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Adding and Subtracting

  • Adding

  • Subtracting

  • The Number Line

  • Carrying and Borrowing

Multiplying and Dividing, including GCF and LCM

  • Multiplying

  • Long Multiplication

  • Dividing

  • Long Division

  • Prime numbers, Greatest Common Factors (GCF), and Least Common Multiples (LCM)


  • Adding and Subtracting Decimals

  • Multiplying and Dividing Decimals


  • Introduction to Fractions

  • Adding Fractions, Simplifying Fractions

  • Subtracting Fractions

  • Multiplying Fractions

  • Dividing Fractions

  • Comparing Fractions

  • Fractions Used in Cooking

Metric System


Percents, Ratios, and Proportions

  • Percentages and Percent Changes

  • Ratios and Proportions

  • Unit Multipliers

  • Using Percentages with Ratios

Negative Numbers and Absolute Value

  • Negative Numbers

  • Absolute Value

  • Adding and Subtracting Negative Numbers

  • Multiplying and Dividing Negative Numbers

Powers, Exponents, Radicals, and Scientific Notation

  • Exponents and Powers

  • Radicals

  • Simplifying and Rationalizing Radicals

  • Scientific Notation

Order of Operations PEMDAS


Introduction to Statistics and Probability

  • Average, Mean, Median, Mode, and Range

  • Box and Whisker Plot

  • Stem and Leaf Plot

  • Frequency Tables and Graphs

  • Pie Chart

  • Probability


Introduction to Algebra

  • Types of Numbers and Algebraic Properties

  • Types of Numbers

  • Algebraic Properties

  • Summary of Algebraic Properties (Chart)

  • Proper Algebraic Notation

Solving Algebraic Equations

  • Solving Linear Equations

  • Solving Literal Equations (Transforming Formulas)

Linear Inequalities

  • Basic Linear Inequalities

  • Inequalities

  • Absolute Value and Inequalities

  • Graphing Linear Inequalities with Two Variables

Word Problems in Algebra

  • English to Math Translation

  • Unit Rate Problem

  • “Find the Numbers” Word Problems

  • Percent Word Problem

  • Percent Increase Word Problem

  • Ratio/Proportion Word Problems

  • Weighted Average Word Problem

  • Consecutive Integer Word Problem

  • Age Word Problem

  • Money (Coins) Word Problem

  • Mixture Word Problem

  • Percent Mixture Word Problem

  • Rate/Distance Word Problem

  • Profit Word Problem

  • Converting Repeating Decimal to Fraction Word Problem

  • Inequality Word Problems

  • Integer Function Problem

  • Direct, Inverse, Joint and Combined Variation Word Problems

  • Work Word Problems (in Rational Functions and Equations)

  • Systems of Equations Word Problems

  • More Word Problems using Rational Functions

  • Absolute Value Word Problems

Coordinate System and Graphing Lines Including Inequalities

  • Coordinate System

  • Slope-Intercept Formula

  • Positive and Negative Slopes

  • Horizontal and Vertical Lines

  • Graphing Lines

    • T-Chart Method

    • Slope-Intercept Method

    • Converting Equations to the Slope-Intercept Method

    • Intercepts Method

    • Point-Slope Method

  • Obtaining an Equation for a Line

  • Parallel and Perpendicular Lines

  • Distance and Midpoint Formulas

  • Graphing Linear Inequalities with Two Variables

Direct, Inverse, Joint and Combined Variation

  • Direct or Proportional Variation

  • Inverse or Indirect Variation

  • Joint and Combined Variation

  • Partial Variation

Introduction to the Graphing Display Calculator (GDC)

  • Basic Graphing

  • Inequalities



Solving Quadratics by Factoring and Completing the Square

  • Factoring Methods

  • Completing the Square (Square Root Method)

