Intermediate Algebra: A STEM Approach

Intermediate Algebra: A STEM Approach, 1st edition

  • George Woodbury

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Overview

Intermediate Algebra: A STEM Approach helps you attain the mathematical skills necessary to be successful in both College Algebra and your ultimate field of study. Author George Woodbury presents broad coverage of STEM disciplines as well as the growing opportunities in STEM fields.

Published by Pearson (January 1st 2021) - Copyright © 2019

ISBN-13: 9780137398867

Subject: Developmental Math

Category: Intermediate Algebra

Table of contents

R. Review of Real Numbers
R.1 Integers, Opposites, and Absolute Value
R.2 Exponents and Order of Operations

1. Linear and Absolute Value Equations and Inequalities
1.1 Introduction to Algebra
1.2 Linear Equations
1.3 Problem Solving: Applications of Linear Equations
1.4 Proportions and Dimensional Analysis
1.5 Absolute Value Equations
1.6 Linear Inequalities
1.7 Absolute Value Inequalities

2. Graphing Linear Equations
2.1 The Rectangular Coordinate System; Equations in Two Variables
2.2 Slope of a Line
2.3 Equations of Lines
2.4 Linear Inequalities
2.5 Linear Functions
2.6 Absolute Value Functions

3. Systems of Equations
3.1 Systems of Two Equations in Two Unknowns
3.2 Applications of Systems of Equations
3.3 Systems of Linear Inequalities
3.4 Systems of Three Equations in Three Unknowns
3.5 Using Matrices to Solve Systems of Equations
3.6 Determinants and Cramer's Rule

4. Exponents, Polynomials, and Factoring Polynomials
4.1 Exponents
4.2 Negative Exponents; Scientific Notation
4.3 Polynomials; Addition, Subtraction, and Multiplication of Polynomials
4.4 Polynomial Division
4.5 An Introduction to Factoring; The Greatest Common Factor; Factoring by Grouping
4.6 Factoring Trinomials of Degree 2
4.7 Factoring Special Binomials
4.8 Factoring Polynomials: A General Strategy
4.9 Solving Quadratic Equations By Factoring
Chapters 1-4 Cumulative Review

5. Rational Expressions and Equations
5.1 Rational Expressions and Functions
5.2 Multiplication and Division of Rational Expressions
5.3 Addition and Subtraction of Rational Expressions
5.4 Complex Fractions
5.5 Rational Equations
5.6 Applications of Rational Equations

6. Radical Expressions and Equations
6.1 Square Roots; Radical Notation
6.2 Rational Exponents
6.3 Simplifying, Adding, and Subtracting Radical Expressions
6.4 Multiplying and Dividing Radical Expressions
6.5 Radical Equations and Applications of Radical Equations
6.6 The Complex Numbers

7. Quadratic Equations
7.1 Solving Quadratic Equations by Extracting Square Roots; Completing the Square
7.2 The Quadratic Formula
7.3 Equations That Are Quadratic in Form
7.4 Graphing Quadratic Equations and Quadratic Functions
7.5 Applications Using Quadratic Equations
7.6 Quadratic and Rational Inequalities
7.7 Other Functions and Their Graphs
Chapters 5-7 Cumulative Review

8. Logarithmic and Exponential Functions
8.1 The Algebra of Functions
8.2 Inverse Functions
8.3 Exponential Functions
8.4 Logarithmic Functions
8.5 Properties of Logarithms
8.6 Exponential and Logarithmic Equations
8.7 Applications of Exponential and Logarithmic Functions
8.8 Graphing Exponential and Logarithmic Functions

9. Conic Sections
9.1 Parabolas
9.2 Circles
9.3 Ellipses
9.4 Hyperbolas
9.5 Nonlinear Systems of Equations

10. Sequences, Series, and the Binomial Theorem
10.1 Sequences and Series
10.2 Arithmetic Sequences and Series
10.3 Geometric Sequences and Series
10.4 The Binomial Theorem
Chapters 8-10 Cumulative Review

Answers to Selected Exercises*

*Additional Instructor's Answers are given in the Annotated Instructor's Edition.

Integrated Review Topics:

Chapter 1
Build variable expressions
Evaluate variable expressions
Find the absolute value of an integer
Find the least common multiple (LCM) of two natural numbers
Graph integers on a number line
Identify linear equations with no solution
Multiply fractions
Perform arithmetic operations with integers
Present the solutions of an inequality on a number line and using interval notation
Simplify a fraction to lowest terms
Simplify variable expressions
Solve compound linear inequalities
Solve linear equations using the five-step general strategy
Solve linear equations using the multiplication property of equality
Solve linear inequalities

Chapter 2
Determine whether a value is a solution of an equation
Determine whether an ordered pair is a solution of an equation in two variables
Determine whether two lines are parallel
Determine whether two lines are perpendicular
Evaluate variable expressions
Find the absolute value of an integer
Find the slope of a line passing through two points using the slope formula
Graph a line using its slope and y-intercept
Graph horizontal lines and vertical lines
Graph integers on a number line
Graph linear equations using their intercepts
Graph linear functions
Interpret the slope and y-intercept in real-world applications
Plot ordered pairs on a rectangular coordinate plane
Simplify a fraction to lowest terms
Solve linear equations using the five-step general strategy
Solve literal equations for a specified variable
Subtract integers

