Kirk Trigsted teaches mathematics at the University of Idaho and has been Director of the Polya Mathematics Center since its inception in 2001. Kirk is the author of a successful precalculus and developmental eText series. Kirk has also been actively involved with the National Center for Academic Transformation (NCAT) for several years.

Kirk has been married for 20 years and has four children. He is an avid fly fisherman and golfer.

REVIEW CHAPTER

R.1 Real Numbers

R.2 The Order of Operations and Algebraic Expressions

R.3 The Laws of Exponents; Radicals

R.4 Polynomials

R.5 Operations with Radicals

R.6 Factoring Polynomials

R.7 Rational Expressions

CHAPTER 1. Equations, Inequalities, and Applications

1.1 Linear and Rational Equations

Readiness Topics for Section 1.1:

• Identifying Terms , Coefficients and Like Terms of an Algebraic Expressions
  
• Writing Equivalent Fractions
  
• Writing Fractions in Simplest Form
  
• Multiplying Fractions
  
• Dividing Fractions
  
• Adding and Subtracting Fractions with Like Denominators
  
• Find the Least Common Denominator of Unlike Fractions
  
• Adding and Subtracting Fractions with Unlike Denominators
  
• Finding the Least Common Denominator of Rational Expressions
  
• Adding and Subtracting Rational Expressions with Unlike Denominators
  
• Factoring Out the Greatest Common Factor from a Polynomial
  
• Factoring Trinomials of the form x ² + bx + c
  
• Factor by Grouping
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method
  
• Factoring Special Forms (Difference of Two Squares)
  
• Factoring Special Forms (Difference of Two Cubes and Sum of Two Cubes)

1.2 Applications of Linear Equations

Readiness Topics for Section 1.2:

• Identifying Terms , Coefficients and Like Terms of an Algebraic Expressions
  
• Simplifying an Algebraic Expression by Combining Like Terms
  
• Finding the Prime Factorization of a Number
  
• Determine if Fractions are Equivalent Fractions
  
• Writing Equivalent Fractions
  
• Writing Fractions in Simplest Form
  
• Multiplying Fractions
  
• Dividing Fractions
  
• Adding and Subtracting Fractions with Like Denominators
  
• Finding the Least Common Denominator of Rational Expressions
  
• Adding and Subtracting Rational Expressions with Unlike Denominators
  
• Finding Reciprocals

1.3 Complex Numbers

Readiness Topics for Section 1.3:

• Finding the Prime Factorization of a Number
  
• Adding and Subtracting Polynomials
  
• Multiplying Polynomials
  
• Multiplying Polynomials (Special Products)
  
• Finding the Least Common Denominator of Rational Expressions
  
• Writing Equivalent Rational Expressions
  
• Adding and Subtracting Rational Expressions with Unlike Denominators
  
• Simplifying Radical Expressions

1.4 Quadratic Equations

Readiness Topics for Section 1.4:

• Finding the Prime Factorization of a Number
  
• Multiplying Polynomials
  
• Multiplying Polynomials (Special Products)
  
• Factoring Out the Greatest Common Factor from a Polynomial
  
• Factoring Trinomials of the form x ² + bx + c
  
• Factor by Grouping
  
• Factoring Trinomials of the Form ax ² + bx + c  using the ac Method
  
• Factoring Special Forms (Difference of Two Squares)
  
• Simplifying Radical Expressions

1.5 Applications of Quadratic Equations

Readiness Topics for Section 1.5:

• Finding the Prime Factorization of a Number
  
• Use the Order of Operations to Simplify Numeric Expressions
  
• Multiplying Polynomials
  
• Multiplying Polynomials (Special Products)
  
• Factoring Out the Greatest Common Factor from a Polynomial
  
• Factoring Trinomials of the Form x ² + bx + c
  
• Factor by Grouping
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method
  
• Factoring Special Forms (Difference of Two Squares)
  
• Simplifying Radical Expressions

1.6 Other Types of Equations

Readiness Topics for Section 1.6:

• Factoring Trinomials of the form x ² + bx + c
  
• Factor by Grouping
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method
  
• Factoring Special Forms (Difference of Two Squares)
  
• Factoring Special Forms (Difference of Two Cubes and Sum of Two Cubes)
  
