APPLIED MATH
FIRST SEMESTER
1.1 - Introduction to Algebra
Algebraic Expressions
Translating to Algebraic Expressions
Translating to Expressions
Models
1.2 - The Commutative, Associative, and Distributive
Laws
Equivalent Expressions
The Commutative Laws
The Associative Laws
The Distributive Law
The Distributive Law and Factoring
1.3 - Fraction Notation
Factors and Prime Factorizations
Fraction Notation
Multiplication and Simplification
Division
Addition and Subtraction
1.8 - Exponential Notation and Order of Operations
Exponential Notation
Order of Operations
Combining Like Terms
Simplifying and the Distributive Law
The Opposite of a Sum
2.1 - Solving Equations
Equations and Solutions
The Addition Principle
The Multiplication Principle
Selecting the Correct Approach
2.2 - Using the Principles Together
Applying Both Principles
Combining Like Terms
Clearing Fractions and Decimals
Contradictions and Identities
2.3 - Formulas
Evaluating Formulas
Solving for a Variable
2.4 - Applications with Percent
Converting Between Percent Notation and
Decimal Notation
Solving Percent Problems
2.5 - Problem Solving
Five Steps for Problem Solving
Organizing Information Using Tables
2.6 - Solving Inequalities
Solutions of Inequalities
Graphs of Inequalities
Set-Builder Notation and Interval Notation
Solving Inequalities Using the Addition Principle
Solving Inequalities Using the Multiplication Principle
Using the Principles Together
2.7 - Solving Applications with Inequalities
Translating to Inequalities
Solving Problems
3.3 – Linear Equations and Intercepts
Recognizing Linear Equations
Intercepts
Using Intercepts to Graph
Graphing Horizontal and Vertical Lines
3.4 – Rates
Rates of Change
Visualizing Rates
3.5 – Slope
Rate and Slope
Horizontal and Vertical Lines
Applications
3.6 – Slope-Intercept Form
Using the y-intercept and the Slope to Graph a Line
3.1 – Reading Graphs, Plotting Points and Scaling Graphs
Problem Solving with Bar, Circle and Line Graphs
Points and Ordered Pairs
Axes and Windows
3.2 – Graphing Equations
Solutions of Equations
Graphing Linear Equations
Applications
Graphing Nonlinear Equations
Equations in Slope-Intercept Form
Graphing and Slope-Intercept Form
Parallel and Perpendicular Lines
3.7 – Point-Slope Form, Introduction to Curve Fitting
Writing Equations in Point-Slope Form
Graphing and Point-Slope Form
Estimations and Predictions Using Two Points
Curve Fitting
3.8 – Functions
Functions and Graphs
Function Notation and Equations
Functions Defined Piecewise
Linear Functions and Applications
4.1 – Systems of Equations and Graphing
Solutions of Systems
Solving Systems of Equations by Graphing
Models
4.2 – Systems of Equations and Substitutions
The Substitution Method
Solving for the Variable First
Problem Solving
4.3 – Systems of Equations and Elimination
Solving by the Elimination Method
Problem Solving
4.4 – More Applications Using Systems
Total – Value Problems
Mixture Problems
Motion Problems
5.1 – Exponents and Their Properties
Multiplying Powers with Like Bases
Dividing Powers with Like Bases
Zero as an Exponent
Raising a Power to a Power
Raising a Product or a Quotient to a Power
5.2 – Negative Exponents and Scientific Notation
Negative Integers as Exponents
Scientific Notation
Problem Solving Using Scientific Notation
5.3 – Polynomials and Polynomial Functions
Terms
Types of Polynomials
Degree and Coefficients
Combining Like Terms
Polynomial Functions
Graphs of Polynomial Functions
5.4 – Addition and Subtraction of Polynomials
Addition of Polynomials
Opposites of Polynomials
Subtraction of Polynomials
Problem Solving
5.5 – Multiplication of Polynomials
Multiplying Monomials
Multiplying a Monomial and a Polynomial
Multiplying Any Two Polynomials
5.6 – Special Products
Products of Two Binomials
Multiplying Sums and Differences of Two Terms
Squaring Binomials
Multiplication of Various Types
5.7 – Polynomials in Several Variables
Evaluating Polynomials
Like Terms and Degree
Addition and Subtraction
Multiplication
Function Notation
5.8 – Division of Polynomials
Dividing by a Monomial
Dividing by a Binomial
Synthetic Division
6.1 – Introduction to Polynomial Factorization and
Equations
Graphical Solutions
The Principle of Zero Products
Terms with Common Factors
Factoring by Grouping
Factoring and Equations
6.2 – Trinomials of the Type x 2  bx  c
Trinomials of the Type x 2  bx  c
Equations Containing Trinomials
Zeros and Factoring
6.3 – Trinomials of the Type ax 2  bx  c
Factoring Trinomials of the Type ax 2  bx  c
Equations and Functions
APPLIED MATH
SECOND SEMESTER
6.4 – Perfect-Square Trinomials and Difference of
Squares
Perfect-Square Trinomials
Difference of Squares
More Factoring by Grouping
Solving Equations
6.5 – Sum and Difference of Cubes
Factoring Sums or Differences of Cubes
Solving Equations
6.6 – Factoring: A General Strategy
