Unit 0: Algebra 2/Pre-AP Algebra 2 Prerequisites
Summer Packet
Unit 1: Expressions, Equations & Inequalities
Video 1: Topic 1.1: Understanding Interval Notation | Set Builder Notation | Open, Closed, and Infinite Intervals.
Video 2: Topic 1.2: Converting Units with Conversion Factors.
Video 3: Topic 1.3: Solving Multi-Step Equations Containing Fractions.
Video 4: Topic 1.4: Solving Advanced Literal Equations.
Video 5: Topic 1.5: Solving Compound Inequalities.
Video 6: Topic 1.6: Solving Absolute Value Equations.
Video 7: Topic 1.7: Solving Absolute Value Inequalities.
Video 8: Topic 1.8: Solving Absolute Value Inequalities Word Problems.
Unit 2: Functions & Their Transformations
Video 9: Topic 2.1: Determine If a Relation is A Function - How to Know If A Function is 1-1?
Video 10: Topic 2.2: Domain of Radical & Rational Functions.
Video 11: Topic 2.3: Evaluate the Value of Functions.
Video 12: Topic 2.4: Average Rate of Change - Rates of Change in Linear and Quadratic Functions - Concavity - Increasing/Decreasing Functions.
Video 13: Topic 2.5: Determine if the Function is EVEN or ODD?
Video 14: Topic 2.6: Transformations of Functions (Translation, Reflection, Dilation) with/without a Graph.
Video 15: Topic 2.7: Graphs of |f(x)| and f(|x|) from f(x).
Video 16: Topic 2.8: Inverse Functions.
Video 17: Topic 2.9: Composition of Functions.
Video 18: Topic 2.10: Domain of Composite Functions.
Unit 3: Advanced Linear Functions & Equations
Video 19: Topic 3.1: Determine the Slopes/Rate of Change of Linear Functions.
Video 20: Topic 3.2: Write the Equations of Parallel & Perpendicular Lines.
Video 21: Topic 3.3: Direct Variation/Proportionality.
Video 22: Topic 3.4: Modeling Functions and Applications | Best-fitting Linear Regression Model.
Video 23: Topic 3.5: Graphing & Writing Piecewise Functions | Domain & Range | Piecewise Function Related Problems.
Video 24: Topic 3.6: Absolute Value Functions: Characteristics, Graphing, Writing, and Transformation.
Video 25: Topic 3.7: Graphing & Writing Linear & Absolute Value Inequality Functions.
Video 26: Topic 3.8: Graphing System of Multiple Inequalities (Linear Inequalities, Absolute Value Inequalities, Quadratic Inequalities, Radical Inequalities).
Unit 4: Systems of Equations & Matrices
Video 27: Topic 4.1: Solving a System of 2 Linear Equations Using a Graphing Calculator.
Video 28: Topic 4.2: Solving a System of 2 Linear Equations by Substitution.
Video 29: Topic 4.3: Solving a System of 2 Linear Equations by Elimination.
Video 30: Topic 4.4: Solving a System of 3 Equations by Substitution, Elimination.
Video 31: Topic 4.5: Solving a System of 2 & 3 Equations Word Problems.
Video 32: Topic 4.6: Adding, Subtracting, and Multiplying Matrices.
Video 33: Topic 4.7: Finding the Determinant of 2x2 Matrices.
Video 34: Topic 4.8: Finding the Determinant of 3x3 Matrices.
Video 35: Topic 4.9: Finding the Inverse of 2x2 Matrices.
Video 36: Topic 4.10: Finding the Inverse of 3x3 Matrices Using Adjoint & Cofactor Method.
Video 37: Topic 4.11: Finding the Inverse of 3x3 Matrices Using Gauss-Jordan Elimination.
Video 38: Topic 4.12: Finding the Area of a Triangle Using Matrix.
Video 39: Topic 4.13: Solving the Matrix Equations.
Video 40: Topic 4.14: Using Inverse Matrices to Solve the Linear System of Equations.
Video 41: Topic 4.15: Solving a System of Equations by Cramer's Rule.
Video 42: Topic 4.16: Solving a System of Equations by Gauss-Jordan Elimination.
Unit 5: Quadratic Functions, Inequalities, Complex Numbers
Video 43: Topic 5.1: Factoring Trinomials.
Video 44: Topic 5.2: Factoring Special Cases of Polynomials.