• Simplifying Radical Expressions

1.7 Linear Inequalities

Readiness Topics for Section 1.7:

• Adding and Subtracting Fractions with Like Denominators
  
• Find the Least Common Denominator of Unlike Fractions
  
• Adding and Subtracting Fractions with Unlike Denominators
  
• Using Set-Builder Notation and Interval Notation to Express a Set

1.8 Absolute Value Equations and Inequalities

Readiness Topics for Section 1.8:

• Finding the Absolute Value of Numbers
  
• Factoring Trinomials of the form x ² + bx + c
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method
  
• Using Set-Builder Notation and Interval Notation to Express a Set

1.9 Polynomial and Rational Inequalities

Readiness Topics for Section 1.9:

• Factoring Trinomials of the form x ² + bx + c
  
• Factor by Grouping
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method
  
• Factoring Special Forms (Difference of Two Squares)
  
• Finding the Least Common Denominator of Rational Expressions
  
• Writing Equivalent Rational Expressions
  
• Adding and Subtracting Rational Expressions with Unlike Denominators
  
• Using Set-Builder Notation and Interval Notation to Express a Set
  

CHAPTER 2. The Rectangular Coordinate System, Lines, and Circles

2.1 The Rectangular Coordinate System

Readiness Topics for Section 2.1:

• Simplifying Radical Expressions
  
• Finding the Average of a List of Numbers

2.2 Circles

Readiness Topics for Section 2.2:

• Factoring Special Forms (Perfect Square Trinomials)

2.3 Lines

Readiness Topics for Section 2.3:

• Find the Least Common Denominator of Unlike Fractions
  
• Adding and Subtracting Fractions with Like Denominators

2.4 Parallel and Perpendicular Lines

Readiness Topics for Section 2.4:

• Finding Reciprocals
  

CHAPTER 3. Functions

3.1 Relations and Functions

Readiness Topics for Section 3.1:

• Use the Order of Operations to Simplify Numeric Expressions
  
• Evaluating Algebraic Expressions Involving Fractions
  
• Using Interval Notation to Express the Intersection and Union of Sets
  
• Graphing Simple Equations by Plotting Points

3.2 Properties of a Function's Graph

Readiness Topics for Section 3.2:

• Factoring Trinomials of the form x ² + bx + c
  
• Factor by Grouping
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method
  
• Factoring Special Forms (Difference of Two Squares)

3.3 Graphs of Basic Functions; Piecewise Functions

Readiness Topics for Section 3.3:

• Finding the Absolute Value of Numbers
  
• Use the Order of Operations to Simplify Numeric Expressions
  
• Evaluating Algebraic Expressions Involving Fractions
  
• Using Interval Notation to Express the Intersection and Union of Sets
  
• Graphing Simple Equations by Plotting Points

3.4 Transformations of Functions

No Readiness Topics for Section 3.4

3.5 The Algebra of Functions; Composite Functions

Readiness Topics for Section 3.5:

• Use the Order of Operations to Simplify Numeric Expressions
  
• Finding the Least Common Denominator of Rational Expressions
  
• Writing Equivalent Rational Expressions
  
• Adding and Subtracting Rational Expressions with Unlike Denominators
  
• Evaluating Algebraic Expressions Involving Fractions
  
• Using Interval Notation to Express the Intersection and Union of Sets
  
• Simplifying Complex Rational Expressions

3.6 One-to-One Functions; Inverse Functions

Readiness Topics for Section 3.6:

• Finding the Least Common Denominator of Rational Expressions
  
• Writing Equivalent Rational Expressions
  
• Adding and Subtracting Rational Expressions with Unlike Denominators
  
• Evaluating Algebraic Expressions Involving Fractions
  
• Using Interval Notation to Express the Intersection and Union of Sets
  
• Simplifying Complex Rational Expressions
  

CHAPTER 4. Polynomial and Rational Functions

4.1 Quadratic Functions

Readiness Topics for Section 4.1:

• Factoring Trinomials of the form x ² + bx + c
  
• Factoring Trinomials of the Form ax ² + bx + c  using the ac Method

4.2 Applications and Modeling of Quadratic Functions

Readiness Topics for Section 4.2:

• Factoring Trinomials of the form x ² + bx + c
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method

