preCalculus

Trimester 3

Unit #14: Due 3/25/24

IXL:

P. Conic sections

• 1 Find properties of parabolas

• 2 Write equations of parabolas in vertex form

• 3 Graph parabolas

• 4 Find properties of circles

• 5 Write equations of circles in standard form

• 6 Graph circles

• 7 Find properties of ellipses

• 8 Find the eccentricity of an ellipse

• 9 Write equations of ellipses in standard form

• 10 Find properties of hyperbolas

• 11 Find the eccentricity of a hyperbola

• 12 Write equations of hyperbolas in standard form

• 13 Convert equations of conic sections from general to standard form 

Worksheet # 30 : Conic Sections : Properties, Equations, and Graphs of Parabolas : IXL P1->P3

https://docs.google.com/document/d/133UDYhtArQPeZ-cNDbmIkonuYUcHklCPxizbxqKE4KI/edit 

Worksheet # 31: Conic Sections : Properties, Equations, and Graphs of Circles : IXL P4->P6 https://docs.google.com/document/d/1uvHD2DXmQHDv7-pAv0GMqT4ulxCjuIpqhnohYRX7L7c/edit 

Worksheet # 32: Conic Sections : Properties, Equations, and Graphs of Ellipses : IXL P7->P9 https://docs.google.com/document/d/1gtdaPqE6rt5z5oG52GYWk69xKgaG6wbS1q4BTr9-bgM/edit 

Worksheet # 33: Conic Sections : Properties, Equations, and Graphs of Hyperbolas : IXL P10->P12 https://docs.google.com/document/d/1BZBZXjPedLsD5VEcQ0cYkmByIPgFf2OdD0jqzP_9CxQ/edit 

Worksheet # 34: Conic Sections : Convert Form of Conic Sections Equations : IXL P13 https://docs.google.com/document/d/1Y8lLzZbLbDkBEIGR1sO_jgyzp5qq1z_UvQ0VTsQTOEM/edit 

AP Question #2 : AP Precalculus Sample FRQ # 2 : To Be Determined

Good Article on Ellipses : 

https://openstax.org/books/college-algebra-2e/pages/8-1-the-ellipse#:~:text=Thus%2C%20the%20standard%20equation%20of,further%20in%20the%20vertical%20direction. 

Cool Video on Conic Sections : https://www.youtube.com/watch?v=HO2zAU3Eppo 

Cool Video on Ellipses : https://www.youtube.com/watch?v=pQa_tWZmlGs 

Cool Video how to say foci : https://www.youtube.com/watch?v=69iSKKfk6M4 

Unit #Optional (Will Be on AP Precalculus Exam): No Due Date

IXL:

T. Polar form (Optional: Will Be on AP Precalculus Exam)

• 1 Find the modulus and argument of a complex number

• 2 Convert complex numbers from rectangular to polar form

• 3 Convert complex numbers from polar to rectangular form

• 4 Convert complex numbers between rectangular and polar form

• 5 Match polar equations and graphs

Worksheet # TBD: Polar Form : TBD : IXL T1->T5

AP Question #2 : AP Precalculus Sample FRQ # 2 : To Be Determined

Good Articles on Polar Equations : 

https://www.andrews.edu/~rwright/Precalculus-RLW/Text/07-08.html

There are five classic polar curves: cardioids, limaҫons, lemniscates, rose curves, and Archimedes’ spirals. We will briefly touch on the polar formulas for the circle before moving on to the classic curves and their variations. 

https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_1e_(OpenStax)/08%3A_Further_Applications_of_Trigonometry/8.04%3A_Polar_Coordinates_-_Graphs

Trimester 2

Unit #6: Due 12/01/23

IXL:

