PreCalculus 2018-2019

Below are the posts from the 2018-2019 school year.

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

Semester 2 Tentative Schedule:  PCSemester2Schedule


Course Feedback – Course Evaluation

Calculus Preview

Day 2:  Examine Limits using a table of values.  Warm-up:  PC9-2WarmUp

Day 1:  Examine Limits Graphically

Final Exam – Semester 2

Review:  2ndSemesterFinalReview  Review Key:  2ndSemesterFinalReviewKEY

Final Exam Schedule:

B-Day – Part 1 of the Final Exam is Tuesday, May 28th.  Part 2 is Thursday, May 30th.

A-Day –  Part 1 of the Final Exam is Wednesday, May 29th.  Part 2 is Friday, May 31st.

Following the final exam, all non-seniors will be get feedback on their final.  The remainder of the year will be a preview of Calculus lessons and ideas.

Chapter 8:  Conic Sections/Polar Coordinates

This unit will be touched upon while AP tests are occurring.  No homework during this time.

Day 74:  May 13th/14th.  Objective:  Students will analyze parametric equations graphically and algebraically.  Notes:  PC8-3Notes Notes Key:  PC8-3NotesKey Practice Problems:  PC8-3EllipsePractice

Day 72 – 73.  Notes on Conic Sections:  PC8-2NotesStudentCopy   Conic Sections Practice:  PC8-2PracticeProblems


Chapter 7:  Vectors

Day 71:  April 26th/29th.  Objective:  Students will review unit concepts to prepare for an individual test next class.  Review:  PC7-Review KEY: PC7-ReviewKEY

Day 69 and 70:  April 22nd – 25th.  Smarter-Balanced Testing for Juniors in room SS220. Practice Problems on Vectors:  PC7-PracticeReview KEY:  PC7-PracticeReviewKEY

Day 68:  April 18th/19th.  Objective:  Students will solve applied vector problems.    Homework: p. 628 #89 and #90.

Day 67:  April 16th/17th.  Objective:  Students will solve applied mathematics problems using vectors. Class Review/Practice:  PC7-3TableGroupPracticeReview Homework:  p. 628 #’s 77 and #78.

Day 66:  April 12th/15th.  Objective:  Students will find the unit vector in the same direction as another given vector.  Students will find the direction angle of a vector, as well as its component form.  Homework:  p. 627 #’s 50, 51, 52, 60, 61, 62, 68, 69, and 70.

Day 65: April 10th/11th.  Objective:  Students will define vectors and learn various notation for working with vectors.  Homework:  If you haven’t already, read and take notes on pages 616 to 620.  Complete the problems on page 626 #’s 3-8, 15, 16, 31, 32, 35, 36, and 37.

Chapter 6:  Applications of Trigonometric Functions

Day 64: April 5th/9th:  Objective:  Students will work collaboratively in order to complete a group portion of a test.  Students will work independently in order to complete an individual portion of a test.  Homework:  TBD

Day 63: April 3rd/4th:  Objective:  Students will persevere in problem solving in order to prepare for a test.  Review Answer Key:  PC6-ReviewKey Homework:  Study the review as well as the PC6-5GroupPractice.

Day 62: April 1st/2nd:  Objective:  Students will draw diagrams to assist in solving elementary vector problems.Notes:  PC6-5Notes  Class Practice: PC6-5GroupPracticeHomework:  Complete at least the front of the unit review: PC6-Review

Day 61:  March 21st/22nd:  Objective:  Students will select the correct mathematical tool to solve application problems. Notes: PC6-4Notes Homework:  p. 552 # 41 (draw the diagram, show work, answer the question in a complete sentence)

Day 60:  March 19th/20th:  Objective:  Students will apply various trigonometric laws and theorems in order to solve word problems.  Homework:  p. 560 # 46 (draw the diagram, show work, answer each piece of the problem)

Day 59:  March 14th/15th:  Objective:  Students will apply the law of cosines to non-right triangles.  Homework:  G 7-5 Law of Cosines and Sines

Day 58:  March 12th/13th:  Objective:  Students will apply the law of sines to non-right triangles.Class Notes 2: PC6-1DiagramNotes Class Notes 2: PC6-1Notes Homework:  G 7-4 Law of Sines

Chapter 5:  Analytic Trigonometry

Day 56:  March 8th/11th.  Objective:  Students will complete an individual test.  Preparation includes the Review, Group Test, Homework, Class Work, and Daily Quizzes.  Use all of them to prepare.  