4.3 The Graphs of Polynomial Functions

Readiness Topics for Section 4.3:

• Use the Order of Operations to Simplify Numeric Expressions
  
• Factoring Trinomials of the form x ² + bx + c
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method
  
• Evaluating Algebraic Expressions Involving Fractions

4.4 Synthetic Division; The Remainder and Factor Theorems

Readiness Topics for Section 4.4:

• Factoring Trinomials of the form x ² + bx + c
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method
  
• Using Long Division to Divide Whole Numbers
  
• Dividing Polynomials Using Long Division

4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra

Readiness Topics for Section 4.5:

• Factoring Trinomials of the form x ² + bx + c
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method
  
• Using Long Division to Divide Whole Numbers
  
• Dividing Polynomials Using Long Division

4.6 Rational Functions and Their Graphs

Readiness Topics for Section 4.6:

• Use the Order of Operations to Simplify Numeric Expressions
  
• Factoring Trinomials of the form x ² + bx + c
  
• Factoring Trinomials of the Form ax ² + bx + c using the ac Method
  
• Evaluating Algebraic Expressions Involving Fractions
  
• Using Long Division to Divide Whole Numbers
  
• Dividing Polynomials Using Long Division

4.7 Variation

Readiness Topics for Section 4.7:

• Use the Order of Operations to Simplify Numeric Expressions
  

CHAPTER 5. Exponential and Logarithmic Functions and Equations

5.1 Exponential Functions

Readiness Topics for Section 5.1:

• Establishing the Laws of Exponents (Integer Exponents)
  
• Simplifying Exponential Expressions using Laws of Exponents (Integer Exponents)
  
• Using Laws of Exponents Involving Rational Exponents
  
• Using Laws of Exponents to Rewrite Exponential Expressions in the Form of 2 ^u , 3 ^u , or 5 ^u

5.2 Logarithmic Functions

Readiness Topics for Section 5.2:

• Using Laws of Exponents Involving Rational Exponents
  
• Using Laws of Exponents to Rewrite Exponential Expressions in the Form of 2 ^u , 3 ^u , or 5 ^u

5.3 Properties of Logarithms

Readiness Topics for Section 5.3:

• Establishing the Laws of Exponents (Integer Exponents)
  
• Simplifying Exponential Expressions using Laws of Exponents (Integer Exponents)
  
• Using Laws of Exponents Involving Rational Exponents
  
• Using Laws of Exponents to Rewrite Exponential Expressions in the Form of 2 ^u , 3 ^u , or 5 ^u

5.4 Exponential and Logarithmic Equations

Readiness Topics for Section 5.4:

• Establishing the Laws of Exponents (Integer Exponents)
  
• Simplifying Exponential Expressions using Laws of Exponents (Integer Exponents)
  
• Using Laws of Exponents Involving Rational Exponents
  
• Using Laws of Exponents to Rewrite Exponential Expressions in the Form of 2 ^u , 3 ^u , or 5 ^u

5.5 Applications of Exponential and Logarithmic Functions

No Readiness Topics for Section 5.5

CHAPTER 6. Conic Sections

6.1 The Parabola

6.2 The Ellipse

6.3 The Hyperbola

(No Readiness Topics For Chapter 6)

CHAPTER 7. Systems of Equations and Inequalities

7.1 Systems of Linear Equations in Two Variables

7.2 Systems of Linear Equations in Three Variables

7.3 Inconsistent and Dependent Linear Systems in Three Variables

7.4 Partial Fraction Decomposition

7.5 Systems of Nonlinear Equations

7.6 Systems of Inequalities

(No Readiness Topics For Chapter 7)

CHAPTER 8. Matrices

8.1 Matrix Operations

8.2 Inverses of Matrices and Matrix Equations

8.3 Determinants and Cramer's Rule

(No Readiness Topics For Chapter 8)

CHAPTER 9. Sequences and Series; Counting and Probability

9.1 Introduction to Sequences and Series

9.2 Arithmetic Sequences and Series

9.3 Geometric Sequences and Series

9.4 The Binomial Theorem

9.5 Mathematical Induction

9.6 The Theory of Counting

9.7 An Introduction to Probability

(No Readiness Topics For Chapter 9)

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