  • Completing the Square to get Vertex Form

  • Obtaining Quadratic Equations from a Graph or Points

  • Quadratics Review

Quadratic Inequalities

  • Graphing Quadratic Inequality Functions

  • Solving Quadratic Inequalities

    • Solving Using Graphing

    • Solving Algebraically, including Completing the Square

    • Sign Chart (Sign Pattern) Method

  • Quadratic Inequality Real World Example

Quadratic Applications

  • Quadratic Projectile Problem

  • Quadratic Trajectory (Path) Problem

  • Optimization of Area Problem

  • Maximum Profit and Revenue Problems

  • Population Problem

  • Linear Increase/Decrease Problem

  • Pythagorean Theorem Quadratic Application

  • Quadratic Inequality Problem

  • Finding a Quadratic Equation from Points or a Graph

Solving Absolute Value Equations and Inequalities

  • Solving Absolute Value Equations

  • Solving Absolute Value Inequalities

  • Graphs of Absolute Value Functions

  • Applications of Absolute Value Equations

Solving Radical Equations and Inequalities

  • Radical Function Graphs

  • Solving Radical Equations Algebraically

  • Solving Radical Equations Graphically

  • Solving Radical Inequalities Algebraically

  • Solving Radical Inequalities Graphically

Imaginary (Non-Real) and Numbers

  • Introduction to Imaginary Numbers

  • Working with “i”

  • Quadratic Formula with Complex Solutions

  • Completing the Square with Complex Solutions

Systems of Linear Equations and Word Problems

  • Introduction to Systems

  • Solving Systems by Graphing

  • Solving Systems with Substitution

  • Solving Systems with Linear Combination or Elimination

  • Types of Equations

  • Word Problems with Systems

    • Investment Word Problem

    • Mixture Word Problems

    • Distance Word Problem

    • Which Plumber Problem

    • Geometry Word Problem

    • Work Problem

    • Three Variable Word Problem

    • The “Candy” Problem

    • Right Triangle Trigonometry Systems Problem

Algebraic Functions, including Domain and Range

  • Algebraic Functions Versus Relations

  • Vertical Line Test

  • Domain and Range of Relations and Functions

  • Finding the Domain Algebraically

Scatter Plots, Correlation, and Regression

  • Scatter Plots

  • Correlation

  • Regression

  • Using Graphing Calculator to Get Line of Best Fit

Exponents and Radicals in Algebra

  • Introducing Exponents and Roots (Radicals) with Variables

  • Properties of Exponents and Roots

  • Putting Exponents and Radicals in the Calculator

  • Rationalizing Radicals

  • Simplifying Exponential Expressions

  • Solving Exponential and Radical Equations

  • Solving Simple Radical Inequalities

Introduction to Multiplying Polynomials

  • What is a Polynomial?

  • Multiplying Polynomials

Introduction to Quadratics

  • Quadratics and the Parabola

  • Graphing Quadratics (Parabolas)

    • Graphing with Vertex Form

    • Graphing with Standard Form

    • Graphing with Factored (Intercept) Form

  • Standard Form to Vertex Form

  • Solving for Roots with Quadratics

    • Quadratic Formula

    • Using the Discriminant to Determine Types of Solutions

    • Using the Graphing Calculator to Find the Vertex and Solve Quadratics

  • Quadratic Transformations


Graphing Rational Functions, including Asymptotes

  • Revisiting Direct and Inverse Variation

  • Polynomial Long Division

  • Asymptotes of Rationals

  • Drawing Rational Graphs — General Rules

  • Rational Inequalities, including Absolute Values

  • Applications of Rational Functions

Graphing and Finding Roots of Polynomial Functions

  • Review of Polynomials

  • Polynomial Graphs

  • Polynomial Characteristics and Sketching Graphs

    • End Behavior of Polynomials

    • Zeros (Roots) and Multiplicity

  • Writing Equations for Polynomials

    • Conjugate Zeros Theorem Problem

  • Finding Roots of Polynomials

    • Synthetic Division

    • Rational Root Test

    • Putting it All Together: Finding all Factors and Roots of a Polynomial Function

