Unit 0: 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: Work, Rate & Distance-Time Word Problems
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 2.6A: Exploring Transformation of Functions
Video 15: Topic 2.6B: Transformations of Functions (Translation, Reflection, Dilation) with/without a Graph.
Video 16: Topic 2.7: Graphs of |f(x)| and f(|x|) from f(x).
Video 17: Topic 2.8: Inverse Functions.
Video 18: Topic 2.9A Adding, Subtracting, Multiplying & Dividing Functions
Video 19: Topic 2.9B: Composition of Functions.
Video 20: Topic 2.10: Domain of Composite Functions.
Unit 3: Advanced Linear Functions & Equations
Video 21: Topic 3.1: Determine the Slopes/Rate of Change of Linear Functions.
Video 22: Topic 3.2: Write the Equations of Parallel & Perpendicular Lines.
Video 23: Topic 3.3: Direct Variation/Proportionality.
Video 24: Topic 3.4: Modeling Functions and Applications | Best-fitting Linear Regression Model.
Video 25: Topic 3.5: Graphing & Writing Piecewise Functions | Domain & Range | Piecewise Function Related Problems.
Video 26: Topic 3.6: Absolute Value Functions: Characteristics, Graphing, Writing, and Transformation.
Video 27: Topic 3.7: Graphing & Writing Linear & Absolute Value Inequality Functions.
Video 28: Topic 3.8: Graphing System of Multiple Inequalities (Linear Inequalities, Absolute Value Inequalities, Quadratic Inequalities, Radical Inequalities).
Unit 4: Systems of Equations & Matrices
Video 29: Topic 4.1: Solving a System of 2 Linear Equations Using a Graphing Calculator.
Video 30: Topic 4.2: Solving a System of 2 Linear Equations by Substitution.
Video 31: Topic 4.3: Solving a System of 2 Linear Equations by Elimination.
Video 32: Topic 4.4: Solving a System of 3 Equations by Substitution, Elimination.
Video 33: Topic 4.5: Solving a System of 2 & 3 Equations Word Problems.
Video 34: Topic 4.6: Adding, Subtracting, and Multiplying Matrices.
Video 35: Topic 4.7: Finding the Determinant of 2x2 Matrices.
Video 36: Topic 4.8: Finding the Determinant of 3x3 Matrices.
Video 37: Topic 4.9: Finding the Inverse of 2x2 Matrices.
Video 38: Topic 4.10: Finding the Inverse of 3x3 Matrices Using Adjoint & Cofactor Method.
Video 39: Topic 4.11: Finding the Inverse of 3x3 Matrices Using Gauss-Jordan Elimination.
Video 40: Topic 4.12: Finding the Area of a Triangle Using Matrix.
Video 41: Topic 4.13: Solving the Matrix Equations.
Video 42: Topic 4.14: Using Inverse Matrices to Solve the Linear System of Equations.
Video 43: Topic 4.15: Solving a System of Equations by Cramer's Rule.
Video 44: Topic 4.16: Solving a System of Equations by Gauss-Jordan Elimination. (Bonus)
Unit 5: Quadratic Functions, Inequalities, & Complex Numbers
Video 45: Topic 5.1: Factoring Trinomials.
Video 46: Topic 5.2: Factoring Special Cases of Polynomials.
Video 47: Topic 5.3: Advanced Factoring of Polynomials.
Video 48: Topic 5.4: Characteristics of Quadratic Functions in Standard Form y = ax^2 + bx + c (a#0).
Video 49: Topic 5.5: Characteristics of Quadratic Functions in Vertex Form y = a(x-h)^2 + k (a#0).
Video 50: Topic 5.6: Characteristics of Quadratic Functions in Intercept Form y = a(x-p)(x-q) (a#0).
Video 51: Topic 5.7: Convert Quadratic Functions from Standard Form <=> Vertex Form <=> Intercept Form <=> Standard Form.
Video 52: Topic 5.8: Maximization/Minimization (Optimization) Problems Using Quadratic Function Models.
Video 53: Topic 5.9: Simplifying Rational Exponents and Radicals.
Video 54: Topic 5.10: Writing Quadratic Functions Given Vertex and a Point, Two Zeros, 3 Points, Tables, Word Problems.
Video 55: Topic 5.11: Solving Quadratic Equations by Factoring.
Video 56: Topic 5.12: Solving Quadratic Equations by Taking Square Root and Completing Squares.
Video 57: Topic 5.13: Solving Quadratic Equations Using Quadratic Formula and Graphing Calculator.
Video 58: Topic 5.14(A): 5 Different Ways to Solve a Quadratic Equation - Part 1.
Video 59: Topic 5.14(B): 5 Different Ways to Solve a Quadratic Equation - Part 2.
Video 60: Topic 5.15: Solving Systems of Linear & Quadratic Equations.
Video 61: Topic 5.16: Solving Quadratic Inequalities.
Video 62: Topic 5.17: Graphing & Writing Quadratic Inequalities & Systems of Quadratic Inequalities.
Video 63: Topic 5.18: Add, Subtract, Multiply, and Divide Complex Numbers.
Video 64: Topic 5.19: Quadratic Equations with Imaginary Solutions.
Video 65: Topic 5.20: De Moivre's Theorem - Complex Numbers in Polar. (Bonus)
Unit 6: Square Root & Cubic & Cube Root Functions & Equations & Inequalities
Video 66: Topic 6.1: Simplifying Radical Expressions.
Video 67: Topic 6.2: Square Root & Quadratic Functions: Key Features, Transformations, and Inverses.
Video 68: Topic 6.3: Solving Square Root Equations.
Video 69: Topic 6.4: Solving Square Root Inequalities.
Video 70: Topic 6.5: Cube Root & Cubic Functions: Key Features, Transformations, and Inverses.
