- Jason Stevens
- Math ~ High School
Welcome to Precalculus! You will find it a fun-filled and challenging educational experience! The course has two primary purposes:
1. Build a general set of skills and thinking skills students can use for the rest of their lives. Students will practice how to be effective communicators, analytical and creative thinkers, adept navigators of technology, inquisitive and persistent problem solvers, and reflective explorers of ideas. We will strive to make many mistakes and see them as opportunities for growing our brains. Students will build flexibility with numbers and sharpen their estimation skills.
2. Build mathematical proficiency around a specific set of Precalculus concepts. The course includes a thorough exploration of trigonometry as well as functions, modeling, mathematical analysis, probability, numbers and patterns, statistics, and calculus. The content is prioritized in terms of its relevance for future math classes, exams like the SAT or the SRJC math placement test, and the life after school. We will strive for deeper conceptual understandings that go beyond procedural skills. There will also be an emphasis on modeling, analyzing data, and writing reports.
Due Friday 5/29
HW: prepare final project presentation for Zoom meeting at 9:30am on May 29th. (See instructions below.) Remember to email Jason as soon as you know your desired topic.
HW #46: Year-End Review Handout. Check answers with answer key. You do not have to submit this assignment.
Due Friday 5/15
5/8 Zoom Meeting: discuss project and look at Feedback Handout and A.L.’s project from last year.
Review and Applications of Vectors
Grouptest: Vectors Practice Test (Answer key attached as a resource. You do not need to complete this on your own.)
HW: complete online Unit 9 - Vectors Quiz (using Google Forms)
HW: complete Vectors Project – Compatibility. Email your digital document or photos.
Due on Friday, 5/8
Vector Equations of Lines. Print HW #44 handout (attached below) and watch the instructional video. Later, check answers with answer key. How can we track the movement of an object along a linear path?
Vector Applications. Print HW #45 handout (attached below) and watch the instructional video. Later, check answers with answer key. How can we track movement in three-dimensional space? How is speed related to the x,y,z components of movement? How can we calculate the distance between objects, or the angle between two objects’ paths?
HW#44: Finish handout on vector equations of lines.
HW #45: Finish handout on vector applications. (#5 is optional challenge problem. Last two pages of equations through two points using Desmos are optional review.)
Due on Friday, 5/1
9.5 Dot Product: Multiplying Vectors and the Angle Between Two Vectors.
- Read this article closely, including watching the video that is there. This is the best website I know of that explains our content for this week.
- Watch this video: Vectors - The Dot Product.
- Read through the CW answer key (print if you can) and then watch the video that takes you through a couple of sample problems.
- Look through book Lessons 9.5 and 9.6 and refer to examples when doing the homework.
HW#43: Lesson 9.5 #2-4,9-19odd. Lesson 9.6 #27-35odd, 51-57odd.
Due on Friday, 4/24
9.4 Vectors: How can we describe the components of movement in 3-dimensional space?
Vector Topics: Definitions & Notations, Combining Vectors, Components of Vectors, Magnitude, Unit Vectors, Practice Problems and Applications
Instructional CW Answer Key is below. Please also watch these instructional videos: Intro to Vectors and Scalars, Components of Vectors, Vector Magnitude from Initial and Terminal Points, Scalar multiplication of vectors, Adding and subtracting vectors, Graphically adding and subtracting vectors, Unit Vector Intro, Worked example: finding unit vector with given direction, Vector components from magnitude and direction.
HW#42: Lesson 9.4 #15-55odd, 59, 60, 65, 71, 73 (use green light policy as necessary).
Due Friday 4/17
HW: Complete the rest of the Coronavirus Math Assignment. I added new material to the end of it specifically for our class, including an equation that can be used to create a bell-shaped curve for modeling the "peak" before the decline.
*NOTE: You do not need to send me any content “classwork” or homework, though you can ask me for help by email or during our optional Friday 10am Zoom HW reviews. You only need to send me your projects, and no projects are due this week, so there is nothing to turn in this week.
Class on 3/13
Palo Alto’s Famous Frisbee over House Problem
Hand out Extension Problems
Hand out Unit 8 Project
Unit 8 Individual Quiz: Triangle Trigonometry
Hand out Final Semester Projects and discuss (will do next class)
HW: Unit 8 Project (Draft due Wed). HW: optional review for extra credit: page 560: 1-5, 7-9, 11-14.