F. Exponential and logarithmic functions

• 1 Domain and range of exponential and logarithmic functions

• 2 Match exponential functions and graphs

• 3 Convert between exponential and logarithmic form

• 4 Solve exponential equations by rewriting the base

• 5 Evaluate logarithms

• 6 Change of base formula

• 7 Product property of logarithms

• 8 Quotient property of logarithms

• 9 Power property of logarithms

• 10 Properties of logarithms: mixed review

• 11 Evaluate logarithms using properties

• 12 Graph logarithmic functions

• 13 Solve exponential equations using logarithms

• 14 Solve logarithmic equations with one logarithm

• 15 Solve logarithmic equations with multiple logarithms

• 16 Exponential functions over unit intervals

• 17 Identify linear and exponential functions

• 18 Describe linear and exponential growth and decay

• 19 Exponential growth and decay: word problems

• 20 Compound interest: word problems

Worksheet # 7 : Exponential and Logarithmic Functions : Domain, Range, Graphs, Conversions, and Base : IXL F1->F4 https://docs.google.com/document/d/1uM2lL9TNpsqSAmIuf89EFlZG6Db5OxSOjMC1tSIC2TU/edit 

Worksheet # 8 : Expon’t’l and Log. Functions : Logs, Change of Base, Product/Quotient/Power Properties : IXL F5->F10

https://docs.google.com/document/d/1IL1oovlab8m0HKTPi6xxrVuujfAUeHzGZhusFZgF9GM/edit?usp=sharing 

Worksheet # 9 : Expon’t’l and Log. Functions : Evaluate, Graph, and Solve with Logs : IXL F11->F15

https://docs.google.com/document/d/1alYP1zwc_vuduvUYTvjtr-3lfubgslkVktdR1vwAR20/edit 

Worksheet # 10 : Expon’t’l and Log. Functions : Expon't'l Growth and Decay : IXL F16->F20

https://docs.google.com/document/d/17k1kXo_Sr60Bgq58um3l4ziGJ9ugp5zEDQEEeFjaH1k/edit?usp=sharing 

AP Challenge: Complete Algebra 2: Unit 7: Exponential models and Algebra 2: Unit 8: Logarithms on Khan Academy by 11/22/23. 

AP Question #2 : AP Precalculus Sample FRQ # 2 : To Be Determined

Good Article on Exponential Decay: https://www.cuemath.com/exponential-decay-formula/ 

Unit #7: Due 12/04/23

IXL:

G. Radical functions

• 1 Domain and range of radical functions

• 2 Solve radical equations 

Worksheet # 11 : Radical Functions : Domain, Range, Graphs, and Solving Radical Eqns : IXL G1->G2 https://docs.google.com/document/d/176lwEdQ7wg4CyKtFUx5csmeg1UZuBdqlAzgY4mD5TxA/edit 

AP Challenge: Complete Precalculus: Unit 3: Complex numbers on Khan Academy by 12/11/23. 

AP Question #2 : AP Precalculus Sample FRQ # 2 : To Be Determined

Unit #8: Due 12/11/23

IXL:

H. Roots and rational exponents

• 1 Roots of integers

• 2 Roots of rational numbers

• 3 Find roots using a calculator

• 4 Evaluate rational exponents

• 5 Operations with rational exponents

• 6 Simplify radical expressions with variables

• 7 Nth roots 

• 8 Simplify expressions involving rational exponents 

AP Challenge: Complete Precalculus: Unit 3: Complex numbers on Khan Academy by 12/11/23. 

AP Question #2 : AP Precalculus Sample FRQ # 2 : To Be Determined

Unit #9: Due 01/05/24

IXL:

I. Systems of equations

• 1 Solve a system of equations by graphing

• 2 Solve a system of equations by graphing: word problems

• 3 Classify a system of equations

• 4 Solve a system of equations using substitution

• 5 Solve a system of equations using substitution: word problems

• 6 Solve a system of equations using elimination

• 7 Solve a system of equations using elimination: word problems

• 8 Solve a system of equations using augmented matrices

• 9 Solve a system of equations using augmented matrices: word problems

• 10 Solve a system of equations in three variables using substitution

• 11 Solve a system of equations in three variables using elimination

• 12 Determine the number of solutions to a system of equations in three variables 

Worksheet # 12 : Systems of Equations : Graphing, Substitution, and Elimination : IXL I1->I7 https://docs.google.com/document/d/10196vD39K4iwIhEDkHDj_pxtBq5UxjvOFlMST40DTXM/edit?usp=sharing

Worksheet # 13 : Systems of Equations : Matrices : IXL I8>I9

https://docs.google.com/document/d/1MKAdTQoW4A3d1qulL3ATq0GHPXR0UOqW7rdetfhjcaI/edit

Worksheet # 14 : Systems of Equations : Three Variables: IXL I10->I12

AP Challenge: Complete Precalculus: Unit 7: Matrices on Khan Academy by 01/05/24. 