  • Factor and Remainder Theorems

  • DesCartes’ Rule of Signs

  • Solving Polynomial Inequalities

  • Polynomial Applications

  • Revisiting Factoring to Solve Polynomial Equations

Exponential Functions

  • Exponential Functions

  • Parent Graphs of Exponential Functions

  • Writing Exponential Equations from Points and Graphs

  • Exponential Regression

  • Exponential Function Applications

  • Exponential Word Problems

  • Solving Exponential Functions by Matching Bases

  • Factoring to Solve with Exponents

Logarithmic Functions

  • Introduction to Logarithms

  • Special Logarithms

  • Using Logs (and Exponents) in the Graphing Calculator

  • Parent Graphs of Logarithmic Functions

  • Basic Log Properties, including Shortcuts

  • Expanding and Condensing Logs

  • Solving Exponential Equations using Logs

  • Solving Log Equations

  • Applications of Logs

Transformations, Inverses, Compositions, and Inequalities of Exponents/Logs

  • Transformations of Exponential and Log Functions

  • Writing Exponential and Logarithmic Functions from a Graph

  • Inverses and Compositions of Exponential and Logarithmic Functions

  • Exponential and Logarithmic Inequalities

Solving Inequalities

  • Linear Inequalities

  • Linear Inequalities in Two Variables

  • Quadratic Inequalities

  • Absolute Value Equations and Inequalities

  • Radical Equations and Inequalities

  • Using Inequalities to Find Domains of Composites

  • Rational Functions Inequalities

  • Polynomial Inequalities

  • Exponential and Log Inequalities

  • Trigonometry Inequalities

Advanced Functions: Compositions, Even and Odd, Increasing and Decreasing

  • Adding, Subtracting, Multiplying and Dividing Functions

  • Increasing, Decreasing and Constant Functions

  • Even and Odd Functions

  • Compositions of Functions (Composite Functions)

    • Decompose Functions

    • Domains of Composites

    • Applications of Compositions

Inverses of Functions

  • Introduction to Inverses

  • Finding Inverses Graphically

  • Finding Inverses Algebraically

  • Inverse Functions with Restricted Domains

  • Using Compositions of Functions to Determine if Functions are Inverses

Parent Functions and Transformations

  • Basic Parent Functions

  • Generic Transformations of Functions

    • Vertical Transformations

    • Horizontal Transformations

  • Mixed Transformations

  • Transformations in Function Notation

  • Writing Transformed Equations from Graphs

  • Rotational Transformations

  • Transformations of Inverse Functions

  • Absolute Value Transformations

  • Applications of Parent Function Transformations

Piecewise Functions

  • Introduction to Piecewise Functions

  • Evaluating Piecewise Functions

  • Graphing Piecewise Functions

  • How to Tell if a Piecewise Function is Continuous or Non-Continuous

  • Obtaining Equations from Piecewise Function Graphs

  • Absolute Value as a Piecewise Function

  • Transformations of Piecewise Functions

  • Piecewise Function Word Problems

The Matrix and Solving Systems with Matrices

  • Introduction to the Matrix

  • Adding and Subtracting Matrices

  • Multiplying Matrices

  • Matrices in the Graphing Calculator

  • Determinants, the Matrix Inverse, and the Identity Matrix

  • Solving Systems with Matrices

  • Solving Word Problems with Matrices

  • Cramer’s Rule

  • Number of Solutions when Solving Systems with Matrices

Introduction to Linear Programming

  • Review of Inequalities

  • Bounded and Unbounded Regions

  • Inequality Word Problem

  • Linear Programming Terms

  • Linear Programming Word Problems

Advanced Factoring

  • Revisiting Factoring Quadratics

  • Factoring with Polynomials

  • Factoring Sum and Difference of Cubes

  • Factoring with Exponents

Rational Functions and Equations

  • Introducing Rational Expressions

  • Finding the Common Denominator

  • Adding and Subtracting Rationals

  • Restricted Domains of Rational Functions

  • Solving Rational Equations

  • Applications of Rationals


Conics: Circles, Parabolas, Ellipses, and Hyperbolas

  • Tables of Conics

  • Circles

  • Applications of Circles

  • Parabolas

  • Applications of Parabolas

  • Ellipses

  • Applications of Ellipses

  • Hyperbolas

  • Applications of Hyperbolas

  • Identifying the Conic

Systems of Non-Linear Equations

  • Systems of Non-Linear Equations

  • Non-Linear Equations Application Problems

Introduction to Vectors

  • Introduction to Vectors

  • Vector Operations

  • Applications of Vectors

  • Dot Product and Angle Between Two Vectors

  • 3D Vectors – Vectors in Space (including Cross Product)

