Introduction to Algebra and Geometry

Douglas Gardner

Description

Introduction to Algebra and Geometry introduces students to the concepts in algebraic relationships that can be applied to further study of math at the college level. Intended for college-level developmental math students, this book gives student the tools to understand and apply algebra and geometry to the fields of engineering, science, welding, diesel mechanics, and more. This book is a reprint of chapters from Douglas Gardner's Applied Algebra I and Applied Algebra II, packaged in a more condensed format. 

Sujets

• Sciences et techniques
• Algebra
• Mathematics

Informations

• Publié par: Chemeketa Press
• Date de parution: 01 août 2022
• Nombre de lectures: 1
• EAN13: 9781955499156
• Langue: English
• Poids de l'ouvrage: 6 Mo

Extrait

Introduction to Algebra
and Geometry
Doug Gardner
Rogue Community College
arranged by Tim Merzenich
Chemeketa Community College
A Chemeketa Press ReprintIntroduction to Algebra and Geometry
A Chemeketa Press Reprint
ISBN: 978-1-943536-03-0
The contents of this book come from Chapters 1-3 of Applied Algebra I and chapter 1
of Applied Algebra II, by Doug Gardner, Rogue Community College. These books
were written with funding from National Science Foundation grant, award numbers
1002822 and 1304307.
All materials © Doug Gardner. Used by permission of the author.
This book was designed and produced by the students and staf of the
Chemeketa Visual Communications Program.
Chemeketa Press
Managing Editor: Steve Richardson
Art Director: Kristen MacDonald
Layout: Terra Hyle
Cover Design: Cierra Maher
Cover Photo: “Brooklyn Bridge,” © 2012 by Cierra Maher. Used by permission of the artist.
Printed in the United States of America.Chapter Objectives
Contents
Chapter 1: Tools of Algebra (page 3) Chapter 3: Right Triangle Geometry (page 83)
Section 1.1: Operations with Real Numbers Section 3.1: Angles
Chapter Objectives
• +,-,x,÷ Fractions and Decimals • Estimate and measure angles in degrees
Chapter 1: Tools of Algebra (page 5) Chapter 3: Right Triangle Geometry (page 8 6 )
• +,-,x,÷ Negative Numbers • Angles with degrees, minutes & seconds
Section 3.1: Angles Section 1.1: Operations with Real NumbersSection 1.2: Measurement • Solve practical problems
• Estimate and measure angles in degrees• +,-,x,÷ Fractions and Decimals
• Measure with cm, mm, and inches Section 3.2: Area & PerimeterAbout This Book (page 1) • Angles with degrees, minutes & seconds• +,-,x,÷ Negative Numbers
• Convert fractions to decimals • Find the perimeter of polygons and circles• Solve practical problems
Section 1.2: MeasurementChapter 1: Tools of Algebra (page 3)• Convert decimals to fractions • Find the area of polygons and circlesSection 3.2: Area & Perimeter
• Measure with cm, mm, and inches
• Round decimal measures to fractions • Solve pr • actical problemsFind the perimeter of polygons and circles
Section 1. • Co1: Operations with Rnvert fractions to deci eal Numbers (page 4)mals
• Find the area of polygons and circlesSection 3.3: Surface area• Convert feet-inch-fraction• Convert decimals to fractions
Section 1.2: Measurement (page 16) • Solve practical problems• Find the surface area of solidsmeasurements to inches and decimals• Round decimal measures to fractions
Section 3.3: Surface area Section 1.3:Section 1.3: R Ratio, Proportion & Percentatio, Proportion & Percent (page 28) • Convert to different units of measure• Convert feet-inch-fraction
• Find the surface area of solidsmeasurements to inches and decimals• Set up and solve proportion problems • Solve practical problemsSection 1.4: Dimensional Analysis (page 40) • Convert to different units of measure
• Convert fractions and decimals to Section 3.4: VolumeSection 1.3: Ratio, Proportion & Percent • Solve practical problemsSection 1.5: Order of Operations (page 46)
• Set up and solve proportion problemspercents • Find the volume of solidsSection 3.4: Volume
• Convert fractions and decimals to• Convert percents to fractions and • Convert to different units of measureChapter 2: Formulas/Equations (page 61) • Find the volume of solids
percents
decimals • Solve pr • actical problemsConvert to different units of measure
• Convert percents to fractions andSection 2.1: Solving simple equations (page 62) • Solve practical problems• Solve percentage problems
decimals Chapter 4: Linear Relationships (page 124)
Section 2.2: Solving for dif erent Variables (page 72)Section 1.4: Dimensional Analysis Chapter 4: Linear Relationships (page 1 2 6 )• Solve percentage problems
Section 4.1: The Shape of a Linear Equation
• Convert to different units of measure:Section 2.3: Solving complex equations (page 77) Section4.1: TheShapeofaLinearEquationSection 1.4: Dimensional Analysis • Calculating Slope•length, area, volume, & weight• Convert to different units of measure:
• GraphingChapter 3: Right Triangle Geometry (page 82) Graphing•• Convert from metric to standard unitslength, area, volume, & weight
Section 4.2: Finding Linear EquationsSection 4.2: Finding Linear Equations• Convert from standar• Convert fromd to metric unitsmetric to standard unitsSection 3.1: Angles (page 83)
• Finding the equation from graphFinding the equation from graph•• Convert from standard to metric unitsSection 1.5: Order of Operations
Section 3.2: Area & Perimeter (page 89) • Finding the equation from an ordered pait• Finding the equation from an ordered pait
• Understand meaning of an exponentSection 1.5: Order of Operations
Finding the equation for a line••Section 3.3: Surface area (page 93)• Understand meaning of an exponent• Apply order of operations with formulas
Section 4.3: Using Linear Equations• Apply order of operations with formulas Appendix:Section 3.4: Volume (page 108)
Chapter 2: Formulas/Equations (page 61) • Abbreviations and Symbols• Using the graphing calculator for regression
Chapter 2: Formulas/Equations (page 61)
• ConversionsChapter 4: Linear Relationships (page 123)Section 2.1: Solving simple equations
Appendix:Section 2.1: Solving simple equations • Area and Perimeter Formulas• Solving equations with addition,Section 4.1: The Shape of a Linear Equation (page 124)• Solving equations with addition, • Abbreviations and Symbols• Volume and Surface Area Formulas
subtraction, multiplication, and division
subtraction, multiplication, and division • Conversions• Decimal/Fraction ConversionsSection 4.2: Finding Linear Equations (page 132)
Section 2.2: Solving for different Variables • Area and Perimeter Formulas• Steel Design TableSection 2.2: Solving for different VariablesAppendix (page 145)• Solving formulas for different letters • Volume and Surface Area Formulas• Solving formulas for different letters
Section 2.3: Solving complex equations • Decimal/Fraction Conversions
Section 2.3: Solving complex equations • Steel Design Table• Solving equations with exponents
• Solving equations with exponents
Legend of Assigment Icons
Legend of assignment icons:
Manufacturing Electronics Construction Automotive Welding Healtaltalthhh Introduction
About this Book:

