Interactive Algebra Ii: Learn By Doing

An Engaged Approach To Teach You Algebra II

What you'll learn

Students will learn about functions and their domain.

Students will learn about inverse functions and composite functions and their domains.

Students will learn about exponential functions and logarithmic functions.

Students will learn how to graph polynomial and rational functions.

Requirements

Completion of an Algebra I course

Description

This is an Algebra II course structured on the OpenStax textbook College Algebra.  Each section begins with an original activity designed to show you the concepts in a way that brings deeper understanding.  Work the activity. And if you need help, watch the video where I walk through every question of the activity. A link to a full, traditional lecture is also available.  Use this course to learn Algebra II for the first time or use this course as a tutoring tool to help you with the course you are already taking.  Designed to mimic the engaged learning approach which I use in my college classrooms, you drive the learning, and I serve as the facilitator.  I also created this course to be an alternative to traditional tutoring.  Tutoring is fantastic, but it can be expensive and hard to find.  Here, my activities are the exact material and concepts which I would share with you in a tutoring session to bring the concepts home.  So, use the index of the textbook to find the topics you need, and search for the activity which you are working on in your traditional classroom.  The choice is yours.Section topics discussed are:Equations and InequalitiesFunctionsLinear FunctionsPolynomial and Rational FunctionsExponential and Logarithmic FunctionsSystems of Equations and InequalitiesAnalytic GeometrySequences, Probability, and Counting Theory

Overview

Section 1: Introduction

Lecture 1 Introduction

Lecture 2 How to Use This Course as a Tutoring Tool

Section 2: Prerequisites

Lecture 3 1.1a: Classifying Numbers and the Order of Operations

Lecture 4 1.1b: Key Math Properties; Evaluating Expressions; Simplifying Expressions

Lecture 5 1.2a: Exponent Rules

Lecture 6 1.2b: Scientific Notation

Lecture 7 1.3a: Working with Roots

Lecture 8 1.3b: Rationalizing Denominators; Fractional Exponents

Lecture 9 1.4a: Adding, Subtracting and Multiplying Polynomials

Lecture 10 1.4b: Special Patterns when Multiplying Polynomials

Lecture 11 1.5a: Factoring Polynomials

Lecture 12 1.5b: Factoring the Sum or Difference of Cubes; Factoring Fractional Exponents

Lecture 13 1.6a: Simplifying Rational Expressions

Lecture 14 1.6b: Adding and Subtracting Rational Expressions

Section 3: Equations and Inequalities

Lecture 15 2.1a: Graphing by Plotting Points; x and y-intercepts

Lecture 16 2.1b: The Midpoint and Distance Formulas

Lecture 17 2.2a: Solving Equations

Lecture 18 2.2b: Slope of a Line; Standard Form of a Line

Lecture 19 2.2c: Parallel and Perpendicular Lines

Lecture 20 2.3a: Word Problems Involving Lines and D=rt

Lecture 21 2.3b: Word Problems Involving Perimeter and Area

Lecture 22 2.4a: Introduction to Complex Numbers

Lecture 23 2.4b: Adding/Subtracting and Multiplying Complex Numbers

Lecture 24 2.4c: Dividing Complex Numbers

Lecture 25 2.5a: Solving Quadratic Equations

Lecture 26 2.5b: The Quadratic Formula

Lecture 27 2.6a: Higher Order Roots and Equations with Rational Exponents

Lecture 28 2.6b: Solving absolute value, higher order, and rational equations

Lecture 29 2.7a: Compound Inequalities

Lecture 30 2.7b: Absolute Value Inequalities

Section 4: Functions

Lecture 31 3.1a: Introduction to Functions

Lecture 32 3.1b: One-to-One Functions

Lecture 33 3.2a: Domain of a Function

Lecture 34 3.2b: Graphs of the Toolkit Functions; Piecewise Functions

Lecture 35 3.3a: Average Rate of Change

Lecture 36 3.3b: Increasing and Decreasing; Extrema of a Function

Lecture 37 3.4a: Mathematical Operations on Functions; Composite Functions

Lecture 38 3.4b: Domain of a Composite Function

Lecture 39 3.5a: Vertical and Horizontal Transformations of Functions

Lecture 40 3.5b: Combining Multiple Transformations

Lecture 41 3.5c: Vertical and Horizontal Stretches/Compressions; Even/Odd Functions