Video 45: Topic 5.3: Advanced Factoring of Polynomials.
Video 46: Topic 5.4: Characteristics of Quadratic Functions in Standard Form y = ax^2 + bx + c (a#0).
Video 47: Topic 5.5: Characteristics of Quadratic Functions in Vertex Form y = a(x-h)^2 + k (a#0).
Video 48: Topic 5.6: Characteristics of Quadratic Functions in Intercept Form y = a(x-p)(x-q) (a#0).
Video 49: Topic 5.7: Convert Quadratic Functions from Standard Form <=> Vertex Form <=> Intercept Form <=> Standard Form.
Video 50: Topic 5.8: Maximization/Minimization (Optimization) Problems Using Quadratic Function Models.
Video 51: Topic 5.9: Simplifying Rational Exponents and Radicals.
Video 52: Topic 5.10: Writing Quadratic Functions Given Vertex and a Point, Two Zeros, 3 Points, Tables, Word Problems.
Video 53: Topic 5.11: Solving Quadratic Equations by Factoring.
Video 54: Topic 5.12: Solving Quadratic Equations by Taking Square Root and Completing Squares.
Video 55: Topic 5.13: Solving Quadratic Equations Using Quadratic Formula and Graphing Calculator.
Video 56: Topic 5.14(A): 5 Different Ways to Solve a Quadratic Equation - Part 1.
Video 57: Topic 5.14(B): 5 Different Ways to Solve a Quadratic Equation - Part 2.
Video 58: Topic 5.15: Solving Systems of Quadratic Equations.
Video 59: Topic 5.16: Solving Quadratic Inequalities.
Video 60: Topic 5.17: Graphing & Writing Quadratic Inequalities & Systems of Quadratic Inequalities.
Video 61: Topic 5.18: Add, Subtract, Multiply, and Divide Complex Numbers.
Video 62: Topic 5.19: Quadratic Equations with Imaginary Solutions.
Video 63: Topic 5.20: De Moivre's Theorem - Complex Numbers in Polar.
Unit 6: Square Root & Cubic & Cube Root Functions & Equations & Inequalities
Video 64: Topic 6.1: Simplifying Rational Exponents and Radicals.
Video 65: Topic 6.2: Simplifying Radical Expressions.
Video 66: Topic 6.3: Square Root & Quadratic Functions: Key Features, Transformations, and Inverses.
Video 67: Topic 6.4: Solving Square Root Equations.
Video 68: Topic 6.5: Solving Square Root Inequalities.
Video 69: Topic 6.6: Cube Root & Cubic Functions: Key Features, Transformations, and Inverses.
Video 70: Topic 6.7: Solving Cube Root Equations.
Unit 7: Polynomial & Rational Functions & Equations
Video 71: Topic 7.1: New Method of Factoring Trinomials WITHOUT Guessing and Checking.
Video 72: Topic 7.2: Factoring Special Cases of Polynomials.
Video 73: Topic 7.3(A): Long Division & Synthetic Division with 8 Specific Examples - The easy way!
Video 74: Topic 7.3(B): Dividing Polynomials using 3 methods: Factoring - Long Division - Synthetic Division.
Video 75: Topic 7.4: Factor Theorem & Remainder Theorem.
Video 76: Topic 7.5: Rational Root Theorem & Fundamental Theorem of Algebra.
Video 77: Topic 7.6: Descartes’ Rule of Signs
Video 78: Topic 7.7: Direct, Inverse, Joint and Combined Variation.
Video 79: Topic 7.8: Polynomial Functions and Rates of Change | Local (Relative) Min/Max | Global (Absolute) Min/Max | Points of Inflection | Turning Points.
Video 80: Topic 7.9: Polynomial Functions and Complex Zeros | Complex Roots, Multiplicity, Polynomial Inequalities, Fundamental Theorem of Algebra, Conjugate Pairs | Write the Polynomial Function given a Graph.
Video 81: Topic 7.10: Solving Polynomial Inequalities.
Video 82: Topic 7.11: Polynomial Functions and End Behavior.
Video 83: Topic 7.12: Polynomial Functions and End Behavior (Foldable Activity) - Easy way to memorize!
Video 84: Topic 7.13: Rational Functions and End Behavior - Horizontal Asymptotes and Slant Asymptotes.