Day 56:  March 7th.  Objective:  Students will complete a unit review.

Day 55:  March 5th/6th.  Objective:  Students will complete a group test and a review.  Group Test:  PC5-GroupTest Review:  PC5-Review Review Key:  PC5-ReviewKey

Day 54:  March 1st/4th.  Objective:  Students will use half-angle formulas to find the exact value of the expression. Video:   Half-Angle Formulas.   More Notes:  PC5-5NotesKey   PowerPoint Notes:  PC5-5HalfAngle  Homework:  p. 518 #’s 20, 21, 26, 27.  Study for the group test on Tuesday.

Day 53:  Period 5:  Homework due on Monday March 4th:  p. 518 #’s 1,4,5,6.  #’s 7 and #8 (part’s A,B, and E only).Sneak Preview of the Group Test:  PC5-GroupTest  Period 1,2,3:  Homework due Friday March 1st is still p. 518 #’s 1,4,5,6.  #’s 7 and #8 (part’s A,B, and E only).

Day 52:  February 25th (Monday)/26th (Tuesday)/28th (Thursday).  Objective: Students will apply double angle formulas to various situations.Skill Builder: PC5-4SkillBuilder  Skill Builder Answer Key: SkillBuilderKey Class Practice: PC5-4A Notes from Class Practice: PC5-4AKey Homework:  p. 518 #’s 1,4,5,6.  #’s 7 and #8 (part’s A,B, and E only).

Day 51: February 21st/22nd.  Objective:  Students will apply the sum and difference formulas to various situations.  Notes:  PC5-4 (includes tangent example)  Homework:  p. 508 #’s 37 and #75.  Period 5 ONLY:  I know most of you were taking the ACT last class.  You need to examine the PC5-4 notes as well as the video from YouTube about Sum and Difference Formulas.  Use that to complete the document PC5-3A.  For homework you will complete the assignment listed on Feb. 19th/20th below.  There is also an older video from YouTube you can watch to help you.


Day 50:  February 19th/20th.  Objective:  Students will use sum and difference formulas to evaluate trigonometric expressions. Notes(PowerPoint):  PC5-3Slides  Homework: p. 508#’s 5,6,7,8,19,23, and 27 (5th period will have an extension on this assignment)

Day 49  February 14th/15th.  Objective:  Students will solve trigonometric equations using factoring and identities.  Assignment:  PC5-2B Notes: PC5-2Notes2 Homework:  p. 497 #’s 28, 29, and 30.  p. 487 #’s 11, 17, and 64.  Bonus problem for an extra stamp:  p. 487 # 109.

Day 48:  February 12th/13th.  Objective:  Students will solve trigonometric equations for solutions on an interval.  Notes: PC5-2Notes  Assignment/Homework:  PC5-2A YouTube video:  Solving Trig Equations

Day 47:  February 8th/11th.  Objective:  Students will establish trigonometric identities.  Homework:  p. 497 #’s 19-27.

Day 46:  February 6th/7th.  Objective:  Students will establish trigonometric identities.  Homework:   Study for re-test in class.

Day 45:  February 4th/5th.  Objective:  Students will establish trigonometric identities.  Homework:  Your new textbook starts section 6.4 on page 491.  First, I want you to add the Even-Odd identities on page 492 into your notes.  Second, complete the practice problems on page 496 #’s 1-14.  Make sure to copy down the entire problem in order to receive full credit.  Do not simply write “true” or “false” for problems 1 and 2.

Day 44:  January 31st/February 1st.  Objective:  Students will provide feedback as to how they would handle a scenario via a google form.  Students will simplify trigonometric expressions. Survey Form: Use this link to provide feedback based on the scenario.  You are welcome to spend about 15 minutes on this if needed.  Please don’t write one word answers – take your time and think about what you would do.    Student Success Form Homework:  PC5-1Assignment (Just do the front) Hint:  Use the notes to match the functions up with the various identities.  Make sure you try each one.  5th period – Sorry I’m not there, but just try your best today.  We will go over this Tuesday.  Don’t forget about your group test corrections!

Unit 4 – Trigonometry and the Unit Circle

2019-01-15 11.16.44

Day 43:  January 29th/30th.  Objective:  Students will prove their knowledge by completing an individual test.  Homework:  Bring your student ID to class so we can check out our new textbook!

Day 42:  January 25th/28th.  Objective:  Students will prove their knowledge by completing a group test.  Homework:  Complete the PC 4 – Review Review Key: PC-4 Review Key and study for the individual test next class.