Lecture 42 3.6: Absolute Value Functions

Lecture 43 3.7a: Inverse Functions

Lecture 44 3.7b: Finding an Inverse of a Function

Section 5: Linear Functions

Lecture 45 4.1a: Applying Lines as Functions

Lecture 46 4.1b: Understanding Lines as Transformations

Lecture 47 4.1c: Investigating Parallel or Perpendicular Lines as Functions

Lecture 48 4.2: Further Applications with Linear Functions

Lecture 49 4.3a: Introduction to Correlation and Scatterplots

Lecture 50 4.3b: Introduction to Linear Regression

Section 6: Polynomial and Rational Functions

Lecture 51 5.1a: The Vertex Form of a Quadratic Function

Lecture 52 5.1b: Intercepts of Quadratics; Max/Min of Quadratics

Lecture 53 5.1c: Applications involving Max/Min of a Quadratic

Lecture 54 5.2a: Introduction to Polynomial Functions

Lecture 55 5.2b: End Behavior of Polynomial Functions

Lecture 56 5.3a: Intercepts of Polynomial Functions; Multiplicity

Lecture 57 5.3b: Graphing Polynomial Functions

Lecture 58 5.4a: Dividing Polynomials Using Long Division

Lecture 59 5.4b: Dividing Polynomials Using Synthetic Division

Lecture 60 5.5a: The Remainder Theorem and the Factor Theorem

Lecture 61 5.5b: The Rational Zero Theorem

Lecture 62 5.5c: Descartes Rule of Signs

Lecture 63 5.6a: Asymptotes of Rational Functions

Lecture 64 5.6b: Graphing Rational Functions

Lecture 65 5.7a: Review of Inverse Functions

Lecture 66 5.7b: Restricting Functions

Lecture 67 5.7c: Finding the Inverse of a Formula

Lecture 68 5.8: Direct and Indirect Variation

Section 7: Exponential and Logarithmic Functions

Lecture 69 6.1a: Introduction to the Exponential Function

Lecture 70 6.1b: Compound and Continuous Interest

Lecture 71 6.2a: Transformations of the Exponential Function

Lecture 72 6.2b: Graphing Exponential Functions

Lecture 73 6.3: Introduction to Logarithms

Lecture 74 6.4a: Graphs of Logarithmic Functions

Lecture 75 6.4b: Graphing Transformations of Logarithms

Lecture 76 6.5a: Properties of Logarithms

Lecture 77 6.5b: Condensing Logarithms and the Change of Base Formula

Lecture 78 6.6a: Solving Equations Involving the Exponential Function

Lecture 79 6.6b: Solving Equations Involving Logarithms

Section 8: Systems of Equations and Inequalities

Lecture 80 7.1a: Solving Systems of Linear Equations by Graphing

Lecture 81 7.1b: Solving Systems of Linear Equations by Substitution

Lecture 82 7.1c: Solving Systems of Linear Equations by Elimination

Lecture 83 7.2: Solving Three-Dimensional Systems of Equations

Lecture 84 7.3a: Solving Systems of Non-Linear Equations

Lecture 85 7.3b: Solving Non-Linear Systems of Inequalities

Lecture 86 7.4a: Decomposing Fractions

Lecture 87 7.4b: Decomposing Fractions which Include Quadratics

Lecture 88 7.5a: Introduction to Matrices

Lecture 89 7.5b: Multiplying Matrices

Lecture 90 7.6a: Solving Systems of Linear Equations with Augmented Matrices

Lecture 91 7.6b: Solving Larger Systems of Equations with Matrices

Lecture 92 7.7a: Inverse Matrices

Lecture 93 7.7b: Solving Systems of Equations with Inverse Matrices

Lecture 94 7.8a: Determinant of a Matrix; Cramer's Rule

Lecture 95 7.8b: Properties of Determinants

Section 9: Analytic Geometry

Lecture 96 8.1a: Understanding the Equation for the Standard Form of an Ellipse

Lecture 97 8.1b: Graphing an Ellipse

Lecture 98 8.1c: Rewriting the Equation for an Ellipse in Standard Form

Lecture 99 8.2a: Understanding the Equation for the Standard Form of a Hyperbola

Lecture 100 8.2b: Graphing Hyperbolas

Lecture 101 8.2c: Write an Equation for a Hyperbola in Standard Form

Lecture 102 8.3a: Understanding the Equation for the Standard Form of a Parabola

Lecture 103 8.3b: Graphing Parabolas

Lecture 104 8.3c: Write an Equation for a Parabola in Standard Form

Section 10: Sequences, Probability and Counting Theory

Lecture 105 9.1a: Explicit Formulas for Sequences

Lecture 106 9.1b: Recursive Formulas for Sequences

Lecture 107 9.2a: Introduction to Arithmetic Sequences

Lecture 108 9.2b: Writing Explicit and Recursive Formulas for Arithmetic Sequences

Lecture 109 9.3a: Introduction to Geometric Sequences

Lecture 110 9.3b: Writing Explicit and Recursive Formulas for Geometric Sequences

Lecture 111 9.4a: Summations

Lecture 112 9.4b: Infinite Geometric Sequences

Lecture 113 9.5: Counting Principle; Combinations and Permutations

Lecture 114 9.6: The Binomial Theorem

Lecture 115 9.7: Basic Probability

High School or College Learners needing help with Algebra II or College Algebra