Comprehensive Algebra 2 with Trig 🍎
SAT Score Range
•
28 sessions
•
KR
MJ
DP
+119
This series ended on June 3, 2023. All 1:1 and group chats related to this series are disabled 7 days after the last session.
About
Hey guys! Along with my Geometry series, here's one for Algebra 2 and Trig! It's never too early/late to start learning, so why not join?
Prerequisites: Algebra 1; good grasp of quadratics (which you can learn concurrently if you haven't already).
We're going to be covering
-Polynomials
-Vectors
-Complex Numbers
-Rational Functions
-Exponents/Logarithms
-Function Transformations
-Linear Transformations using Matrices
-Types of triangles
-Right Triangle Trigonometry
-Unit Circle and Trigonometric Identities/Values
-Radians and Degrees
-Trigonometric Functions
-Inverse Trigonometric Functions
-Sinusoidal Graphs/Equations
-Other Trigonometric Identities
Tutored by
A little about me: I'm about the biggest Indie fan there is, I almost exclusively watch (John Hughes>>) 80s movies or the upcoming Star Wars series, and I read sci-fi in my spare time. I tutor for the sake of those aha moments, and have taken Multivariable Calc, Linear Algebra, Real Analysis, and Complex Analysis. Who knows what I'll tutor next, hope to see you soon.
Schedule
✋ ATTENDANCE POLICY
Attendance is optional but highly recommended since topics build on each other; however I understand that everyone has a busy schedule, so if you can't make it and want a catch-up session just ask!
SESSION 1
14
Nov
SESSION 1
Polynomial arithmetic
Polynomial arithmetic
Mon 2:15 AM - 3:35 AM UTCNov 14, 2:15 AM - 3:35 AM UTC
Hey guys, today we will start by
-Introducing the series
-Defining polynomials
-Learning how to add, subtract, and multiply polynomials (FOIL)
As always, catch-up sessions are available, just ask.
SESSION 2
21
Nov
SESSION 2
Polynomial division
Polynomial division
Mon 2:15 AM - 3:35 AM UTCNov 21, 2:15 AM - 3:35 AM UTC
-Learn how to apply polynomial division in addition to the remainder and factor theorems to find the linear factors of polynomials
-Proving the factor and remainder theorem, and applying them to prove factors of a polynomial
SESSION 3
5
Dec
SESSION 3
Polynomial factorization
Polynomial factorization
Mon 12:00 AM - 1:30 AM UTCDec 5, 12:00 AM - 1:30 AM UTC
-Learn how to apply polynomial division in addition to the remainder and factor theorems to find the linear factors of polynomials
-Proving the factor and remainder theorem, and applying them to prove factors of a polynomial
SESSION 4
11
Dec
SESSION 4
Review
Review
Sun 1:30 AM - 2:30 AM UTCDec 11, 1:30 AM - 2:30 AM UTC
-Reviewing quadratic factorization
-Learn about the features of polynomials represented visually in graphs including factors (zeros), the multiplicity of their zeros, the graphs y-intercept, and end behavior (odd or even or none).
Hey guys, today we will review the concepts in our first unit, polynomials. We will be focused more on practicing our skills and resolving any remaining doubts.
SESSION 5
12
Dec
SESSION 5
Trigonometry
Trigonometry
Mon 2:15 AM - 3:45 AM UTCDec 12, 2:15 AM - 3:45 AM UTC
Hey guys,
Today we're going to learn the trigonometric ratios (SOHCAHTOA), reciprocal ratios, and build some intuition around them (it would be helpful to know about Similarity beforehand). We'll find the lengths of missing sides of right triangles, learn about complementary angles, and do some other practice.
SESSION 6
19
Dec
SESSION 6
Polynomial factorization
Polynomial factorization
Mon 2:15 AM - 3:45 AM UTCDec 19, 2:15 AM - 3:45 AM UTC
-Learn how to apply polynomial division in addition to the remainder and factor theorems to find the linear factors of polynomials
-Proving the factor and remainder theorem, and applying them to prove factors of a polynomial
SESSION 7
20
Dec
SESSION 7
Trigonometry
Trigonometry
Tue 1:00 AM - 2:30 AM UTCDec 20, 1:00 AM - 2:30 AM UTC
CONTINUING
-Learn how to apply polynomial division in addition to the remainder and factor theorems to find the linear factors of polynomials
-Proving the factor and remainder theorem, and applying them to prove factors of a polynomial
SESSION 8
27
Dec
SESSION 8
Trigonometry
Trigonometry
Tue 2:15 AM - 3:45 AM UTCDec 27, 2:15 AM - 3:45 AM UTC
Hey guys,
Today we're going to learn the trigonometric ratios (SOHCAHTOA), reciprocal ratios, and build some intuition around them (it would be helpful to know about Similarity beforehand). We'll find the lengths of missing sides of right triangles, learn about complementary angles, and do some other practice.