Day 41:  January 23rd/24th. Objective:  Students will find the inverse of a trigonometric function.  Course Survey:  Semester 1 Survey  Notes: PC4-6 Notes 1 of 2  PC 4-6 Notes 2 of 2 Homework:  PC 4-6 Inverse.  Also, check out this STEM opportunity.

Day 40:  January 16th/17th/18th.  Objective: Students will locate zeros on a graph.  PC 4-5 Notes From Class Homework:  PC 4-5 Practice Problems2019-01-16 19.34.43

Day 39:  January 15th.  Objective:  Students will review trigonometry.  Skinny Day! All 8 periods today

Day 38:  January 11th/14th. Objective:  Students will graph one cycle of a trigonometric function. Notes:  PC 4-4 Notes Practice Problems: PC4-4 Practice Homework:  p. 450 #’s 1-9 odd, #’s 21-26, #’s 43- 46 (you may just graph #’s 43-46, don’t worry about the “steps” for them).

Answer Keys (Due to popular demand)

 PC4-3 Front PC 4-3 Back
PC 4-4 Front  PC 4-4 Back

Day 37:  January 9th/10th. Objective:  Students will draw reference triangles and determine the quadrants given a trigonometric function.  Notes: PC 4-3 Notes  Homework:  p 429#’s 1-7 odd, 17, 19, 25, 29.  #’s 33 – 39 odd.

Day 36:  January 7th/8th.  Objective:  Students will draw reference triangles to define the value of the six trigonometric functions.  Counting to Pi:  Count to Pi Notes:  pc4-2notes  Homework:  p. 417 #’s 1-9 odd, #’s 33, 37, 41, 45, 47, 53, and 57.

Day 35:  January 3rd/4th.  Objective:  Students will convert between radian and degree angle measure.  Students will recognize patterns in the unit circle.Notes:  PC4-1Notes2 Skill Builder: PC4-1Skillbuilder  Homework: p 404 #’s 3-39 odd, 57, 61, 69 and 75.  Finish the Unit Circle!


First Semester Final Exams

A-Days:  Monday – Final Part 1        Wednesday – Final Part 2

B-Days:   Tuesday – Final Part 1        Wednesday – Final Part 2

Day 34:  December 10/11/12/13:  Objective:  Students will prove their knowledge by completing a final exam. Homework:  Have a safe and restful winter break.  When we return we will start Trigonometry!

Day 33:  December 6th/7th.  Objective:  Students will prepare for their final exam.  Homework:  Study.  PC-FinalSemester1-Glue IN (What to study)

Day 32:  December 4th/5th.  Objective:  Students will identify learning targets that will be assessed on the final exam.  Students will review material from final exam learning targets.  Study Guide:  Math 111 Study GuideAnswer Key:  Math 111 Answer Key Homework:  PC-1stSemesterReviewProblems Review KEY:  PC-1stSemesterReviewProblemsKEY

Chapter 3:  Exponentials and Logarithms

Group Test:  Wednesday/Thursday  Individual Test:  Friday/Monday

Day 31:  November 30th/December 3rd. Objective:  Students will complete an individual test.  Homework:  Start reviewing for the final – math_111_final_exam_review. (you don’t need to complete the whole thing!  Work on it for about 30 – 45 min)

Day 30:  November 28th/29th.  Objective:  Students will complete a group test.  Homework:  Study for the individual test.

Day 29:  November 26th/27th.  Objective:  Students will interpret logistic growth models using a graphing utility.  Notes:  PC3-4Notes In-Class Practice:  PC3-4PracticeProblems Review Key: PC3-ReviewKey Homework:  PC3-Review

Day 28:  November 15th/16th.  Objective:  Students will apply growth and decay models to real world problems.  Notes: PC3-3Notes Practice Problems from this class: PC3-3GroupPractice New Video on Carbon-Dating: Exponential Decay (Carbon Dating) Video Second New Video on Population Growth: Exponential Growth Homework:  p. 367 #’s 1, 2, 3, 9, and 11.

Day 27:  November 13th/14th.  Objective:  Students will calculate the future value of a lump sum of money as well as the time required to double or triple an investment. Notes:  PC3-2Notes(Part1) and PC3-2Notes(Part2)  Homework:  PC3-2InterestPracticeProblems

Day 26:  November 8th/9th.  Objective:  Students will determine the domain of a logarithmic function.  Students will apply properties of logarithms to solve for x.  Notes: PC3-1Notes Students that need extra practice:  Do the homework, but also complete #’s 2, 4, 6, 12, and 49 too.  Homework:   p. 349 #’s 1, 3, 7, 9, 13, 15, 21, 52.

