DEVELOPMENTAL MATHEMATICS - Hawkes Learning

[Pages:120]DEVELOPMENTAL

MATHEMATICS

SECOND EDITION

D. Franklin Wright

Instructor Preview

NLY Editor:Nina Waldron O Project Manager:Patrick Vande Bossche IEW Assistant Editors:Chelsey Cooke, S. Rebecca Johnson, Barbara Miller, V Designers:D. Kanthi, E. Jeevan Kumar, U. Nagesh, James Smalls, E Patrick Thompson, Tee Jay Zajac R R Cover Design:Patrick Thompson FO VP Research & Development:Marcel Prevuznak LY Director of Content:Kara Roch? REVIEW ON A division of Quant Systems, Inc. R 546 Long Point Road, Mount Pleasant, SC 29464 FO Copyright ? 2017 by Hawkes Learning/Quant Systems, Inc. All rights reserved.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written consent of the publisher.

Printed in the United States of America

ISBN:978-1-946158-71-0

Instructor Sample Contents

Developmental Mathematics Second Edition Table of Contents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Developmental Mathematics: Content Highlights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Strategies for Academic Success

How to Read a Math Textbook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Tips for Success in a Math Course. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

LY Tips for Improving Math Test Scores. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Practice, Patience, and Persistence! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

ON Note Taking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Do I Need a Math Tutor?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

IEW Tips for Improving Your Memory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 V Overcoming Anxiety. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 E Online Resources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 R Preparing for a Final Math Exam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 FOR Chapter Project

Before and After. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

LY CHAPTER 2 N Fractions and Mixed Numbers O 2.1Introduction to Fractions and Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 W 2.2Multiplication with Fractions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 VIE CHAPTER 10 E Graphing Linear Equations and Inequalities R 10.1 The Cartesian Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 R 10.2 Graphing Linear Equations in Two Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 FO 10.3 SlopeIntercept Form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

CHAPTER 17

Exponential and Logarithmic Functions

17.3Exponential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 17.4Logarithmic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

FOR

REVIEW ONLY FOR REVIEW ONLY

Developmental Mathematics Second Edition Table of ContentsPreface

v

Developmental Mathematics Second Edition Table of Contents

Note:Content subject to change

CHAPTER 1

CHAPTER 3

Whole Numbers

Decimal Numbers

1.1 Introduction to Whole Numbers

3.1 Introduction to Decimal Numbers

1.2 Addition and Subtraction with Whole Numbers

LY 1.3 Multiplication with Whole Numbers

1.4 Division with Whole Numbers

N 1.5 Rounding and Estimating O with Whole Numbers

W 1.6 Problem Solving with Whole Numbers IE 1.7 Exponents and Order of Operations V 1.8 Tests for Divisibility E 1.9 Prime Numbers and Prime Factorizations R R CHAPTER 2 FO Fractions and Mixed Numbers

2.1 Introduction to Fractions

LY and Mixed Numbers N 2.2 Multiplication with Fractions O 2.3 Division with Fractions

2.4 Multiplication and Division

W with Mixed Numbers IE 2.5 Least Common Multiple (LCM) EV 2.6 Addition and Subtraction with Fractions R 2.7 Addition and Subtraction

R with Mixed Numbers FO 2.8 Comparisons and Order of

Operations with Fractions

3.2 Addition and Subtraction with Decimal Numbers

3.3 Multiplication with Decimal Numbers 3.4 Division with Decimal Numbers 3.5 Estimating and Order of Operations

with Decimal Numbers 3.6 Decimal Numbers and Fractions

CHAPTER 4

Ratios, Proportions, and Percents

4.1 Ratios and Unit Rates 4.2 Proportions 4.3 Decimals and Percents 4.4 Fractions and Percents 4.5 Solving Percent Problems

Using Proportions 4.6 Solving Percent Problems Using Equations 4.7 Applications of Percent 4.8 Simple and Compound Interest

CHAPTER 5

Measurements

5.1 US Measurements 5.2 The Metric System: Length and Area

5.3 The Metric System: Capacity and Weight

5.4 US and Metric Equivalents

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PrefaceDevelopmental Mathematics Second Edition Table of Contents

CHAPTER 6

CHAPTER 9

Geometry

6.1 Angles and Triangles

Solving Linear Equations and Inequalities

6.2 Perimeter

9.1 Solving Linear Equations:

6.3 Area

x + b = c and ax = c

6.4 Circles

9.2 Solving Linear Equations: ax + b = c

6.5 Volume and Surface Area

9.3 Solving Linear Equations: ax + b = cx + d

6.6 Similar and Congruent Triangles 6.7 Square Roots and the

LY Pythagorean Theorem ON CHAPTER 7 W Statistics, Graphs, and Probability IE 7.1 Statistics: Mean, Median, Mode, and Range V 7.2 Reading Graphs E 7.3 Constructing Graphs from a Database

