top of page #### BASIC MATH

• 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

• Multiplying and Dividing Decimals

Fractions

• Introduction to Fractions

• Subtracting Fractions

• Multiplying Fractions

• Dividing Fractions

• Comparing Fractions

• Fractions Used in Cooking

Metric System

#### PRE-ALGEBRA

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

• 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

• 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

# 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

• Solving Using Graphing

• Solving Algebraically, including Completing the Square

• Sign Chart (Sign Pattern) Method

• Quadratic Inequality Real World Example

• Optimization of Area Problem

• Maximum Profit and Revenue Problems

• Population Problem

• Linear Increase/Decrease 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

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

• Introducing Exponents and Roots (Radicals) with Variables

• Properties of Exponents and Roots

• Putting Exponents and Radicals in the Calculator

• Simplifying Exponential Expressions

• Solving Exponential and Radical Equations

Introduction to Multiplying Polynomials

• What is a Polynomial?

• Multiplying Polynomials

• Graphing with Vertex Form

• Graphing with Standard Form

• Graphing with Factored (Intercept) Form

• Standard Form to Vertex Form

• Solving for Roots with Quadratics

• Using the Discriminant to Determine Types of Solutions

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

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

• Absolute Value Equations and Inequalities

• Using Inequalities to Find Domains of Composites

• Rational Functions Inequalities

• Polynomial 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

• 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

• Factoring with Polynomials

• Factoring Sum and Difference of Cubes

• Factoring with Exponents

Rational Functions and Equations

• Introducing Rational Expressions

• Finding the Common Denominator

• 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 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

#### ​TRIGONOMETRY

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

#### 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

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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