Developmental Mathematics Second Edition

Developmental Mathematics Second Edition coverThis new edition offers more robust exercise sets that include conceptual assessment, an increased focus on real-world application, new lessons on study skills to develop the academic mindset of mathematics learners, chapter projects and collaborative opportunities for discovery-based learning with peers, and additional content to cover all topics through intermediate algebra.

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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:

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
Exponents and Order of Operations
Tests for Divisibility
Prime Numbers and Prime Factorizations

2. Fractions and Mixed Numbers

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

3. Decimal Numbers

Introduction to Decimal Numbers
Addition and Subtraction with Decimal Numbers
Multiplication with Decimal Numbers
Division with Decimal Numbers
Estimating and Order of Operations with Decimal Numbers
Decimal Numbers and Fractions

4. Ratios, Proportions, and Percents

Ratios and Unit Rates
Proportions
Decimals and Percents
Fractions and Percents
Solving Percent Problems Using Proportions
Solving Percent Problems Using Equations
Applications of Percent
Simple and Compound Interest

5. Measurements

US Measurements
The Metric System: Length and Area
The Metric System: Capacity and Weight
US and Metric Equivalents

6. Geometry

Angles and Triangles
Perimeter
Area
Circles
Volume and Surface Area
Similar and Congruent Triangles
Square Roots and the Pythagorean Theorem

7. Statistics, Graphs, and Probability

Statistics: Mean, Median, Mode, and Range
Reading Graphs
Constructing Graphs from a Database
Probability

8. Introduction to Algebra

The Real Number Line and Absolute Value
Addition with Real Numbers
Subtraction with Real Numbers
Multiplication and Division with Real Numbers
Order of Operations with Real Numbers
Properties of Real Numbers
Simplifying and Evaluating Algebraic Expressions
Translating English Phrases and Algebraic Expressions

9. Solving Linear Equations and Inequalities

Solving Linear Equations: x + b = c
Solving Linear Equations: 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
Solving Linear Inequalities in One Variable
Compound Inequalities
Absolute Value Equations
Absolute Value Inequalities

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. Conic Sections

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

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