Today we are going to review inverse functions. First, we will go over the homework. Then we will look at how to determine if a function has an inverse function. The we will find the inverse of a basic function. We will look at composite functions and see how to identify an inverse function. We will look at the graph of a function and it's inverse. We will also look at what the original and inverse functions are reflected over. We will then look at inverses with restricted domains.
1.8 HW - Inverse Functions
We will start by going over the homework. I will walk through the class through anything that they are having difficulty with. I will then review how to find the distance and the midpoint between 2 points. Then we will review how to complete the square, to factor polynomials. I will show the students how completing the square is used to convert a circle equation from general to standard form. We will then review how to graph a circle in standard form. We will go over some of the properties of circles, and how the point/line formulas would be used with circles. We may have a quiz on 1.7-1.8 next class.
1.9 HW - Distance and Midpoint Formulas; Circles
First, we will review the homework. Then we will look at mathematically modeling situations. We will review percentages, modeled line equations, volumes, graph distances and cost per part. I will review the benefits of drawing a picture when mathematically modeling a situation. We will then look at how to set and solve equations based on the situation. This is a fun lesson based on real life situations.
Then we will have the quiz on 1.7-1.8
1.10 HW - Modeling with Functions
First, we will review the homework and the quiz from last class. Then we will talk about the best day for the Chapter 1 test. I will answer any questions that any student has in chapter 1. We have been over all questions on the homework and the quizzes. Students can look over their chapter 1 to review in any way they want.
Today we are going to start Chapter 2. The First section is Complex numbers. So we will go over what "i" is. I will show students how the algebra works with respect to complex numbers. There may be a quiz next class on Complex numbers.
I will also review how to solve different quadratics. We need to be ready for parabola's next class.
2.1 HW - Complex Numbers
We will go over any questions on the homework. I will then ask if there are any questions on Chapter 1. I will go through any review that the kids need. I will go over the informational form for a parabola. I will work with the students on how to complete the square to create an informational form. We will go over how to find the axis of symmetry, vertex, domain, range, opening up or down, etc. Then we may take a 2.1 quiz.
We need to find a day to take the Chapter 1 test
Quiz tomorrow 2.1-2.2
2.2 HW - Quadratic Functions
Quiz tomorrow 2.1-2.2
Have questions for Chapter 1 ready
Quiz 2.1-2.2. We will start with a review of Chapter 1. Then we will review the homework from 2.2. I will then go over 2.3 Polynomial Functions and Their Graphs. We will review what a polynomial is. I will then review how to find the degree of a polynomial. We will then work on what end behavior, zeros, even, odd mean with respect to a polynomial. We will then work on graphing polynomials.
After all of this we will take the 2.1-2 quiz
2.3 HW - Polynomial Functions and Their Graphs
Today we will first go over any questions on the homework. I will then ask if there are any more questions on Chapter 1. We have the test next class, and today is the last day you can ask questions. I will then review Long Division and how it relates to polynomial long division. We will then look at synthetic division and how it is used to solve polynomial division. We will also look at how to totally factor a polynomial and how to use the Remainder theorem.
2.4 HW - Dividing Polynomials; Remainder and Factor Theorems
Notes
Chapter 1 test
Chapter 1 test
Today we are back to normal. First, we will go over the homework from 2.4. Then we will look at rational functions and their graphs. We will review how to simplify equations, find their domain, learn about asymptotes (vertical, horizonal, and slant), review how to divide polynomials, and the 7 steps to graphing polynomials. I can't release the test yet, I still have people that need take it.
2.6 HW - Rational Functions and Their Graphs
Today we are going to learn about Exponential functions. We will look at how to graph these functions and how they are used in life. We use these equations both in nature and business. But first we will go over the homework for 2.6. The we will have some fun using exponential functions.
3.1 HW - Exponential Functions
Today we will go over the homework first. We will then go over the concept of a logs, and compare it to exponential functions. I will then introduce the properties of logs and natural logs. Then the class can work on the homework.