  • Parametric Form of the Equation of a Line in Space

  • More Practice

Parametric Equations

  • Introduction to Parametric Equations

  • Parametric Equations in the Graphing Calculator

  • Converting Parametric Equations to Rectangular Equations: Eliminating the Parameter

  • Finding Parametric Equations from a Rectangular Equation

  • Simultaneous Solutions

  • Applications of Parametric Equations

  • Projectile Motion Applications

  • Parametric Form of the Equation of a Line in Space

Sequences and Series

  • Introduction to Sequences and Series

  • Summary of Formulas for Sequences and Series

  • Sequences and Series Terms

  • Explicit Formulas Versus Recursive Formulas

  • Arithmetic Sequences

  • Geometric Sequences

  • Writing Formulas

  • Arithmetic Series

  • Summation Notation

  • Geometric Series

  • Applications of Sequences and Series

Binomial Expansion

  • Introduction to Binomial Expansion

  • Expanding a Binomial

  • Finding a Specific Term with Binomial Expansion

Trigonometric Identities

  • Reciprocal and Quotient Identities

  • Pythagorean Identities

  • Solving with Reciprocal, Quotient and Pythagorean Identities

  • Sum and Difference Identities

  • Solving with Sum and Difference Identities

  • Double Angle and Half Angle Identities

  • Solving with Double and Half Angle Identities

  • Trig Identity Summary and Mixed Identity Proofs

Law of Sines and Cosines and Areas of Triangles

  • Review of Right Triangle Trig

  • Law of Sines

  • Law of Cosines

  • Area of Triangles

  • Applications/Word Problems

Polar Coordinates, Equations and Graphs

  • Plotting Points Using Polar Coordinates

  • Polar-Rectangular Point Conversions

  • Drawing Polar Graphs

  • Converting Equations from Polar to Rectangular

  • Converting Equations from Rectangular to Polar

  • Polar Graph Points of Intersection

Trigonometry and the Complex Plane

  • Review of Complex Numbers

  • Polar (Trig) Form of a Complex Number

  • Products and Quotients of Complex Numbers in Polar Form

  • De Moivre’s Theorem: Powers of Complex Numbers

  • Roots of Complex Numbers

  • Complex Trig in the Graphing Calculator


Right Triangle Trigonometry

  • Basic Trigonometric Functions (SOH-CAH-TOA)

  • Trigonometry Word Problems

Angles and the Unit Circle

  • Angles in Trigonometry

  • Degrees, Radians, and Co-Terminal Angles

  • The Unit Circle

Linear and Angular Speeds, Area of Sectors, and Length of Arcs

  • Linear Speed

  • Angular Speed

  • Area of Sectors

  • Length of Arcs

Graphs of Trig Functions

  • Table of Trigonometric Parent Functions

  • Graphs of the Six Trigonometric Functions

Transformations of Trig Functions

  • T-Charts for the Six Trigonometric Functions

  • Sine and Cosine Transformations

  • Cosecant and Secant Transformations

  • Tangent and Cotangent Transformations

  • Transformations of all Trig Functions without T-Charts

The Inverses of Trigonometric Functions

  • Introduction to Inverse Trig Functions

  • Graphs of Inverse Functions

  • Evaluating Inverse Trig Functions – Special Angles

  • Transformations of the Inverse Trig Functions

Solving Trigonometric Equations

  • Solving Trigonometric Equations Using the Unit Circle

  • Solving Trigonometric Equations – General Solutions

  • Solving Trigonometric Equations with Multiple Angles

  • Factoring to Solve Trigonometric Equations

  • Solving Trigonometric Equations on the Calculator

  • Solving Trig Systems of Equations

  • Trigonometric Inequalities


Introduction to Calculus

Differential Calculus Quick Study Guide

Limits and Continuity

  • Introduction to Limits

  • Finding Limits Algebraically

  • Continuity and One Side Limits

  • Continuity of Functions

  • Properties of Limits

  • Limits with Sine and Cosine

  • Intermediate Value Theorem (IVT)

  • Infinite Limits

  • Limits at Infinity

Definition of the Derivative

  • Tangent Line

  • Definition of the Derivative

  • Equation of a Tangent Line

  • Definition of Derivative at a Point (Alternative Form of the Derivative)