AP Question #2 : AP Precalculus Sample FRQ # 2 : To Be Determined

Unit #10: Due 01/09/24

IXL:

J. Systems of inequalities

• 1 Solve systems of linear inequalities by graphing

• 2 Solve systems of linear and absolute value inequalities by graphing

• 3 Find the vertices of a solution set

• 4 Linear programming 

Worksheet # 15 : Systems of Inequalities : Linear Ineq., Abs. Val. Ineq., and Linear Programming : IXL J1->J4

https://docs.google.com/document/d/1tQsswYVJcJ9187ocoAXJqooqZco7tjs_a9HHOMr-M1s/edit?usp=sharing 

AP Challenge: 

AP Question #2 : AP Precalculus Sample FRQ # 2 : To Be Determined

Unit #11: Due 01/12/24

IXL:

K. Nonlinear inequalities

• 1 Graph solutions to quadratic inequalities

• 2 Solve quadratic inequalities

• 3 Graph solutions to higher-degree inequalities 

• 4 Solve higher-degree inequalities 

Worksheet # 16 : Nonlinear Inequalities : Quadratic and Higher-Degree Inequalities : IXL K1->K4 https://docs.google.com/document/d/1_PqU_kHn3d9FKQnGykkwnmZJR3rXcde80eB0YRH4-cg/edit 

AP Challenge: 

AP Question #2 : AP Precalculus Sample FRQ # 2 : To Be Determined

Unit #12: Due 02/02/24

IXL:

M. Trigonometry

• 1 Convert between radians and degrees

• 2 Radians and arc length

• 3 Quadrants

• 4 Coterminal and reference angles

• 5 Find trigonometric ratios using right triangles

• 6 Find trigonometric ratios using the unit circle

• 7 Find trigonometric ratios of special angles

• 8 Find trigonometric ratios using reference angles

• 9 Inverses of trigonometric functions

• 10 Inverses of trigonometric functions using a calculator

• 11 Solve trigonometric equations

• 12 Trigonometric ratios: find a side length

• 13 Trigonometric ratios: find an angle measure

• 14 Solve a right triangle

• 15 Law of Sines

• 16 Law of Cosines

• 17 Solve a triangle

• 18 Area of a triangle: sine formula 

• 19 Area of a triangle: Heron's formula 

Worksheet # 17 : Trigonometry : Radians, Degrees, Arc Length, and Quadrants : IXL M1->M3

https://docs.google.com/document/d/151EKZPWsI4lI9qK3HdG8JITbo1diLf1FfYj2G0InjJM/edit 

Worksheet # 18 : Trigonometry : Coterminal Angles and Trig Ratios : IXL M4->M6  https://docs.google.com/document/d/1rmWhc6276zy1IXQriXZaj8p072cLGX0THlsesTAHawo/edit 

Worksheet # 19 : Trigonometry : Special Angles, Reference Angles, and Inverse Trig Functions : IXL M7->M10   https://docs.google.com/document/d/1A66jBgE7-lpGmVJyxeDke5Y7d4jFQqKImy3E0V7Bulk/edit 

Worksheet # 20 : Trigonometry : Trig Equations, and Finding Sides and Angles : IXL M11->M13 https://docs.google.com/document/d/1CFhxhGtDsOlgI297KU3adFRp91_sJWlT1N2W504Ra_o/edit 

Worksheet # 21 : Trigonometry : Right Triangles, Law of Sines, and Law of Cosines : IXL M14->M16 https://docs.google.com/document/d/1M3uVnZI-XcABRLwi2kNxg84SIrQSYJiQk1dx007zT1E/edit 

Worksheet # 22 : Trigonometry : Solve a Triangle and Area of a Triangle : IXL M17->M19  https://docs.google.com/document/d/1dIb9To1BblfQpV-dOZ7VT4-xV_dhUoo6GFbGFHmQ4lY/edit

AP Challenge: Complete Precalculus: Unit 2: Trigonometry  on Khan Academy by 02/09/24. 