Video 85: Topic 7.14: Rational Functions and Zeros | Solving Rational Inequalities.
Video 86: Topic 7.15: Vertical Asymptotes and Holes - Horizontal Asymptotes and Slant Asymptotes - Graphing Rational Functions
Video 87: Topic 7.16: If Vertical Asymptotes, Holes, and Zeros (x-intercepts) occur simultaneously, which one beats?
Video 88: Topic 7.17: Find the Domain & Range of Continuous Functions and Discontinuous Functions.
Video 89: Topic 7.18: How to Write a Rational Function Given a Graph.
Video 90: Topic 7.19: Add, Subtract, Multiply, and Divide Rational Expressions.
Video 91: Topic 7.20: Partial Fraction Decomposition.
Video 92: Topic 7.21: Solving Rational Equations & Complex Fractions Equations.
Video 93 (Challenge): Using Partial Fraction Decomposition to Solve the finite Rational Equation.
Unit 8: Exponential & Logarithmic Functions & Equations
Video 94: Topic 8.1: Change in Arithmetic and Geometric Sequences.
Video 95: Topic 8.2: Change in Linear and Exponential Functions. How to Predict the Future Values?
Video 96: Topic 8.3: Exponential Functions | Characteristics, End Behavior & Concavity |Determine if the function is increasing/decreasing at an increasing/decreasing rate?
Must watch Videos 97 - 100 since they are prerequisites for videos 101 - 102.
Video 97: Topic 8.4: Find the Domain, Range, Y-intercept, Asymptote of an Exponential Function.
Video 98: Topic 8.5: Find the Domain, Range, Y-intercept, Asymptote of an Exponential Function Word Problems.
Video 99: Topic 8.6: Exponential Growth & Decay Functions.
Video 100: Topic 8.7: Modeling Exponential Functions in Finance | Compound Interest.
Video 101: Topic 8.8: Exponential Function Manipulation | Why is the Horizontal Translation the same as Vertical Dilation?
Video 102 Topic 8.9: Exponential Function Context and Data Modeling with a TI-Nspire & TI-84 Plus CE Calculator.
Video 103: Topic 8.10: Properties of Logarithms | Proof and Walkthrough Examples.
Video 104: Topic 8.11: Logarithmic Expressions.
Video 105: Topic 8.12: Inverses of Exponential Functions & Logarithmic Functions.
Video 106: Topic 8.13: Logarithmic Functions |Characteristics, End Behavior, Concavity, and Transformations |Determine if the function is increasing/decreasing at an increasing/decreasing rate?
Video 107: Topic 8.14: Expand & Condense Logarithmic Expressions | Is the Horizontal Dilation the same as the Vertical Translation?
Video 108: Topic 8.15: Exponential and Logarithmic Equations.
Video 109: Topic 8.16: Mastering Compound Interest: Step-by-Step Proofs & Real-Life Examples.
Video 110: Topic 8.17: Exponential and Logarithmic Equations Word Problems in Finance| Interest Compounded Annually & Continuously.
Video 111: Topic 8.18: Exponential and Logarithmic Inequalities.
Video 112: Topic 8.19: Logarithmic Function Context and Data Modeling with TI-Nspire & TI-84 Plus CE Calculator.
Unit 9: Trigonometric Functions & Equations
Video 113: Topic 9.1: Law of Sines: Proof of the Formula & Step-by-Step Examples
Video 114: Topic 9.2: Law of Cosines: Proof of the Formula & Step-by-Step Examples
Video 115: Topic 9.3: Area of Triangles Using Sines Formula: Proof of the Formula & Step-by-Step Examples
Video 116: Topic 9.4: Area of Triangles Using Heron Formula: Proof of the Formula & Step-by-Step Examples
Video 117: Topic 9.5: Periodic Phenomena
Video 118: Topic 9.6: Using the Unit Circle Activity to Verify Why π = 180?
Video 119: Topic 9.7: Trigonometry in Right Triangles - Sine, Cosine, and Tangent - SOH, CAH - TOA
Video 120: Topic 9.8: Reference & Coterminal Angles
Video 121: Topic 9.9: Sine, Cosine & Tangent in the Unit Circle
Video 122: Topic 9.10: Unit Circle & Radians
Video 123: Topic 9.11: Sine and Cosine Function Values
Video 124: Topic 9.12: A Complete Guide to Deriving the Unit Circle from Scratch - Evaluate the Value of Sine & Cosine of BIG Angles.