Class on 3/11
8.4 Area of Oblique Triangles & Heron’s Formula
Notes – Unit 8
Groupquiz – Unit 8
HW#41: Ch 8 Review #7-9, 13, 21, 23, 24, 31, 44. Extension: #37.
Class on 3/6
8.2 Law of Sines – SSA Ambiguous Case
8.3 Law of Cosines
HW#40: 8.2 #27, 31, 33. 8.3 #2-4, 9, 15, 25-29odd, 44.
Class on 3/4
No kickoff: could just start challenge problem on 8.2 handout
(show parametric…. since we are skipping. optional to share conic art projects.)
Start Unit 8: Soh-Cah-Toa Review
Height of a Mountain Problem
8.2 Law of SinesHW#39 : 8.1 #77. 8.2 #3, 4, 9, 11, 17, 23, 37, 49, 56.
Class on 2/28
Unit 6 Individual Test: Conic SectionsHW: Finish Unit 6 Project - Conic Art
Class on 2/21
Unit 6 Grouptest: Conic Sections
HW#36: Handout – Applications of Conics & Review
Class on 2/19
Presentation - Conic Reflection Properties & Their Real-World Appearances and Uses
Notes – Unit 6
HW#35: USE GRAPH PAPER!!! 10.2 #33, 35(equation and graph only ). 10.3 #33, 49, 75. 10.4 #29, 35, 37, 43, 49, (center, vertices, asymptotes, and sketch only). Extra Credit +2 HW Pts: 10.4 #77
Class on 2/12
10.1 Conic Sections and Slicing of a Cone
1.4 Circles & 10.2 Parabolas & 10.3 Ellipses and Foci
HW#34: Section 1.4 #25, 27, 59, 61. Section 10.2 #2-6, 21-31odd (equation and graph only), 39, 51, 53, 57-61odd (use vertex form). Section 10.3 #7-9, 17-21odd, 27-31odd, 39-47odd, 57.
Class on 2/7
Discuss Unit 6 and hand out Unit 6 Conic Art Project (and show demonstration)
10.0 Introduction to Conic Sections.
Examples of definitions: circle string, line and point on field, ellipse video
HW #33: 1. Read all page 639. 2. Read all of pages 34-35. 3. Section 1.4 #1, 4-7, 9-17odd (write standard form only), 37, 41, 49, 51. 4. Explore and record how having a nonpositive number on the right (nonvariable) side of a conic section equation affects the existence of solutions. For example, can x2 + y2 = -5 ? Can x2 + y2 = 0 ?
HW: (due on 2/19) Unit 5 Project Tasks
Class on 1/31
Time to go over unit 5 Review Handout
Unit 5 Project Scaffold – Discussion & Examples: How can we model situations with all six trig functions: sin, cos, tan, csc, sec, and cot?
Desmos crazy graph example
Unit 5 Take-Home Test and Projects Handed Out
HW: Unit 5 Take-home quiz (including “crazy” graph that involves a combination of functions) (due Friday, 2/7)
HW: Unit 5 Project (due Wednesday 2/19)
Class on 2/5
AMC Math Exam (not graded)
HW: Finish Unit 5 Take-Home Test
Class on 1/29
Building y = sinx + sin(2x). More on combinations of functions.
Unit 5 Partner Practice Test
HW#30: Unit 5 Review Handout
HW Extra Credit: Work on the 2009 Math AMC 12 Practice Test
Class on 1/17
Presentation of HW graphs
Practice Solving and Simplifying Trig Functions
Activity: Flip over function and operation cards. Determine three points and sketch graph.
Combo Functions – Intro & Combo Functions: Use the context of CO2 levels in the atmosphere.
Hand out the following early: HW #29, HW #30, Unit 5 Notes
HW: Finish 1st Semester Project (due by 4pm, Tuesday, 1/21 – late projects not accepted)
HW #29: Combination of functions handout.
Class on 1/15
6.3 and 6.5 Tangent, Pythagorean Identity Overview of Trig Properties
HW#28: 6.5 #7, 17, 21. pg 434 #5-9odd.