AP Question #2 : AP Precalculus Sample FRQ # 2 : To Be Determined

Good Articles on Special Right Triangles :

https://en.wikipedia.org/wiki/Special_right_triangle#:~:text=A%20special%20right%20triangle%20is,angle%2Dbased%22%20right%20triangle.

Unit #12: Due 02/16/24

IXL:

N. Trigonometric functions

• 1 Find properties of sine functions

• 2 Write equations of sine functions from graphs

• 3 Write equations of sine functions using properties

• 4 Graph sine functions

• 5 Graph translations of sine functions

• 6 Find properties of cosine functions

• 7 Write equations of cosine functions from graphs

• 8 Write equations of cosine functions using properties

• 9 Graph cosine functions

• 10 Graph translations of cosine functions

• 11 Find properties of sine and cosine functions

• 12 Write equations of sine and cosine functions from graphs

• 13 Write equations of sine and cosine functions using properties

• 14 Graph sine and cosine functions

• 15 Graph translations of sine and cosine functions

Worksheet # 23 : Trig Fcns : Sine Function : IXL N1->N3 

https://docs.google.com/document/d/1JidxkpyGTlQ0Ai3cu7MlnixRGicJNevExp-BaaYOGcs/edit

Worksheet # 24 : Trig Fcns : Graph Sine Functions + Cosine Functions : IXL N4->N6

https://docs.google.com/document/d/15Gm6tu9-SIzBkkHHFAYzi2tXK-rQVg9f83NBGTR9pe0/edit 

No Worksheet #25 : TBD

Worksheet # 26 : Trig Fcns : Properties and Graphs of Sine and Cosine Functions : IXL N10->N12

https://docs.google.com/document/d/1V0yMc78x-5N8D9jlHoewF9IF3p_ImXwD9p_PNLiY6dA/edit 

AP Challenge: Complete Precalculus: Unit 2: Trigonometry  on Khan Academy by 02/09/24. 

AP Question #2 : AP Precalculus Sample FRQ # 3 : To Be Determined

Good Article On ... : 

https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGShift.html#:~:text=the%20horizontal%20shift%20is%20obtained,The%20horizontal%20shift%20is%20C.&text=The%20easiest%20way%20to%20determine,to%20the%20right%20or%20left.

Unit #13: Due 02/27/24

IXL:

O. Trigonometric identities

• 1 Complementary angle identities

• 2 Symmetry and periodicity of trigonometric functions

• 3 Find trigonometric ratios using a Pythagorean or reciprocal identity 

• 4 Find trigonometric ratios using multiple identities 

• • New! Trigonometric sum and difference identities

Worksheet # 28 : Trig Identities : Complementary Angles, Symmetry, and Periodicity : IXL O1->O2

https://docs.google.com/document/d/1UT9CAykJ814jeO6lF4WndzEpYejpL25j3MO3acDLwps/edit 

Worksheet # 29 : Trig Identities : Pythagorean, Reciprocal, Sum, and Difference Identities : IXL O3->ONew!

https://docs.google.com/document/d/1e2oEkhtZkRzZudA_wNpRjEfSI4NXefXvunomIHe43QY/edit 

AP Challenge: Complete Precalculus: Unit 2: Trigonometry  on Khan Academy by 02/09/24. 

AP Question #2 : AP Precalculus Sample FRQ # 3 : To Be Determined

Good Article On ... : 

https://mathbitsnotebook.com/Algebra2/TrigGraphs/TGShift.html#:~:text=the%20horizontal%20shift%20is%20obtained,The%20horizontal%20shift%20is%20C.&text=The%20easiest%20way%20to%20determine,to%20the%20right%20or%20left.

Trimester 1

Do Today: 11/15/2023

End-of-Trimester 1 Student Evaluations of Precalculus Course:

Here's the link: Link: https://forms.gle/tiQ5sMAoMPXpuSaN6  

Intro: Remember to pick up course materials as described in the Course Description. See Syllabus above!