Video 125: Topic 9.13: Cool Trick to memorize the Unit Circle in Seconds!
Video 126: Topic 9.14: Cool Trick to memorize the Trigonometric Values of Special Angles!
Practice: Follow this link to quiz yourself about finding the value of the Sine & Cosine w/wo the Unit Circle after you watch the videos 123-126.
Video 127: Topic 9.15: Master Sine & Cosine Graphs | Finding Maximum, Minimum, Midline, Amplitude, Period, Frequency, Increasing, Decreasing, and Concavity.
Video 128: Topic 9.16: Writing Sine & Cosine Functions Given Amplitude, Period, Phase Shift, and Vertical Shift.
Video 129: Topic 9.17: Graphing Sine & Cosine Functions.
Video 130: Topic 9.18: Writing Sine & Cosine Functions Given a Graph.
Video 131: Topic 9.19: How to Write Sinusoidal Functions Given a Data Set with a TI-Nspire Calculator and TI-84 Plus CE Calculator?
Video 132: Topic 9.20: Sinusoidal Function Context and Data Modeling.
Video 133: Topic 9.21: Sinusoidal Function Word Problems.
Video 134: Topic 9.22: Sinusoidal Regression with TI-Nspire & TI-84 Plus CE Calculators and Related Questions.
Video 135: Topic 9.23: How to Evaluate the Value of the Tangent Function?
Practice: Follow this link to quiz yourself about finding the value of the Tangent function w/wo the Unit Circle after you watch the video 135.
Video 136: Topic 9.24: Mastering Tangent Functions: Period, Inflection Points, Asymptotes & Graphing Made Easy!
Video 137: Topic 9.25: Writing the Tangent Function Given A Graph, Finding the Formula for the Vertical Asymptotes, and Finding the Slope of the Terminal Ray.
Video 138: Topic 9.26: Mastering the Graphs of Inverse Trigonometric Functions arcsin, arccos, arctan.
Video 139: Topic 9.27: Evaluating (Finding the Exact) Value of the Composition of Inverse Trigonometric Functions.
Video 140: Topic 9.28: Find the Inverse Trigonometric Functions & Their Domains and Ranges
Video 141: Topic 9.29: Exploring Graphs of Inverse Sine and Cosine Functions & Their Transformation.
Video 142: Topic 9.30: Solving Trigonometric Equations.
Video 143: Topic 9.31: Solving Trigonometric Inequalities.
Video 144: Topic 9.32: Trigonometric Inequalities with Double & Triple Angles.
Video 145: Topic 9.33: How to Prove Fundamental Trigonometric Identities | Step-by-Step Guide.
Video 146: Topic 9.34: Trick to Memorize Trigonometric Identities | Super Hexagon for Trigonometric Identities.
Video 147: Topic 9.35: Verifying Trigonometric Identities | Step-by-Step Guide.
Video 148: Topic 9.36: Finding the Exact Values of Trigonometric Functions Using Trigonometric Identities.
Video 149: Topic 9.37: Solving Trigonometric Equations Involving Fundamental Trigonometric Identities.
If you're looking to deepen your understanding of advanced concepts, give this a read:
Video 150: Topic 10.1: Writing the Equations of a Circle.
Video 151: Topic 10.2: Convert Circle Equations from Standard Form to General Form.
Video 152: Topic 10.3: Convert Circle Equations from General Form to Standard Form.
Video 153: Topic 10.4: Writing the Equation of an Ellipse.
Video 154: Topic 10.5: Writing the Equation of a Parabola.
Video 155: Topic 10.6: Writing the Equation of a Hyperbola.
Video 156: Topic 10.7: Classifying Conic Sections - Circle, Ellipse, Parabola, Hyperbola.
Video 157: Topic 10.8: Solving Systems of Equations Involving Conics.
Assorted Advanced Concepts
Dive into a collection of advanced math concepts!
This series of videos covers a variety of challenging topics designed to deepen your understanding and sharpen your problem-solving skills. Whether you’re preparing for competitions, exams, or just love advanced math, these concepts will push your thinking and expand your toolkit. Ready to level up? Let’s get started!
Explore my playlist of nearly 1000 Math Olympiad problem videos, with new content added regularly. Dive in and challenge yourself!