Precalculus Algebra – Project Greater Ed

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Hundreds of Worked-Out Example Problems with written and/or video explanations
Short Mini Lesson Videos to help with learning key concepts in a fraction of the time
Key takeaways and written content after each mini lesson video to deepen understanding

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Sets

Notations for Sets Sample Lesson

Set Membership and Set Inclusion 2 Topics Sample Lesson

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Set Membership

Set Inclusion and Subsets

Set Operations 4 Topics Sample Lesson

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Set Unions

Set Intersections

Set Complements and Set Differences

Combining Set Operations

Exponents and Exponential Expressions

What Exponents Actually Mean Sample Lesson

Arithmetical Rules For Exponential Expressions 2 Topics Sample Lesson

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Exponent Rules

Negative Exponents and Cancellation

Polynomial Arithmetic

What Is (and Isn’t) a Polynomial

Adding and Subtracting Polynomials

Multiplying Polynomials (aka “Distribution” or “FOILing”)

Factoring

Basic Factoring Methods 2 Topics

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Factoring Out Greatest Common Factors

Factoring By Grouping

Factoring Quadratic Expressions 2 Topics

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Factoring Quadratics where \(a=1\)

Factoring Harder Quadratics, where a isn’t 1

Factoring Differences of Squares

Rational Expressions

Arithmetic with Rational Expressions 3 Topics

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Multiplying and Dividing Rational Expressions, and Cancellation

Adding, Subtracting, and Common Denominator Finding with Rational Expressions

Simplifying Compound/Complex Fractions

Radical Expressions

Simplifying Radical Expressions 4 Topics

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Radical Cancellation and Fractional Power Representation

The Multiplication Rule for Radicals and Factor Trees

Simplifying Radical Expressions Involving Multiplication and Division

Adding, Subtracting, and FOILing with Radical Expressions

Rationalizing Denominators 2 Topics

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Basic Rationalizing of Denominators

Rationalizing Denominators Using Conjugates

Functions Basics

What Functions Are and How They are Represented 4 Topics

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Using Potato Diagrams

Using Sets/Lists of Ordered Pairs and Tables

Using a Given (Algebraic) Rule

Using Graphs and Plotting Them from Rules

Domains and Ranges of Functions 2 Topics

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Finding Domains and Ranges Using Potato Diagrams and Sets of Ordered Pairs or Tables

Finding Domains and Ranges Using Graphs of Functions

Function Arithmetic (with Numerical Substitutions) 3 Topics

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Basic Function Arithmetic Using Function Rules, and Numerical Substitutions

Function Arithmetic: Using Tables to Evaluate Various Combinations of Functions at a Given Value

Function Arithmetic: Using Graphs to Evaluate Various Combinations of Functions at a Given Value

Function Composition: Plugging One Function Into Another 3 Topics

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Composing Two Function Rules

Composing Functions Using Tables

Composing Functions Using Graphs

The Difference Quotient

New Functions Constructed From Old

A Library of Commonly Used Functions (and Their Graphs)

Function Transformations: Shifting, Scaling, Reflecting

Piecewise-Defined Functions 2 Topics

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Evaluating Piecewise-Defined Functions at a Given x-Value

Graphing Piecewise-Defined Functions

Linear Functions

Intro to Linear Functions and their Uses

Graphing Linear Functions from Slope-Intercept Form

Finding Equations of Lines Using Point-Slope Form

Average Rates of Change

Solving Linear Equations

Quadratic Functions

Solving Quadratic Equations 3 Topics

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Using the Zero-Factor Property

Using the Square Root Property

Using the Quadratic Formula

Quadratic Functions Praxis

Exponential Functions

Exponential Functions Basics 2 Topics

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Evaluating Exponential Functions at a Point

Graphing Exponential Functions and their Transformations

Compound Interest and the Natural Exponential Function 2 Topics

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Compound Interest – Multiplying Your Money

The Natural Exponential Function

Exponential Functions Praxis

Logarithms

Logarithms 4 Topics

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Evaluating Logarithmic Functions at Given x-Values

Graphing and Transforming Logarithmic Functions

Log Laws and Change-of-Base Formula

Solving Logarithmic and Exponential Equations

Logarithms Praxis