First Assignment: Make your own My Picture Story like Michael did and showed in class in Google Docs or Google Sheets. You should have pictures, music, links, and websites of things you like, and try to tell a story. You may present it to the class. Please make the file viewable and send a viewable link to me at michaelw@school-one.org . Present your My Picture Story by Friday, Tuesday, or Wednesday, September 6th.

Sample My Picture Story: https://docs.google.com/document/d/1oP-9D-tBzsGV1NOxqLoFidDQecSJ04nFBhU-NS3CEoA/edit?usp=drive_link 

Announcement: Join our KhanAcademy.org Class! Go to Teachers, and put in this code: R6STN9R8 . Thank you all!

Tips to Become a Math Genius by New Year's Day!

IXL:

• Method 1: Work on IXL - Assessment, and see the "recommended skills" under each of the six domains. Work on these recommended skills and try to get a SmartScore of 90 on each topic. If your IXL - Assessment page runs out of recommended skills, you can pop back into Step into the Arena, do six questions, and then pop back out to Assessment to see more recommended skills.

• Method 2: Since you're enrolled in Precalculus, you can go to IXL - Learning - Math - Precalculus, and work on the topics in each section to work ahead and learn more!  The more that you do, the more you will learn. 

• Challenge Opportunity: For your challenge opportunity for Precalculus, you have the opportunity to take the AP Precalculus Exam with the College Board for advanced placement in college. This can move you ahead faster in your program or lighten your load in college if you don't have to take this math class for your major. The AP Precalculus Exam is on May 13, 2024 at 12:00pm this year, which we will take at another school on that day. You need to notify your teacher now if you want this option so that we can start to take the steps that will need to be done throughout the year, including enrolling you with the College Board that you're going to take this exam. 

Unit #1: Due 9/8/23

IXL:

A. Functions

• 1 Domain and range

• 2 Identify functions

• 3 Evaluate functions

• 4 Find values using function graphs

• 5 Complete a table for a function graph

• 6 Find the slope of a linear function

• 7 Graph a linear function

• 8 Write the equation of a linear function

• 9 Linear functions over unit intervals

• 10 Add, subtract, multiply, and divide functions

• 11 Composition of functions

• 12 Identify inverse functions

• 13 Find values of inverse functions from tables

• 14 Find values of inverse functions from graphs

• 15 Find inverse functions and relations

Khan Academy:

Precalculus Challenge : Try this Precalculus Course Challenge Test on KhanAcademy.org. How much do you know about Precalculus? How much will you know by the end of the year https://www.khanacademy.org/math/precalculus/test/x9e81a4f98389efdf:course-challenge . Let me know after you try the Khan Academy Precalculus Challenge Test, and I will record your BOY score. 

Unit #2: Due 9/22/23

IXL:

B. Families of functions

• 1 Function transformation rules

• 2 Translations of functions

• 3 Reflections of functions

• 4 Dilations of functions

• 5 Transformations of functions

• 6 Describe function transformations

AP Challenge: Complete Precalculus Unit 1: Composite and inverse functions on Khan Academy by 9/22/23.

Project #1 : Absolute Value Project

Part I : Data Collection Sheet : https://docs.google.com/document/d/1fzcpcMpx9Lt3NHQj9GAdA_T7LUyOMVwIVh8Y7jVPZyA/edit

Part II : Example to Follow : Data, Calculations, and Graph:

https://docs.google.com/spreadsheets/d/1x9eaDjQLRzt4qsJLAuzT1ZnVzPb6YCq4rpY0Zdw70Mc/edit#gid=0

Unit #3: Due 10/06/23

IXL:

C. Quadratic functions

• 1 Find the maximum or minimum value of a quadratic function

• 2 Characteristics of quadratic functions

• 3 Graph a quadratic function

• 4 Match quadratic functions and graphs

• 5 Solve a quadratic equation using square roots

• 6 Solve a quadratic equation by factoring

• 7 Solve a quadratic equation by completing the square

• 8 Solve a quadratic equation using the quadratic formula

• 9 Solve quadratic equations: word problems

• 10 Using the discriminant

AP Challenge: Complete Algebra 2: Unit 1: Polynomial arithmetic and Algebra 2: Unit 3: Polynomial factorization on Khan Academy by 10/06/23. [Khan Academy doesn't have polynomials in Precalculus, but it's an essential skill, assumed that the student has this knowledge.]

