BASIC MATH
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)
Decimals

Adding and Subtracting Decimals

Multiplying and Dividing Decimals
Fractions

Introduction to Fractions

Adding Fractions, Simplifying Fractions

Subtracting Fractions

Multiplying Fractions

Dividing Fractions

Comparing Fractions

Fractions Used in Cooking
Metric System
PREALGEBRA
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

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
BEGINNING ALGEBRA
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

SlopeIntercept Formula

Positive and Negative Slopes

Horizontal and Vertical Lines

Graphing Lines

TChart Method

SlopeIntercept Method

Converting Equations to the SlopeIntercept Method

Intercepts Method

PointSlope 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
MMT MATH CURRICULUM
INTERMEDIATE ALGEBRA
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 (NonReal) 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
ADVANCED ALGEBRA
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 NonContinuous

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
PRECALCULUS
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 NonLinear Equations

Systems of NonLinear Equations

NonLinear 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

PolarRectangular 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
TRIGONOMETRY
Right Triangle Trigonometry

Basic Trigonometric Functions (SOHCAHTOA)

Trigonometry Word Problems
Angles and the Unit Circle

Angles in Trigonometry

Degrees, Radians, and CoTerminal 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

TCharts for the Six Trigonometric Functions

Sine and Cosine Transformations

Cosecant and Secant Transformations

Tangent and Cotangent Transformations

Transformations of all Trig Functions without TCharts
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
CALCULUS (DIFFERENTIAL)
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
Optimization

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
USubstitution Integration

Introduction to USubstitution

USubstitution 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 USubstitution with Definite Integration