Also, prepare your short presentation on how to build the graph of: y=cscx , y=secx , y=cotx , or y=3tan((pi/2)(x-1))+5 (*You’ll be assigned one of these.)
HW: Continue to work on 1st Semester Project
Class on 1/10
Unit 5 Modeling Handout: Modeling, Algebraic Equations through Specific Points, Extrapolation, etc. (Scaffolding for 1st Semester Project)
Look at Project Examples from Previous Years
HW: Continue to work on 1st Semester Project. Optional HW: Finish Unit 5 Modeling Handout from class
Class on 1/8
Check-in regarding 1st Semester Project Topic and Data
Final Exams returned
5.8 Logistic Functions
HW#26: Lesson 5.8 #23, 26. Then, determine a logistic equation by hand with a carrying capacity of 500 that goes through the points (0 , 10) and (2 , 50). Show all work. Next, determine a logistic equation by hand with a carrying capacity of 500 that goes through the points (1 , 10) and (2 , 50). You will get stuck on Part III—work through it!
Class on 12/18
Final Exam – Semester 1: Units 1-4
HW: Start working on your semester project (due Jan 21st).
Class on 12/13
Get Review Handout Answer Key. Get Semester Project (due on 1/21) Handout & Discuss
HW: No new assignment, just continue to practice and prepare for the final.
Class on 12/11
Finish Lesson 7.7 Solving Sine Equations
Grouptest – Fall Practice Final Exam
HW#25: Finals Review Handout. To prepare for the Final, you might also want to practice problems from all prior tests and grouptests.
Class on 12/6
Taking the inverse of Sine and Cosine
7.7 Solving Sine and Cosine Equations
Handout out HW#25 Finals Review Handout
HW#24: 7.1 #15-18, 24-28 only one PV solution. 7.3 #13, 14. Start HW #25 Finals Review Handout.
Class on 12/4
Fitting Sine Functions to Data
Applications of Sine Functions (Modeling periodic change related to daylight, temperature, tides, wheels, pendulums, etc.)
HW#23: Handout: Applications of Sine Functions. Book: 6.6 #27, 29, 35a-c, 42-44. pg 437 #1,2,6,7,10,12-15red light only on this page
6.6 Sine and Cosine Graphs (finish last page from Wed CW)
6.6 Completing the Process of Graphing Sine Waves
Quiz – The Unit Circle
6.4 Sine and Cosine Graphs (Finnish Part I, Part II)
6.4 Transforming the Sine and Cosine Graphs: Amplitude, Frequency, Hor. Shift, Vert. Shift
6.2 Introduction to the Unit Circle
6.2 Exact Values of Trig Expressions
6.4 Sine and Cosine Graphs (Part I)
HW#20: 6.2 #5,6,8-10,21,22,27,28. Prepare for Unit Circle Quiz. Memorize or know how to build the Unit Circle from the base angles of 30°, or pi/6 and 45°, or pi/4. You will also need to know sin270° or cos 3pi/4, for example, without a calculator.
Introduction to Periodic Functions
Converting Between Radians and Degrees
Notes – Unit 3
Grouptest – Unit 3
HW#18: Unit 4 Intro Handout (very very important…do everything on here including the research and videos
Compound Interest, e, and Continuous Growth
page 347 #56 use desmos regression equation for part b…. y1 ~ a(b)X1
Class on 10/25
Notes – Update Library of Functions
Intro to Limits: How does limit notation help us summarize situations with holes or asymptotes?
HW#14: Limits Handout and Exponential Webs
Class on 10/23
5.3 Exploring Exponential Functions (Using Chromebooks and Spreadsheets)
What is a Log? Basic Log Properties, Solving Exponentials Using Logs
HW#13: 5.3 #1, 3, 5, 9, 11, 13, 27-33odd, 43, 45, 47 (use desmos to help check graphs), 63-69odd, 89, 91, 97. 5.4 #27-33odd, 89-93odd. 5.6 #41-47odd. Finish Unit 2 Project
Class on 10/18
Test – Units 1-2
HW: Unit 2 Project – Rough Draft due Wed. Final draft due Fri.