AP Question #1 : AP Precalculus Sample FRQ # 1 : Functions, Composition of Functions, Limits, Modeling

https://drive.google.com/file/d/16Wsq8kwedqWgvbAbKWg7u-Zibr8Wq_fS/view?usp=sharing 

Unit #4: Due 10/27/23

(NEW DUE DATE 10/27/23: We need more Time to go over notes on D11->D20.) 

IXL:

D. Polynomials

• 1 Divide polynomials using long division

• 2 Divide polynomials using synthetic division

• 3 Evaluate polynomials using synthetic division

• 4 Find the roots of factored polynomials

• 5 Write a polynomial from its roots

• 6 Rational root theorem

• 7 Complex conjugate theorem

• 8 Conjugate root theorems

• 9 Descartes' Rule of Signs

• 10 Fundamental Theorem of Algebra

• 11 Match polynomials and graphs

• 12 Domain and range of polynomials

• • New! Even and odd functions

• 13 Factor sums and differences of cubes

• 14 Solve equations with sums and differences of cubes

• 15 Factor using a quadratic pattern

• 16 Solve equations using a quadratic pattern

• 17 Pascal's triangle

• 18 Pascal's triangle and the Binomial Theorem

• 19 Binomial Theorem I

• 20 Binomial Theorem II 

Worksheet #1 : Polynomials : Long Division and Synthetic Division : IXL D1->D3

https://docs.google.com/document/d/16eld3jesCqXGDkeMlwPiYlBevgkm-roiGxsRrXqBU2g/edit

Worksheet #2 : Polynomials : Roots of a Polyn. and Rational Root Thm : IXL D4->D6

https://docs.google.com/document/d/14AZcDHDqVC37vg5Q5KAyyS4sxbNURpK8AoQs6PLwRmg/edit?usp=sharing

Worksheet #3 : Polynomials : Build Polynomials from Real and Complex Roots : IXL D7->D10

https://docs.google.com/document/d/1caO5zhLsvVVER2slRNFdo5-JX7qJmPSg8Z6TkRUGwUg/edit

Worksheet #4 : Polynomials : Odd, Even, Cubes, and Factoring : IXL D13->D16

https://docs.google.com/document/d/1vjp2OhVzxtRisOh5lePX46TrWvfq5JtDoPp-Ar-7SUo/edit?usp=sharing

Worksheet #5 : Polynomials : Pascal's Triangle and Binomial Theorem : IXL D16->D20

https://docs.google.com/document/d/1yrMA16F7m1tTb7A4-iAYDxfPW8azuMtsxqBrz9CdQP4/edit?usp=sharing

AP Challenge: Complete Algebra 2: Unit 4: Polynomial division and Algebra 2: Unit 5: Polynomial graphs on Khan Academy by 10/20/23. [Khan Academy doesn't have polynomials in Precalculus, but it's an essential skill, assumed that the student has this knowledge.]

Unit #5: Due 11/03/23

IXL:

E. Rational functions

• 1 Rational functions: asymptotes and excluded values

• 2 Solve rational equations

• 3 Check whether two rational functions are inverses 

Worksheet # 6 : Rational Functions : Asymptotes, Solving Equations, and Inverses : IXL E1->E3 

https://docs.google.com/document/d/1AQbe3m2VEXhhlEY2Sm0PVmJ3IoBPpZJwvvNK3dvg2ks/edit 

AP Challenge: Complete Precalculus: Unit 4: Rational functions on Khan Academy by 11/05/23. 

AP Question #2 : AP Precalculus Sample FRQ # 2 : To Be Determined

END OF Trimester 2 TO DO:

TODO: End of Tri 2 Student Class Evaluation Form:

https://forms.gle/WdFpnbp2wrryGiYh7  

Final IXL End of Tri 2 Diagnostic: All students: Bring your IXL Diagnostic up to date to the highest level possible. I will give you a report on how well you're doing. If you're up significantly, then I can praise you on that in your Trimester 2 evaluation.