SESSION 9
28
Dec
SESSION 9
Complex numbers
Complex numbers
Wed 1:00 AM - 2:30 AM UTCDec 28, 1:00 AM - 2:30 AM UTC
Hey guys, these two sessions will be on Vectors, but I put it as about Complex Numbers because their relation will lay the foundations for our understanding of Complex Numbers.
- What is a Vector? What are n-vectors?
-Zero vectors
-Vector quantities vs Scalar quantities
-Finding the x and y component of a vector, adding and subtracting vectors together (the parallelogram rule
-The argument and modulus of a vector, what they are and how to derive them (inverse trig functions)
-Some more advanced problems on vectors from Khan Academy
SESSION 10
16
Jan
SESSION 10
Complex numbers
Complex numbers
Mon 3:00 AM - 4:30 AM UTCJan 16, 3:00 AM - 4:30 AM UTC
Hey guys, today we will begin to cover Complex Numbers
-What they are,
-Complex solutions to quadratics,
-Factoring by sum of squares (and solving for the complex roots of polynomials using sum of squares),
-De Moivre's Theorem
-Euler's Formula
SESSION 11
23
Jan
SESSION 11
Complex numbers
Complex numbers
Mon 2:15 AM - 3:45 AM UTCJan 23, 2:15 AM - 3:45 AM UTC
Hey guys, today we're going to find all the complex solutions to polynomials in general (not just through sum of squares or in quadratics) by covering
-Rectangular Form of Complex numbers and converting it to
-Polar Form of Complex Numbers
- The Imaginary Plane
-The Argument and Modulus of Complex Numbers.
SESSION 12
30
Jan
SESSION 12
Complex numbers
Complex numbers
Mon 2:15 AM - 3:45 AM UTCJan 30, 2:15 AM - 3:45 AM UTC
(CONTINUING LAST SESSION)
Hey guys, today we're going to find all the complex solutions to polynomials in general (not just through sum of squares or in quadratics) by covering
-Rectangular Form of Complex numbers and converting it to
-Polar Form of Complex Numbers
- The Imaginary Plane
-The Argument and Modulus of Complex Numbers.
SESSION 13
6
Feb
SESSION 13
Review
Review
Mon 2:15 AM - 3:45 AM UTCFeb 6, 2:15 AM - 3:45 AM UTC
Hey guys, today we will review the concepts in our second unit, complex numbers. We will be focused more on practicing our skills and resolving any remaining doubts.
SESSION 14
13
Feb
SESSION 14
Trigonometry
Trigonometry
Mon 2:15 AM - 3:45 AM UTCFeb 13, 2:15 AM - 3:45 AM UTC
We're starting our Trigonometry Unit!
We're going to start with a brief series overview, then get into
-Types of Triangles
-Angle Properties
-The Triangle Inequality Theorem
-The Pythagorean Theorem
-Review of SOHCAHTOA
SESSION 15
20
Feb
SESSION 15
Trigonometry
Trigonometry
Mon 2:15 AM - 3:45 AM UTCFeb 20, 2:15 AM - 3:45 AM UTC
Hey guys, today we're going to go over the law of sines and cosines (and their proofs) to find the missing sides of arbitrary triangles (and provide some more intuition to some congruence theorems using these laws)
SESSION 16
6
Mar
SESSION 16
Trigonometry
Trigonometry
Mon 2:15 AM - 3:45 AM UTCMar 6, 2:15 AM - 3:45 AM UTC
Hey guys, today we'll learn what radians are and how to convert between them and degrees. Then we'll go over the Unit Circle, trig identities/values that we can derived from the unit circle, and then we'll practice computing trig values.
As always, catch-up sessions are available.
SESSION 17
21
Mar
SESSION 17
Trigonometry
Trigonometry
Tue 2:15 AM - 3:45 AM UTCMar 21, 2:15 AM - 3:45 AM UTC
Hey guys, today we'll learn what radians are and how to convert between them and degrees. Then we'll go over the Unit Circle, trig identities/values that we can derived from the unit circle, and then we'll practice computing trig values.