9.4 Working with Formulas 9.5 Applications: Number Problems

and Consecutive Integers 9.6 Applications: DistanceRateTime,

Interest, Average 9.7 Solving Linear Inequalities in One Variable 9.8 Compound Inequalities 9.9 Absolute Value Equations 9.10 Absolute Value Inequalities

R 7.4 Probability

CHAPTER 10

FOR CHAPTER 8

Introduction to Algebra

LY 8.1 The Real Number Line and Absolute Value N 8.2 Addition with Real Numbers O 8.3 Subtraction with Real Numbers

8.4 Multiplication and Division

W with Real Numbers IE 8.5 Order of Operations with Real Numbers EV 8.6 Properties of Real Numbers R 8.7 Simplifying and Evaluating

R Algebraic Expressions

Graphing Linear Equations and Inequalities

10.1 The Cartesian Coordinate System

10.2 Graphing Linear Equations in Two Variables

10.3 Slope-Intercept Form

10.4 Point-Slope Form

10.5 Introduction to Functions and Function Notation

10.6 Graphing Linear Inequalities in Two Variables

FO 8.8 Translating English Phrases

and Algebraic Expressions

Developmental Mathematics Second Edition Table of ContentsPreface

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CHAPTER 11

CHAPTER 13

Systems of Linear Equations

Factoring Polynomials

11.1 Systems of Linear Equations: Solutions by Graphing

13.1 Greatest Common Factor (GCF) and Factoring by Grouping

11.2 Systems of Linear Equations:

13.2 Factoring Trinomials: x2+bx+c

Solutions by Substitution

13.3 Factoring Trinomials: ax2+bx+c

11.3 Systems of Linear Equations:

13.4 Special Factoring Techniques

Solutions by Addition

11.4 Applications: Distance-Rate-Time, Number Problems, Amounts, and Costs

LY 11.5 Applications: Interest and Mixture N 11.6 Systems of Linear Equations:

O Three Variables W 11.7 Matrices and Gaussian Elimination IE 11.8 Systems of Linear Inequalities EV CHAPTER 12 R Exponents and Polynomials R 12.1 Rules for Exponents FO 12.2 Power Rules for Exponents

12.3 Applications: Scientific Notation

LY 12.4 Introduction to Polynomials N 12.5 Addition and Subtraction with Polynomials O 12.6 Multiplication with Polynomials

12.7 Special Products of Binomials

IEW 12.8 Division with Polynomials V 12.9 Synthetic Division and the

FOR RE Remainder Theorem

13.5 Review of Factoring Techniques 13.6 Solving Quadratic Equations by Factoring 13.7 Applications: Quadratic Equations

CHAPTER 14

Rational Expressions

14.1 Introduction to Rational Expressions 14.2 Multiplication and Division

with Rational Expressions 14.3 Least Common Multiple of Polynomials 14.4 Addition and Subtraction with

Rational Expressions 14.5 Simplifying Complex Fractions 14.6 Solving Rational Equations 14.7 Applications: Rational Expressions 14.8 Applications: Variation

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PrefaceDevelopmental Mathematics Second Edition Table of Contents

CHAPTER 15

CHAPTER 17

Roots, Radicals, and Complex Numbers

Exponential and Logarithmic Functions

15.1 Evaluating Radicals

17.1 Algebra of Functions

15.2 Simplifying Radicals

17.2 Composition of Functions

15.3 Rational Exponents

and Inverse Functions

15.4 Addition, Subtraction, and

17.3 Exponential Functions

Multiplication with Radicals 15.5 Rationalizing Denominators

LY 15.6 Solving Radical Equations N 15.7 Functions with Radicals O 15.8 Introduction to Complex Numbers

15.9 Multiplication and Division

IEW with Complex Numbers

17.4 Logarithmic Functions

17.5 Properties of Logarithms

17.6 Common Logarithms and Natural Logarithms

17.7 Logarithmic and Exponential Equations and Change-of-Base

17.8 Applications: Exponential and Logarithmic Functions

EV CHAPTER 16 R Quadratic Equations R 16.1 Quadratic Equations:

FO The Square Root Method

16.2 Quadratic Equations: Completing the Square

LY 16.3 Quadratic Equations: N The Quadratic Formula

O 16.4 More Applications of Quadratic Equations

16.5 Equations in Quadratic Form

IEW 16.6 Graphing Quadratic Functions V 16.7 More on Graphing Functions

E and Applications R 16.8 Solving Polynomial and

FOR Rational Inequalities

CHAPTER 18

Conic Sections

18.1 Translations and Reflections 18.2 Parabolas as Conics 18.3 Distance Formula, Midpoint

Formula, and Circles 18.4 Ellipses and Hyperbolas 18.5 Nonlinear Systems of Equations

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