  • Derivative Feature on a Graphing Calculator

  • Determining Differentiability

  • Derivatives from the Left and the Right

Basic Differentiation Rules: Constant, Power, Product, Quotient and Trig Function Rules

  • Constant Rule

  • Power Rule

  • Product Rule

  • Quotient Rule

  • List of Rules

  • Examples of Constant, Power, Product and Quotient Rules

  • Derivatives of Trig Functions

  • Higher Order Derivatives

Equations of the Tangent Line, Tangent Line Approximation, and Rates of Change

  • Equation of the Tangent Line

  • Equation of the Normal Line

  • Horizontal and Vertical Tangent Lines

  • Tangent Line Approximation

  • Rates of Change and Velocity

The Chain Rule

  • The Chain Rule Basics

  • The Equation of the Tangent Line with the Chain Rule

Implicit Differentiation and Related Rates

  • Implicit Differentiation

  • Equation of the Tangent Line with Implicit Differentiation

  • Related Rates

Curve Sketching

  • Extreme Value Theorem, Rolle’s Theorem, and Mean Value Theorem

  • Relative Extrema and First Derivative Test

  • Concavity and the Second Derivative

  • Curve Sketching: General Rules


  • Introduction to Optimization

  • Absolute Extrema

  • Optimization Problems

Differentials, Linear Approximation and Error Propagation

  • Differentials

  • Linear Approximation

  • Error Propagation

Exponential and Logarithmic Differentiation

  • Introduction to Exponential and Logarithmic Differentiation and Integration

  • Differentiation of the Natural Logarithmic Function

  • General Logarithmic Differentiation

  • Inverses and Derivative of an Inverse

  • Derivative of e

  • Derivatives of Inverse Trig Functions

Exponential and Logarithmic Integration

  • Introduction to Exponential and Logarithmic Integration

  • Review of Logarithms

  • The Log Rule for Integration

  • Integrals of Trigonometric Functions using “ln”

  • Integrals of eu and au

Exponential Growth using Calculus

  • Introduction to Exponential Growth and Decay

  • Solving Exponential Growth Problems Using Differential Equations

  • Exponential Growth Word Problems

Derivatives and Integrals of Inverse Trig Functions

  • Derivatives of the Inverse Trig Functions

  • Integrals Involving the Inverse Trig Functions

Applications of Integration: Area and Volume

  • Area Between Curves

  • Volumes of Solids by Cross Sections

  • Volumes of Solids: The Disk Method

  • Volumes of Solids: The Washer Method

  • Volumes of Solids: The Shell Method

Integration by Parts

  • Introduction to Integration by Parts

  • Guidelines for Integration by Parts using LIATE

  • Integration by Parts Problems

  • Tabular Method for Integration by Parts

Integration by Partial Fractions

  • Introduction to Integration by Partial Fractions

  • Integration by Partial Fractions with Improper Fractions

  • Example of Rational Function where Partial Fractions are not Needed

  • Integration by Partial Fractions with Higher Degrees

  • More Practice

Integral Calculus Quick Study Guide

Antiderivatives and Indefinite Integration, including Trig Integration

  • Antiderivatives

  • Basic Integration Rules

  • Trigonometric Integration Rules

  • Indefinite Integration Problems

  • Initial Conditions and Particular Solutions

  • Position, Velocity, and Acceleration

U-Substitution Integration

  • Introduction to U-Substitution

  • U-Substitution Integration Problems

Differential Equations and Slope Fields

  • Differential Equations and Separation of Variables

  • Slope Fields

L’Hopital’s Rule

Riemann Sums and Area by Limit Definition

  • Introduction to Riemann Sums

  • Using Upper and Lower Sums to Approximate Areas

  • Using Midpoint Rule to Approximate Area

  • Upper, Lower, and Midpoint Rule Sums Problems

  • Trapezoidal Rule

  • Area by Limit Definition Problems

Definite Integration

  • Introduction to Definite Integrals

  • Properties of Definite Integrals

  • 1st Fundamental Theorem of Calculus

  • Definite Integrals on the Graphing Calculator

  • Definite Integration and Area

  • Mean Value Theorem (MVT) for Integrals

  • Average Value of a Function

  • Integration as Accumulated Change and Average Value Applications

  • 2nd Fundamental Theorem of Calculus

  • Using U-Substitution with Definite Integration


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