3.2 HW - Logarithmic Functions
Today we will review the homework from last class. We will then look at the unit circle. We will look at what Radians are and how they are related to the unit circle. We will look into the ratios and how to show which radians matchup with which angles. We will go over standard position, positive and negative angles, arc lengths and linear and angular speed.
4.1 HW - Angles and Radian Measure
We need to set a date for the Chapter 2 and 3 Test. I will combine the lessons we completed in those 2 chapters into one test. Today we will review the homework. Then we will look at 4.3 (Trigonometric Functions: The Unit Circle). First, we will review how to rationalize fractions. I will then go over special right triangles and how they relate to the unit circle. I will then have the kids fill in a unit circle with me. We will use this unit circle to identify how trig values are related to the unit circle.
4.2 HW - Trigonometric Functions: The Unit Circle
First, we will go over the homework. I will then introduce the concepts that are covered in 4.3. I will review the basics of sin
, cos, tan, cot, sec, csc with respect to a triangle, we will look at how radians and degrees are used throughout the trig process. I will then go through some real life problems where trig functions are used. Then we will have a quiz on 2.3-2.4. The quiz will be available to review right after class. We will have the test on Chapter 2 and 3 on Friday.
4.3 Right Triangle Trig
Quiz today on 2.3-2.4
Today, we will first go over the homework. Then I will go through the concepts in 4.4. I will then go over the quiz from last class. Then students can argue for points on both quiz and test. If there is time left, I will answer any questions on Chapter 2-3. Section 4.4 has a few interesting concepts I will introduce. I will introduce how to find the trig functions of any angle (not just the unit circle). We will review which functions are positive and negative based on which quadrant the terminal side is in. I will also go through how to use the trig theorems using both values and quadrant.
4.4 HW - Trigonometric Functions of Any Angle(not due until Tuesday Dec 17)
Test on Chapter 2 and 3 on Friday Dec 13, 2024
First, we will review the trig functions of any angle assignment. I will answer any questions on this assignment. We will then start to look at the graphs of sin and cos. I will show how these graphs are manipulated with different periods, phase shifts, vertical shifts, etc. I will also introduce how the techniques that I use with sin/cos can be used to graph the other trig functions.
4.5 HW - Graphs of Sine and Cosine
Today we will first go over the homework. I will then go through the different graphing patterns of Tan, Cot , Sec, Csc. We will review how to apply these patterns to graph these different trig functions. We will also go over the terms reciprocal function and cosecant function.
4.6 HW - Graphs of Other Trigonometric Functions
Graphing hints video (works for trig functions)
Notes
We didn't get to do this lesson on the 19th. So it will be todays lesson.
Today we will first go over the homework. I will then go through the different graphing patterns of Tan, Cot , Sec, Csc. We will review how to apply these patterns to graph these different trig functions. We will also go over the terms reciprocal function and cosecant function.
4.6 HW - Graphs of Other Trigonometric Functions
Maybe a graphing quiz on sin,cos.sec,csc,tan.cot. Be ready to graph.
First, we will go over the homework. Then we will look at how trig functions are used to determine values of angles and sides of triangles. I will go over angle of elevation and depression. I will go over how to write headings. We will look at triangle combinations and how to solve those.
4.8 Applications of Trigonometric Functions
Notes
Zoom
Need to have all late work in by Tuesday 1/14
First, we will go over any questions on 4.6. I will then review 4.8. I've given the students until 1/16 to finish this assignment. If we have time, I would like to start 5.1. This is a challenging assignment, so I would like for the students to have a chance to work some in class. We will see where we end up.
5.1 HW - Verifying Trigonometric Identities
Today we are going to review the unit circle. First we will go over the homework. I will pull kids to the board to go over homework questions. We will review the proofs. Section 5.2 requires that the students be comfortable with the unit circle. Today I will go over the special right triangles, and how they work in the unit circle. There will be a quiz next class on the unit circle. Need to fill in an entire unit circle.
With the remaining time in the class I will allow the students to challenge any questions that they had on the last test. The last kids just made up the last test.
Homework (complete a unit circle)
look at 3rd quarter