As always, catch-up sessions are available.
SESSION 18
26
Mar
SESSION 18
Trigonometry
Trigonometry
Sun 2:15 AM - 3:45 AM UTCMar 26, 2:15 AM - 3:45 AM UTC
Hey guys, today we're going to be plotting the values of trigonometric functions that we derived using the unit circle onto a graph; then we'll play around with inverse functions and make the trigonometric functions invertible (For background knowledge on making functions invertible, go to https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:composite/x9e81a4f98389efdf:invertible/a/intro-to-invertible-functions). We'll also determine the domain and range of these inverse functions and see their graphs as well.
As always, catch-up sessions are available.
SESSION 19
27
Mar
SESSION 19
Trigonometry
Trigonometry
Mon 1:30 AM - 3:00 AM UTCMar 27, 1:30 AM - 3:00 AM UTC
Hey guys, today we're going to take a look at the features of sinusoidal (sine and cosine) functions today: amplitude, period, midline, and phase shift, and how each of these features corresponds to a different part of the sinusoidal equation af(b(x+c))+d, where f is either sin or cosine.
As always, catch-up sessions are available.
SESSION 20
4
Apr
SESSION 20
Trigonometry
Trigonometry
Tue 2:30 AM - 4:00 AM UTCApr 4, 2:30 AM - 4:00 AM UTC
Today we'll just practice what we learnt last session, deriving the equations of sinusoidal functions using their graphs. This is a very tedious process, so we will have an additional session on this.
As always, catch-up sessions are available.
SESSION 21
10
Apr
SESSION 21
Trigonometry
Trigonometry
Mon 2:15 AM - 3:45 AM UTCApr 10, 2:15 AM - 3:45 AM UTC
(CONTINUING)
Today we'll just practice what we learnt last session, deriving the equations of sinusoidal functions using their graphs. This is a very tedious process, so we will have an additional session on this.
As always, catch-up sessions are available.
SESSION 22
17
Apr
SESSION 22
Trigonometry
Trigonometry
Mon 1:45 AM - 3:15 AM UTCApr 17, 1:45 AM - 3:15 AM UTC
Today we're going to be applying trig identities to solve sinusoidal equations!
Have fun, see you soon.
As always, catch-up sessions are available.
SESSION 23
24
May
SESSION 23
Exponential models
Exponential models
Wed 2:15 AM - 3:45 AM UTCMay 24, 2:15 AM - 3:45 AM UTC
Hey guys, today we're going to be covering
-Properties of exponents (rational exponents as well) (review)
-Exponential function properties (growth and decay)
SESSION 24
25
May
SESSION 24
Logarithms
Logarithms
Thu 2:15 AM - 3:45 AM UTCMay 25, 2:15 AM - 3:45 AM UTC
-What logarithms are and converting expressions into exponential/logarithmic form
-Logarithm properties
- Logarithmic functions
SESSION 25
28
May
SESSION 25
Trigonometry
Trigonometry
Sun 3:30 AM - 5:00 AM UTCMay 28, 3:30 AM - 5:00 AM UTC
Today we're going to be applying trig identities to solve sinusoidal equations!
Have fun, see you soon.
As always, catch-up sessions are available.
SESSION 26
29
May
SESSION 26
Logarithms
Logarithms
Mon 2:15 AM - 3:45 AM UTCMay 29, 2:15 AM - 3:45 AM UTC
-What logarithms are and converting expressions into exponential/logarithmic form
-Logarithm properties
- Logarithmic functions
SESSION 27
30
May
SESSION 27
Transformations of functions
Transformations of functions
Tue 2:15 AM - 3:45 AM UTCMay 30, 2:15 AM - 3:45 AM UTC
Hey guys, today we're going to be doing something different. We'll be play with different functions on desmos to build some intuition on...
-Vertical and horizontal translations
-Vertical and horizontal stretches/compressions
-Reflections
SESSION 28
3
Jun
SESSION 28
Transformations of functions
Transformations of functions
Sat 2:30 AM - 4:00 AM UTCJun 3, 2:30 AM - 4:00 AM UTC
Hey guys, today we're going to be doing something different. We'll be play with different functions on desmos to build some intuition on...
-Vertical and horizontal translations
-Vertical and horizontal stretches/compressions
-Reflections
We'll also cover vectors and matrices--what they are, how to add and subtract them, as well as multiply them.
We'll use this to prove the rotation matrix, a linear function to rotate functions or points by a given angle.