Chapter 2:  Polynomials and Rational Functions

Scheduled Testing Day’s:  A-Day:  11/6  B-Day:  11/7

Day 25:  November 6th/7th.  Objective:  Students will prove their knowledge by completing a chapter test.  Homework:  1) Preview the next unit by completing PC3-0Homework 2)  Watch Circle of Logs Video

Day 24:  November 2nd/5th.  Objective:  Students will review for a chapter test.  Review:  PC2-Review Review Key: PC2-ReviewKEY Homework:  Prepare for our unit test next class!

Day 23:  October 31st/November 1st.  Objective:  Students will analyze rational function graphs in order to write a possible equation of the rational function.  Warm-Up: Complete this survey Quarter 1 Survey  Homework: PC2-7Homework

Day 22:  October 26th/30th.  Objective:  Students will find horizontal and oblique asymptotes of rational functions in addition to any points of intersection with horizontal/oblique asymptotes and the graph of the rational function. Notes:  PC2-6Notes Notes Key: Front – PC2-6NotesKeyFRONT back – PC2-6NotesKey Homework:  PC 2-6 Homework

Day 21:  October 24th/25th.  Objective:  Students will identify x and y-intercepts, vertical asymptotes, and holes in the graph of a rational function.  Notes/Practice:  PC2-5Notes Notes Key: PC2-5NotesKey(part1) (front)  PC2-5NotesKeyBack(part1) and PC2-5NotesKey(part2) Homework:  Read pages 231-235.  Copy all of example 7 on page 235.  Complete the PC2-5 Practice Problems   Page 243 complete #’s 11-16 all

Day 20:  October 22nd/23rd.  Objective:  Students will apply Descartes Rule of Signs to determine the number of positive, negative, and imaginary zeros of a polynomial.  Students will apply the Rational Zeros Theorem to a polynomial to determine the potential rational zeros. Notes/Practice: PC2-4Notes Notes Key: PC2-4DescartesNotes and PC2-4RationalZerosNotes Homework:  p. 264 #’s 11-17 odd, 23-29 odd, 61 and 63.

Day 19:  October 18th/19th.  Objective:  Students will use complex roots to write the equation of a polynomial in standard form.  Notes:  Part 2 of PC2-2Notes Notes Key: PC2-2Part2NotesKey Class Practice: Part 2 of PC2-2PracticeClasswork Homework:  p. 279 #’s 1-9 odd, #’s 11-15 odd, #’s 17-23 odd.

Day 18: October 16th/17th.  Objective:  Students will write the equation of a polynomial given the roots and the degree of the polynomial.Warm-Up:  PC2-2WarmUpKey Notes: Part 1 of PC2-2Notes Notes Key: PC2-2Part1NotesKey Class Practice: Part 1 of PC2-2PracticeClasswork  Homework: p. 224 #’s 1-9 all, #’s 11-19 odd, #’s 57, 58, and 59.

Day 17:  October 11th/15th.  Objective:  Students will construct polynomials from roots.  Notes:  PC2-1Notes Class Practice:PC2-1(a)  Homework: p. 263 #’s 1-8 all.  The Factor Theorem uses the same skill you had for homework last class.  In problem #1, use c=2 to write the factor (x-2) to see how f(x) can be fully factored or not.  Try each problem.  Ch3PCBook

Chapter 1 – Part 2:  Transformations, Inverses, and Compositions of Functions

Day 16:  October 8th/9th.  Objective:  Students will prove their knowledge by completing an individual test.  Homework:  PC2-0

Day 15:  October 4th/5th. Objective:  Students will collaborate to complete a group test in order to prepare for an individual test on Monday/Tuesday.  Homework:   Study for the individual test!

Day 14:  October 2nd/3rd.  Objective:  Students will review unit material to prepare for a group test and individual test. Unit Review: PC1-Review(2) Review Key:  PC1-Review(2)KEY Group Test is next class!  Individual Test will be Monday/Tuesday!  Homework:  study!

Day 13:  September 28th/October 1st.  Objective:  Students will find the inverse of a function algebraically and graphically. Class Notes:  PC1-9InverseNotes Additional Notes Scan:  PC1-9NotesFrontScan  Homework:  1) Finish classwork worksheet Classwork PC 1-9 and 2)  p.  309 #’s 43, 44, 47, 49, 51, and 52 (Just find the inverse of these functions) Ch4PCBook.  Side Note:  If you are wondering why you can’t divide by 0, watch this video:  Dividing by zero?  It might help you conceptualize some things that we’ve discussed before.