Chapter 3
Build variable expressions
Complete ordered pairs for a linear equation in two variables
Create an augmented matrix for a system of three equations in three unknowns
Create an augmented matrix for a system of two equations in two unknowns
Determine if an ordered pair is a solution of an equation
Determine if an ordered pair is a solution to a system of equations
Graph a line using its slope and y-intercept
Graph a line using the most efficient strategy
Graph a linear inequality in two variables
Graph linear equations using their intercepts
Identify linear equations that are contradictions or identities
Solve linear equations containing fractions
Solve linear equations using the five-step general strategy
Solve systems of linear equations by using the addition method
Solve systems of linear equations by using the substitution method
Solve systems of linear equations using the addition method
Solve systems of three linear equations in three unknowns

Chapter 4
Evaluate functions
Factor a difference of squares
Factor a difference or sum of cubes
Factor a polynomial by grouping
Factor a trinomial of the form ax2 + bx + c
Factor a trinomial of the form x2 + bx + c
Factor the GCF out of each term of a polynomial
Find special products
Find the prime factorization of a natural number
Multiply a monomial by a polynomial
Multiply polynomials
Perform arithmetic operations with decimals
Simplify a fraction to lowest terms
Simplify exponents
Simplify variable expressions
Solve linear equations containing fractions
Solve linear equations using the five-step general strategy
Solve problems involving consecutive integers
Subtract integers
Understand the strategy for factoring a general polynomial
Use the distributive property of real numbers
Use the product rule for exponents
Use the quotient rule for exponents
Use unit factors for dimensional analysis

Chapter 5
Add and subtract fractions with the same denominator
Add and subtract fractions with unlike denominators
Add and subtract polynomials
Divide fractions
Evaluate algebraic expressions
Evaluate functions
Factor polynomials
Find the least common denominator (LCD) of two or more rational expressions
Find the least common multiple (LCM) of two natural numbers
Identify factors that are opposites of each other
Multiply fractions
Simplify a fraction to lowest terms
Simplify rational expressions to lowest terms
Solve a quadratic equation by factoring
Solve linear equations containing fractions
Solve literal equations for a specified variable
Solve linear equations using the five-step general strategy
Solve problems involving motion
Solve rational equations
Understand the six steps for solving applied problems

Chapter 6
Evaluate functions
Find nth roots
Find the prime factorization of a number
Find the square root of a number
Multiply polynomials
Multiply radical expressions
Rationalize a denominator with one term
Rationalize a denominator with two terms
Simplify variable expressions
Simplify expressions using the rules of exponents
Solve a quadratic equation by factoring
Solve linear equations
Solve linear inequalities
Use the power rule for exponents

Chapter 7
Determine the domain and range of a function from its graph
Factor trinomials of degree 2
Find the square root of a number
Find the x- and y-intercepts of a line from its equation
Graph absolute value functions by shifting
Graph quadratic functions of the form ƒ(x) = a(x - h)2 + k by shifting
Present the solutions of an inequality on a number line and using interval notation
Solve a quadratic equation by factoring
Solve applied geometry problems
Solve applied work-rate problems
Solve radical equations
Solve rational equations
Solve quadratic equations by completing the square
Solve quadratic equations by factoring or by using the quadratic formula
Solve quadratic equations by using the quadratic formula

Chapter 8
Add and subtract polynomials
Convert an equation from logarithmic form to exponential form
Evaluate exponential functions
Evaluate functions
Evaluate logarithms and logarithmic functions
Find the composite function of two functions ƒ(x) and g(x)
Find the inverse of a one-to-one function
Graph exponential functions
Graph linear functions
Graph logarithmic functions
Interpret graphs of functions
Multiply polynomials
Simplify expressions with exponents
Simplify rational expressions to lowest terms
Solve a logarithmic equation by converting it to exponential form
Solve an exponential equation by using logarithms
Solve linear equations
Solve literal equations for a specified variable
Solve quadratic equations by factoring
Use the product and quotient rules for logarithms
Use the product rule for exponents
Use the quotient rule for exponents

Chapter 9
Find a vertex by completing the square
Find the center of a circle and its radius by completing the square
Find the center of an ellipse and the lengths of its axes by completing the square
Find the square root of a number
Graph circles centered at a point (h, k)
Graph ellipses centered at a point (h, k)
Graph equations of the form y = a(x - h)2 + k
Graph quadratic equations in standard form
Graph quadratic functions of the form ƒ1x2 = 1x - h22 + k by shifting
Solve a quadratic equation by factoring
Solve quadratic equations by completing the square
Solve quadratic equations by extracting square roots
Solve quadratic equations by using the quadratic formula
Solve systems of linear equations by using the addition method
Solve systems of linear equations by using the substitution method

Chapter 10
Add, subtract, multiply, and divide integers
Evaluate functions
Find partial sums of a sequence
Find partial sums of an arithmetic sequence
Find special products
Find the general term of a sequence
Find the general term of an arithmetic sequence
Multiply polynomials

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