MMT Math Curriculum

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

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

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

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

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

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

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

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

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

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

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

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

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