Video 71: Topic 6.6: Solving Cube Root Equations.
Unit 7: Polynomial & Rational Functions & Equations & Inequalities
Video 72: Topic 7.1: New Method of Factoring Trinomials WITHOUT Guessing and Checking.
Video 73: Topic 7.2: Factoring Special Cases of Polynomials.
Video 74: Topic 7.3(A): Long Division & Synthetic Division with 8 Specific Examples - The easy way!
Video 75: Topic 7.3(B): Dividing Polynomials using 3 methods: Factoring - Long Division - Synthetic Division.
Video 76: Topic 7.4: Factor Theorem & Remainder Theorem.
Video 77: Topic 7.5: Rational Root Theorem & Fundamental Theorem of Algebra.
Video 78: Topic 7.6: Descartes’ Rule of Signs (Bonus)
Video 79: Topic 7.7: Direct, Inverse, Joint and Combined Variation.
Video 80: Topic 7.8: Polynomial Functions and Rates of Change | Local (Relative) Min/Max | Global (Absolute) Min/Max | Points of Inflection | Turning Points.
Video 81: 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 82: Topic 7.10: Solving Polynomial Inequalities.
Video 83: Topic 7.11(A): Polynomial Functions and End Behavior.
Video 84: Topic 7.11(B): Polynomial Functions and End Behavior (Foldable Activity) - Easy way to memorize!
Video 85: Topic 7.12: Rational Functions and End Behavior - Horizontal Asymptotes and Slant Asymptotes.
Video 86: Topic 7.13: Rational Functions and Zeros | Solving Rational Inequalities.
Video 87: Topic 7.14(A): Vertical Asymptotes and Holes - Horizontal Asymptotes and Slant Asymptotes - Graphing Rational Functions
Video 88: Topic 7.14(B): If Vertical Asymptotes, Holes, and Zeros (x-intercepts) occur simultaneously, which one beats?
Video 89: Topic 7.15: How to Write a Rational Function Given a Graph.
Video 90: Topic 7.16: Add, Subtract, Multiply, and Divide Rational Expressions.
Video 91: Topic 7.17: Partial Fraction Decomposition.
Video 92: Topic 7.18: Solving Rational Equations & Complex Fractions Equations.
Video 93 (Challenge): Using Partial Fraction Decomposition to Solve the finite Rational Equation. (Bonus)
Unit 8: Exponential & Logarithmic Functions & Equations & Inequalities
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: Find the Domain, Range, Y-intercept, Asymptote of an Exponential Function.
Video 98: Find the Domain, Range, Y-intercept, Asymptote of an Exponential Function Word Problems.
Video 99: Exponential Growth & Decay Functions.
Video 100:Modeling Exponential Functions in Finance | Compound Interest.
Video 101: Topic 8.4: Exponential Function Manipulation | Why is the Horizontal Translation the same as Vertical Dilation?
Video 102 Topic 8.5: Exponential Function Context and Data Modeling with a TI-Nspire & TI-84 Plus CE Calculator.
Video 103: Topic 8.6: Properties of Logarithms | Proof and Walkthrough Examples.
Video 104: Topic 8.7: Logarithmic Expressions.
Video 105: Topic 8.8: Inverses of Exponential Functions & Logarithmic Functions.
Video 106: Topic 8.9: Logarithmic Functions |Characteristics, End Behavior, Concavity, and Transformations |Determine if the function is increasing/decreasing at an increasing/decreasing rate?
Video 107: Topic 8.10: Expand & Condense Logarithmic Expressions | Is the Horizontal Dilation the same as the Vertical Translation?
Video 108: Topic 8.11: Exponential and Logarithmic Equations.
Video 109: Topic 8.12: Mastering Compound Interest: Step-by-Step Proofs & Real-Life Examples.
Video 110: Topic 8.13: Exponential and Logarithmic Equations Word Problems in Finance| Interest Compounded Annually & Continuously.
Video 111: Topic 8.14: Exponential and Logarithmic Inequalities.
Video 112: Topic 8.15: Logarithmic Function Context and Data Modeling with TI-Nspire & TI-84 Plus CE Calculator.
Unit 9: Trigonometric Functions & Equations & Inequalities
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 & Graphing 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 & Graphing the Equation of an Ellipse.
Video 154: Topic 10.5: Writing & Graphing the Equation of a Parabola.
Video 155: Topic 10.6: Writing & Graphing the Equation of a Hyperbola.
Video 156: Topic 10.7: Identifying & Classifying Conic Sections: Circle, Ellipse, Parabola, Hyperbola.
Video 157: Topic 10.8: Solving Systems of Equations Involving Conic Sections.
Unit 11: Area & Sequences & Series
Video 158: Topic 11.1 Exploring Accumulation of Change
Video 159: Topic 11.2 Approximating Areas with Left, Right, and Midpoint Riemann Sums as well as Trapezoidal Rules
Video 160: Topic 11.3 Riemann Sums, Summation Notation, and Definite Integral Notation
Video 161: Topic 11.4 Change in Arithmetic and Geometric Sequences.
Video 162: Topic 11.5 Defining Convergent and Divergent Infinite Series
Video 163: Topic 11.6A Proof of Finite & Infinite Geometric Series
Video 164: Topic 11.6B Convergent and Divergent Geometric Series | Telescoping Series
Unit 12: Position & Velocity & Acceleration
Video 165: Topic 12.1 Interpreting the Meaning of the Derivative in Context
Video 166: Topic 12.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
Video 167: Topic 12.3 Rates of Change in Applied Contexts Other Than Motion
Assorted Advanced Concepts
Dive into a collection of advanced math concepts!
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Explore my playlist of nearly 1000 Math Olympiad problem videos, with new content added regularly. Dive in and challenge yourself!