Day 12:  September 26/27.  Objective:  Students will perform operations on functions as well as compositions of functions. Notes Part 1: PC1-8NotesPart1 Notes Part 2: PC1-8NotesPart2 Classwork Practice Problems:  PC1-8Practice Homework:  p. 170 #’s 1, 3, 5, 7, 21, 23, 25 (you don’t need to find the domain)

Day 11:  September 24th/25th.  Objective:  Students will perform transformations and write coordinate rules for them. Notes: PC1-7Notes  Homework:  complete this document:  PC1-7PracticeProblems

Day 10: September 20th/21st.  Objective:  Students will perform transformations given a graph, equation, or point on a graph. New YouTube video of Notes: Transformations  Exploration Notes Part 1:  PC1-6ExplorationPart1Completed  Exploration Notes Part 2: PC1-6ExplorationPart2Front  and PC1-6ExplorationPart2Back Homework:  p. 162 #’s 1-24 all (make sure to graph the equations shown).

Day 9:  September 18th/19th: Objective:  Students will evaluate the difference quotient given a function. Notes: PC1-5Notes  Completed Notes: PC1-5NotesCompleted Homework:  Finish all the classwork problems here:  PC1-5ClassPracticeProblems.  Also complete p. 150 #’s 81-84.  In these problems, simply evaluate the difference quotient.

Chapter 1:  Functions and Their Graphs

Day 8:  September 14th/17th.  Objective:  Students will prove their knowledge on Functions and their graphs.  Homework:  None.

Day 7: September 12th/13th.  Objective:  Students will review unit material to prepare for a test next class.  Unit Review:  PC1-Review(1) Review Key:  PC1-Review(1)KEY (I made a mistake on number 4, so I apologize).  We will go over exactly why #4 isn’t a good example problem later, but you can use other example problems from homework and daily quizzes instead.  TEST NEXT CLASS!

Day 6:  September 10th/11th.  Objective:  Students will determine if a function is even, odd, or neither both algebraically and graphically. Glue-In: PC1-4 Notes Completed Glue-In: PC1-4GlueComplete Class work: PC1-4PracticeProblems Homework:  p 148 #’s 9-19 odd (part c only) #’s 41-51 all problems.

Day 5:  September 6th/7th.  Objective:  Students will determine the intervals for which a function is concave up or concave down. Glue-In:  PC1-3GlueIn Glue-In(Completed):  PC1-3GlueInCompleted Class Investigation: PC1-3InvestigationNotes Investigation Answer Key: PC1-3InvestigationNotesSolutions  Homework:  Tonight’s homework will be to complete all of these problems: PC1-3HomeworkSet.  Homework Set Solutions:  PC1-3HomeworkSetSolutions

Day 4: September 4th/5th.  Objective:  Students will define piecewise functions from a graph.  Students will determine the intervals that a function is increasing, decreasing, and constant. Investigation #1 and #2 (Piecewise Functions/Intervals Increasing and Decreasing): Investigation and Notes Completed Notes #1: Piecewise Functions Completed Notes #2: Intervals Increasing/Decreasing  Homework:  p. 148 #’s 1-8 all (draw the graphs too) #’s 9 – 19 odd (only do a and b parts – skip part c and d), #’s 85, 86, 87, and 88 (draw the graphs too).

Day 3: August 30th/31st.  Objective:  Students will write the domain of a function using set notation given an equation or graph.  Students will write the range of a function using set notation given a graph.  Notes(blank):  PC1-1Notes Filled in Notes: PC1-1NotesComplete Practice Problems from class:  PC1-1 Homework:  p. 125 #’s 17, 23-31 odd, #’s 37, 39, and 41, #’s 49 – 59 odd.

Day 2:  August 28th/29th. Objective:  Students will assess quiz feedback, familiarize themselves with classroom routines, and find the domain and range of a function.  Classwork:  PC1-0Stations Classwork Solutions:  PC1-0StationsSolutions Homework:  p. 125 #’s 1-11 odd, #’s 13, 15, 21, and 33.  Show your work.

Day 1: August 27.  Objective:  Students will familiarize themselves with class rules and routines as they analyze the learning objectives for the school year.  Course Syllabus: PCSyllabus Homework:  Visit this website (if you are reading this, congratulations).  Watch the first three videos on My Channel for Precalculus .  Begin obtaining necessary course materials and see me if you need help.