Preparation for College Mathematics Second Edition

Preparation for College Mathematics coverThe new edition of Preparation for College Mathematics now covers even more intermediate-level algebraic topics and increases focus on application, conceptual understanding, and the development of the academic mindset. Request an examination copy.

The goal of this newly enhanced title is to develop holistic learners who are adequately prepared for subsequent, higher-level math courses on their path to college success.

View a free sample of the new edition of Preparation for College Mathematics.


NEW features include:

  • Strategies for Academic Success – study skills and learning strategies build stronger learners with tips on note taking, time management, test taking, and more
  • Chapter Projects – discovery-based projects promote collaboration and practical applications of mathematics
  • Concept Checks – exercise sets assess students’ conceptual understanding of topics before each practice set
  • Applications – exercise sets for each section challenge students to apply topics learned to real-world contexts
  • Extra Material – more advanced topics cover all learning outcomes to prepare students for future college math courses
  • Writing & Thinking – opportunities for students to independently explore and expand on chapter concepts


Table of Contents:

Preface: Strategies for Academic Success

How to Read a Math Textbook
Tips for Success in a Math Course
Tips for Improving Math Test Scores
Practice, Patience, and Persistence!
Note Taking
Do I Need a Math Tutor?
Tips for Improving Your Memory
Overcoming Anxiety
Online Resources
Preparing for a Final Math Exam
Managing Your Time Effectively

1. Whole Numbers

Introduction to Whole Numbers
Addition and Subtraction with Whole Numbers
Multiplication with Whole Numbers
Division with Whole Numbers
Rounding and Estimating with Whole Numbers
Problem Solving with Whole Numbers
Solving Equations with Whole Numbers (x + b = c and ax = c)
Exponents and Order of Operations
Tests for Divisibility
Prime Numbers and Prime Factorizations

2. Integers

Introduction to Integers
Addition with Integers
Subtraction with Integers
Multiplication, Division, and Order of Operations with Integers
Simplifying and Evaluating Expressions
Translating English Phrases and Algebraic Expressions
Solving Equations with Integers (ax + b = c)

3. Fractions, Mixed Numbers, and Proportions

Introduction to Fractions and Mixed Numbers
Multiplication with Fractions
Division with Fractions
Multiplication and Division with Mixed Numbers
Least Common Multiple (LCM)
Addition and Subtraction with Fractions
Addition and Subtraction with Mixed Numbers
Comparisons and Order of Operations with Fractions
Solving Equations with Fractions
Ratios and Rates

4. Decimal Numbers

Introduction to Decimal Numbers
Addition and Subtraction with Decimal Numbers
Multiplication and Division with Decimal Numbers
Estimating and Order of Operations with Decimal Numbers
Statistics: Mean, Median, Mode, and Range
Decimal Numbers and Fractions
Solving Equations with Decimal Numbers

5. Percents

Basics of Percent
Solving Percent Problems Using Proportions
Solving Percent Problems Using Equations
Applications of Percent
Simple and Compound Interest
Reading Graphs

6. Measurement and Geometry

US Measurements
The Metric System: Length and Area
The Metric System: Weight and Volume
US and Metric Equivalents
Angles and Triangles
Volume and Surface Area
Similar and Congruent Triangles
Square Roots and the Pythagorean Theorem

7. Solving Linear Equations and Inequalities

Properties of Real Numbers
Solving Linear Equations: x + b = c and ax = c
Solving Linear Equations: ax + b = c
Solving Linear Equations: ax + b = cx + d
Working with Formulas
Applications: Number Problems and Consecutive Integers
Applications: Distance-Rate-Time, Interest, Average, and Cost
Solving Linear Inequalities
Compound Inequalities
Absolute Value Equations
Absolute Value Inequalities

8. Graphing Linear Equations and Inequalities

The Cartesian Coordinate System
Graphing Linear Equations in Two Variables
Slope-Intercept Form
Point-Slope Form
Introduction to Functions and Function Notation
Graphing Linear Inequalities in Two Variables

9. Systems of Linear Equations

Systems of Linear Equations: Solutions by Graphing
Systems of Linear Equations: Solutions by Substitution
Systems of Linear Equations: Solutions by Addition
Applications: Distance-Rate-Time, Number Problems, Amounts, and Costs
Applications: Interest and Mixture
Systems of Linear Equations: Three Variables
Matrices and Gaussian Elimination
Systems of Linear Inequalities

10. Exponents and Polynomials

Rules for Exponents
Power Rules for Exponents
Applications: Scientific Notation
Introduction to Polynomials
Addition and Subtraction with Polynomials
Multiplication with Polynomials
Special Products of Binomials
Division with Polynomials
Synthetic Division and the Remainder Theorem

11. Factoring Polynomials

Greatest Common Factor (GCF) and Factoring by Grouping
Factoring Trinomials: x^2+bx+c
Factoring Trinomials: ax^2+bx+c
Special Factoring Techniques
Review of Factoring Techniques
Solving Quadratic Equations by Factoring
Applications: Quadratic Equations

12. Rational Expressions

Introduction to Rational Expressions
Multiplication and Division with Rational Expressions
Least Common Multiple of Polynomials
Addition and Subtraction with Rational Expressions
Simplifying Complex Fractions
Solving Rational Equations
Applications: Rational Expressions
Applications: Variation

13. Roots, Radicals, and Complex Numbers

Evaluating Radicals
Rational Exponents
Simplifying Radicals
Addition, Subtraction, and Multiplication with Radicals
Rationalizing Denominators
Solving Radical Equations
Functions with Radicals
Introduction to Complex Numbers
Multiplication and Division with Complex Numbers

14. Quadratic Equations

Quadratic Equations: The Square Root Method
Quadratic Equations: Completing the Square
Quadratic Equations: The Quadratic Formula
More Applications of Quadratic Equations
Equations in Quadratic Form
Graphing Quadratic Functions
More on Graphing Functions and Applications
Solving Polynomial and Rational Inequalities

15. Exponential and Logarithmic Functions

Algebra of Functions
Composition of Functions and Inverse Functions
Exponential Functions
Logarithmic Functions
Properties of Logarithms
Common Logarithms and Natural Logarithms
Logarithmic and Exponential Equations and Change-of-Base
Applications: Exponential and Logarithmic Functions

16. Conic Sections

Translations and Reflections
Parabolas as Conic Sections
Distance Formula, Midpoint Formula, and Circles
Ellipses and Hyperbolas
Nonlinear Systems of Equations

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