Class on 10/16
Grouptest – Unit 2
Notes – Unit 2 Summary & Notes – Library of Functions
HW#12: Unit 2 Review Handout
Class on 10/11
4.3 Rational Function Graphs
Vertical and End-Behavior Asymptotes: Why do they exist in rational functions?
Rational Function Webs & Rational Function Models
HW#11: 4.2 #33, 44, 45. 4.3 #7-11odd (analyze means sketch, D, R, inc, dec, max, min, intercepts, asymptotes), 33, 55 (use Desmos). Handout: Rational Function Webs
Class on 10/9
4.1 Polynomial Models (finish if necessary)
4.2 Intro to Rational Functions. How are rational function models useful? How can we understand the dynamics of their graphs?
HW#10: 4.2 #15-25odd, 27a-d, 28a-d. 4.3 #1, 51, 52.
Class on 10/5
3.4 Quadratic Models. How can quadratics model projectiles or things related to area?
4.1 Intro to Polynomials. 4.1 Polynomials, Graph, Roots, and Models
HW#9: 3.4 #7, 9, 17, 29. pg 165 #1-7,9-11, 15. redlightonly (only do problems you aren’t sure you know how to do… and then check answers). 4.1 #2, 3, 4, 17-25odd, 43, 45, 57abd, 69-73, 123d (use desmos), 126.
Class on 10/2
How do the dynamics of the equations change when we move from linear equations to higher degree polynomials? How does the math get crazy?
3.3 Quadratic Functions. 3.3 Quadratic Application. 3.3 Quadratic Webs
HW#8: 3.3 #1-9, 21, 23, 27, 35, 39, 49-57odd, 97, 99, 100.
Class on 9/27
CW: Creating a Math Report or Project
Test – Unit 1
HW: Unit 1 Project due Friday, 10/4 (draft by Wed)
Class on 9/25
Notes – Unit 1 Summary
Grouptest – Unit 1
HW#7: Unit 1 Review Handout
Class on 9/20
Modeling Practice. Practice Project and Challenge Tasks. Hand out Unit 1 Project.
HW#6: 3.2 #5-10, 11-12a-d, 19. Optional: start Unit 1 Project (due Fri 10/4)
Class on 9/18
2.5 Transformations (5 min review)
Discuss Using Desmos and Linear Regression Equations. Start 3.2 Linear Models of Best Fit (By Hand & With Technology). Bucket Water Draining Problem.
HW#5: 2.5 #7-26, 35. pg 114-115 #1-3, 6, 7, 10, 16, 17a&b, 37c. 3.1 #21-28, 31, 37.
Class on 9/13
Piecewise Function Challenge
2.4 Piecewise Functions
Skydive & General Practice. Discuss tax system (page 92 - #53)
HW#4: 2.1 #51-61 odd, 91, 95. 2.2 #11, 25, 39, 41, 43, 44. 2.4 #31-37odd (graph only), 43-45 (equation only), 70.
Class on 9/11
2.1 and 2.2 Functions, Domain and Range & 2.3 Analyzing Functions
Cliff Jumping Example
1st Semester Extra Credit Problems – Start Number Bracelets Task & Discuss
Class on 9/6
1.1 Distance and Midpoint & 1.3 Equations of Lines
Day 2 Course Overview PPT, Structures, Advice
Get Books, Calendar and Syllabus, Discuss Grades. Discuss Projects & Final Project.
HW#A: Complete Info Sheet to turn in. HW#B: Show me your signed syllabus. HW#C: Show me your math binder with dividers (or come see me outside of class for assistance).
HW#2: 1.1 #19-25odd, 29-32, 41, 43, 53, 67. 1.3 #39-89e.o.odd (red light only), 131. Create graph: Your Enjoyment Level (y-axis) vs Difficulty of Math Problem (x-axis)
Class on 9/4
Welcome & Kickoff Problems
1.0 – Review Problems & Cats Multiplying Problem
Day 1 Goals & Intro PPT. What does doing math look and feel like?
Videos – Maryam Mirzakhani & Counting to One Million
Introduce Drying Apples and Counting Tasks on HW
HW#1: Handout – Alg/Geo Review and Challenge Problems (Drying Apples & Counting to One Million Tasks)