewhw (Due next class)

**Day 3-7: October 26th/27th. **Objective: Students will write equations of rational functions given a graph. Students will solve rational equations. **Assignment: PC 3-7 ****Homework: **Finish the assignment. (Due next class)

**Day 3-6: October 24th/25th. **Objective: Students will identify horizontal asymptotes and oblique asymptotes algebraically. **Practice Problems: ****pc-3-6 . YouTube videos: ****Horizontal Asymptotes and Oblique Asymptotes. Homework: ***p. 245 #’s 51, 55 59, 61, 66, (Identify x & y intercepts, find vertical/horizontal/oblique asymptotes, and graph the functions neatly). Also complete #’s 87, 88, and 90. *

**Day 3-5: ****October 20th/21st. **Objective: Students will identify the domain, x-intercepts, y-intercepts, and vertical asymptotes of rational functions. **Notes(Glue-In): **PC3-5 Notes **Practice Problems/Packet: PC3-5 Practice Problems **(this document actually says 2-4, but rest assured, we are doing this for our 5th lesson of chapter 3. **Homework: ***pg 243 #’s 1 and 5, graph #’s 21 and 25, find the vertical asymptotes on #’s 33, 35, and 40, complete problem #85, and preview material on horizontal asymptotes.*

**Extra Calculator Review: **As a practice, you may want to solve these problems to help you with your calculator chops. PC – Calculator Practice

**Day 3-4: ****October 13th/17th. **Objective: Students will find real roots of a polynomial using Descartes Rule of Signs and the Rational Roots Theorem. **Worksheet/Notes: PC 3-4****. Homework: ***p 263 # 3, 11, 14, 17, 23, 25, 30, 43, 44, 63.* Answer to number 63 on the homework. **YouTube Video: **Find the roots I’ve added a few videos on the concepts here. Look at the playlist.

**Day 3-3: ****October 11th/12th. **Objective: Students will find the equation of a polynomial given a root. Students will identify the roots of a polynomial. **Worksheet/Notes: ** PC 3-3 **Homework: **Finish the worksheet from class if not already completed.

**Day 3-2: ****October 7th/10th. **Objective: Students will find the equation of a polynomial given the roots and multiplicity of the zeros. **Worksheet: pc-3-2 **** Homework: **P 202 # 1-8 odd # 21, 41, and 55. P. 224 #1-9 odd, 11, 13, 17, 23, and 67

**Day 3-1: ** **October 5th/6th. **Objective: Students will review concept on quadratics and multiply polynomials. **Worksheets: **PC 3-0 and PC 3-1 . **Homework**: Finish worksheets.

# Unit 2: Functions and Their Graphs

**Helpful Link:** Khan Academy – Functions** **(You could easily familiarize yourself with many concepts using Khan Academy) My Channel for Precalculus

Day 1: **August 29th/30th**. Objective: Students will read syllabus, understand course expectations, and pre-assess unit 1 material. **Worksheet: **Day 1 what do you know. **Supplemental Links:** Is it a function? or What is a function?

Day 2.1 **August 31st/Sept 1st. **Objective: Students will determine if a relation is a function, and determine the domain, range, intercepts, and symmetry. **Homework: **p.125 # 1-13 odd, #21-63 odd. **Scanned copy of HW problems: **2.1-prob.-set-page-1 and 2.1-prob.-set-page-2. (COMPLETE HOMEWORK NEATLY IN A NOTEBOOK SO I CAN EASILY CHECK IT. DO THIS FOR ALL HOMEWORK)

Day 2.2(1) **September 2nd/6th. **Objective: Students will identify intervals in which a function is increasing, decreasing, concave up, and concave down. **Homework: **p. 148 #1-8 all, 9-25 odd NOT (c) and the half-page PC 2-2 supplement max and concavity. **Scanned copy of HW problems:** 2.2-prob.-set-1-page-1 and** **2.2-prob.-set-1-page-2. (COMPLETE HOMEWORK NEATLY IN A NOTEBOOK SO I CAN EASILY CHECK IT. DO THIS FOR ALL HOMEWORK)

Day 2.2(2) **September 7th/8th. **Objective: Students will determine if a function is even, odd, or neither. **Helpful Link: **mathisfun.com **Homework: **p 148 # 9-23 odd (c only) #41-53 odd. **Special Note: ** I teach this on my channel here.

Day 2.2(3) **September 9th/12th. **Objective: Students will learn to graph piecewise functions and write piecewise functions from a graph. **Homework: **p 150 #55-73 odd, #85-88 all. **Helpful Link: **mathisfun.com. **Special Note: **I teach this on my channel here.

Day 2.3 (1) **September 13th/14th. ** Objective: Students will explore horizontal transformations and compare with vertical transformations. **Toolkit Document: PC 2-3 Transformations 1 ****Homework: **p. 162 #1-12 all, #17-51 odd.

Day 2.3(2) **September 15th/16th. **Objective:Students will review parent functions and transformations involving a, h, and k. **Investigation Document: pc2-3trans2 Homework:** Finish the investigation. **QUIZ TODAY!**

Day 2.- REVIEW! **September 19th/20th. **Objective: Students will clarify misconceptions regarding notation and review domain and range. Students will review function notation graphically and algebraically. **Notes: Domain and Range Notes **and PC-NotationGuidelines **Homework: **Read the next lesson on composite functions and preview the homework assignment for next class. ALSO: p. 186 #’s 7, 8, 9, 14, 18, 23, 26, 30, and 45.

Day 2.3 (4) **September 21st/22nd. ** Objective: Students will summarize transformations of functions using a, h, and k. Students will learn how to transform a graph given a transformation without an equation, and apply this to a single point. **Homework: 1) **Finish the assignment **2) **Finish the toolkit **3) **Finish the Glue In . These explain it: video #1 and video #2. Preview composition of functions in book. WATCH THIS VIDEO: Khan Academy **Here is why horizontal transformations work the way they do: Graphing Transformations**

Day 2.4(1) ** September 23rd/26th ** Objective: Students will write the sum, difference, product, and quotient of functions and composite functions, noting the domain of the new function.

**Class work: Functions with tables practice and Creating Functions Practice**

**Homework:**p 170 #5, 7, 9, 11, 27, 36, 38, and 55-65 (odd).

Day 2.4(2) **September 27th/28th.**Objective: Students will find inverses of functions. **Assignment:** PC2-5 Inverses **Homework: **p 308 # 9-14 (all), 21, 25, 27, 30, 43, 47, 52, 64, 65

Review Day: ** September 29th/30th. **Remember, working together is a great strategy for learning. Spend this time wisely!

**Homework:**Review in-class quizzes, all homeworks, and the review from today. REVIEW

**Answer Key**: pc2-reviewkey (Hidden for now)

TEST DAY: **October 3rd/4th**

What questions do you have?

Why does it only go to the end of september? what is the HW assigned on Oct. 10?

Never mind. I was looking at the bottom of the page.

Caleb,

It does list the homework, look up at the top of the page. 🙂 I always put the most recent chapter first.