Choosing the Right Method
6.7 – Applications of Polynomial Equations
Problem Solving
The Pythagorean Theorem
Fitting Polynomial Functions to Data
7.1 – Rational Expressions and Functions
Rational Functions
Simplifying Rational Expressions
Factors That Are Opposites
Vertical Asymptotes
7.2 – Multiplication and Division
Multiplication
Division
7.3 – Addition, Subtraction and Least Common
Denominators
Addition When Denominators Are the Same
Subtraction When Denominators Are the Same
Least Common Multiples and Denominators
7.4 – Addition and Subtraction with Unlike
Denominators
Adding and Subtracting With LCD’s
When Factors Are Opposites
7.5 – Complex Rational Expressions
Multiplying by the LCD
Using Division to Simplify
7.6 – Rational Equations
Solving Rational Equations
7.7 – Applications Using Rational Equations and
Proportions
Problems Involving Work
Problems Involving Motion
Problems Involving Proportion
7.8 – Formulas, Applications and Variation
Formulas
Direct Variation
Inverse Variation
Joint Variation and Combined Variation
Models
8.1 – Graphical Solutions and Compound Inequalities
Solving Inequalities Graphically
Intersections of Sets and Conjunctions of
Sentences
Unions of Sets and Disjunctions of Sequences
Interval Notation and Domains
8.2 – Absolute-Value Equations and Inequalities
Equations with Absolute Value
Inequalities with Absolute Value
8.3 – Inequalities in Two Variables
Graphs of Linear Inequalities
Systems of Linear Inequalities
8.4 – Polynomial Inequalities and Rational
Inequalities
Quadratic and Other Polynomial Inequalities
Rational Inequalities
9.1 – Systems of Equations in Three Variables
Identifying Solutions
Solving Systems in Three Variables
Dependency, Inconsistency and Geometric
Considerations
9.2 – Solving Applications: Systems of Three
Equations
Applications of Three Equations in Three
Unknowns
9.5 – Business and Economics Applications
Break-Even Analysis
Supply and Demand
10.1 – Radical Expressions, Functions and Models
Square Roots and Square Root Functions
Expressions of the Form a 2
Cube Roots
Odd and Even nth Roots
Radical Functions and Models
10.2 – Rational Numbers as Exponents
Rational Exponents
Negative Rational Exponents
Laws of Exponents
Simplifying Radical Expressions
10.3 – Multiplying Radical Expressions
Multiplying Radical Expressions
Simplifying by Factoring
Multiplying and Simplifying
10.4 – Dividing Radical Expressions
Dividing and Simplifying
Rationalizing Denominators or Numerators
with One Term
10.5 – Expressions Containing Several Radical Terms
Adding and Subtracting Radical Expressions
Products and Quotients of Two or More
Radical Terms
Rationalizing Denominators and Numerators
with Two Terms
Terms with Differing Indices
10.6 – Solving Radical Equations
The Principle of Powers
Equations with Two Radical Terms
10.7 – The Distance Formula, the Midpoint Formula
and Other Applications
Using the Pythagorean Theorem
Two Special Triangles
The Distance and Midpoint Formulas
10.8 – The Complex Numbers
Imaginary and Complex Numbers
Addition and Subtraction
Multiplication
Conjugates and Division
Powers of i
11.1 – Quadratic Equations
The Principle of Square Roots
Completing the Square
Problem Solving
11.2 – The Quadratic Formula
Solving Using the Quadratic Formula
Approximating Solutions
11.3 – Studying Solutions of Quadratic Equations
The Discriminant
Writing Equations from Solutions
11.4 – Applications Involving Quadratic Equations
Solving Problems
Solving Formulas
11.6 – Quadratic Functions and Their Graphs
The Graph of f  x   ax2
The Graph of f  x   a  x  h 
2
The Graph of f  x   a  x  h   k
2
11.7 – More About Graphing Quadratic Functions
Finding the Vertex
Finding Intercepts
11.8 – Problem Solving and Quadratic Functions
Maximum and Minimum Problems
Fitting Quadratic Functions to Data
12.1 – Composite Functions and Inverse Functions
Composite Functions
Inverses and One-to-One Functions
Finding Formulas for Inverses
Graphing Functions and Their Inverses
Inverse Functions and Composition
12.2 – Exponential Functions
Graphing Exponential Functions
Equations with x and y interchanged
Applications of Exponential Functions
12.3 – Logarithmic Functions
Graphs of Logarithmic Functions
Common Logarithms
Equivalent Equations
Solving Certain Logarithmic Equations
12.4 – Properties of Logarithmic Functions
Logarithms of Products
Logarithms of Powers
Logarithms of Quotients
Using the Properties Together
12.5 – Natural Logarithms and Changing Bases
The Base e and Natural Logarithms
Changing Logarithmic Bases
Graphs of Exponential Functions and
Logarithmic Functions, Base e
12.6 – Solving Exponential and Logarithmic Equations
Solving Exponential Equations
Solving Logarithmic Equations
12.7 – Applications of Exponential and Logarithmic
Functions
Applications of Logarithmic Functions
Applications of Exponential Functions