This book is designed to be read. Some humor and stories of my personal journey in understanding and
applying this beautiful language are included to keep it interesting. There are no shortcuts, however! If you
are to understand the material deeply enough to apply it to all the rich problems that life presents, you will
need to add a considerable amount of your own thought and dedication to the process. The biggest
problem math students have is attempting to memorize steps to solve problems. This guarantees that you
will not remember it well enough, or know it deeply enough, to apply it. All mathematics can be understood
by any student willing to invest the time to ask questions, think and scribble (and sometimes throw things).
Your goal should be to “own” the material rather than merely “borrow” it. Owning it means that you carry
the knowledge with you, like a carpenter carries his or her tools, ready to use them as needed. Ownership,
however, comes at a cost and the amount you must pay is dependent on your natural ability, interest and
the time you have to study. Remember, if it was as easy as digging a ditch, everyone could do it and you
would not get paid extra for knowing it.
After a brief introduction, each section will offer rate, and the time it takes to pay off the loan. If
examples to introduce new concepts and show either the car’s price or the interest rate go up,
how they can be applied. The examples are not so will the monthly payment. On the other
intended to provide a step-by-step procedure hand, if you increase the time period over
for you to copy when you solve the problems in which you will pay off the loan, the monthly
payment will decrease. Without the algebraic the assignment. In fact, you will find that the
assigned problems may not even resemble the formula, however, there would be no way to
examples. Real-life problems, such as those figure out what the monthly payment should
that arise in the workplace, are so varied that be. The formula that expresses this relationship
you cannot expect to follow a memorized set of precisely is:
steps to solve them.

Algebra is, ultimately, a useful method for
expressing relationships in the world that Where M = monthly payment, P = price of the
people use every day. Every section of this
car, R = annual percentage rate (APR), I =
book is devoted to exposing you to, and (the modified interest rate representing
increasing your skill with, formulas (numerical
monthly growth), and T = time to pay off the
relationships). Of course there are relationships
loan in months.
in the world that you may find more interesting,

but you are probably reading this because you Though this is a daunting formula, complete
have already discovered that you cannot live on with multiplication, division, addition,
love alone. subtraction, exponents and parenthesis, indeed,
every operation that will be studied in this
Consider the common experience of making a
course, the meaning and order of operations
car payment. You understand that there is a
can be understood by anyone willing to invest
relationship between your monthly car
the time necessary to speak this most
payment and the price of the car, the interest
interesting and useful language called algebra.

1
3 Introduction

Although you might not understand all the details until the end of the course, let’s attempt to calculate a car
payment. Don’t worry if you find it too difficult right now. This should motivate your study of algebra since
money is an arena of life that every person spends some time caged in, and algebra provides an e