MyMathLab eCourse for
Developmental Mathematics
John Tobey, North Shore Community College
Jeffrey Slater, University of New Orleans
Jamie Blair, Orange Coast College
Jennifer Crawford, Normandale Community College
Table of Contents
Module 1: Whole Numbers and
Introduction to Algebra
Topic 1: Understanding Whole Numbers
1 Understand place values of whole numbers
2 Write whole numbers in expanded notation
3 Write word names for whole numbers
4 Use inequality symbols with whole
numbers
5 Round whole numbers
Topic 2: Adding Whole Number
Expressions
1 Use symbols and key words for addition
2 Use properties of addition to rewrite
expressions
3 Evaluate algebraic expressions (addition)
4 Add whole numbers when carrying is
needed
5 Find the perimeters of geometric figures
Topic 3: Subtracting Whole Number
Expressions
1 Understand subtraction of whole numbers
2 Use symbols and key words for subtraction
3 Evaluate algebraic expressions
(subtraction)
4 Subtract whole numbers with two or more
digits
5 Solve applied problems involving
subtraction
Topic 4: Multiplying Whole Number
Expressions
1 Understand multiplication of whole
numbers
2 Use symbols and key words for
multiplication
3 Use the multiplication properties with
expressions
4 Multiply two several-digit numbers
5 Solve applied problems involving
multiplication
Topic 5: Dividing Whole Number
Expressions
1 Understand division of whole numbers
2 Use symbols and key words for division
3 Master basic division facts
4 Perform long division with whole numbers
5 Solve applied problems involving division
Topic 6: Exponents and the Order of
Operations
1 Write whole numbers and variables in
exponent form
2 Evaluate expressions in exponent form
3 Use symbols and key words for expressing
exponents
4 Follow the order of operations
Topic 7: More on Algebraic Expressions
1 Use key words for expressing algebraic
expressions
2 Evaluate algebraic expressions (multiply,
divide)
3 Use the distributive property with expressions
Topic 8: Introduction to Solving Linear
Equations
1 Combine like terms
2 Translate English statements into equations
3 Solve equations using basic arithmetic facts
4 Translate and solve equations
Topic 9: Solving Applied Problems Using
Several Operations
1 Solve applied problems involving estimation
2 Solve applied problems involving charts
3 Use the Mathematics Blueprint for Problem
Solving
Module 2: Integers
Topic 1: Understanding Integers
1 Use inequality symbols with integers
2 Find the opposite of numbers
3 Find the absolute value of numbers
4 Read line graphs
Mathematics and Statistics
To request an examination copy, for more information, or to locate your Pearson representative,
please visit us at www.pearsonhighered.com/math
MyMathLab eCourse for Developmental Mathematics
John Tobey
Jeffrey Slater
Jamie Blair
Jennifer Crawford
Topic 2: Adding Integers
1 Add integers with the same sign
2 Add integers with different signs
3 Evaluate algebraic expressions involving addition
4 Solve applied problems involving addition
Topic 3: Subtracting Integers
1 Subtract integers
2 Perform several integer operations
3 Solve applied problems involving subtraction
Topic 4: Multiplying and Dividing Integers
1 Multiply two integers
2 Multiply two or more integers
3 Use exponents with integers as bases
4 Divide integers
Topic 5: The Order of Operations and
Applications
1 Follow the order of operations with integers
2 Solve applied problems with multiple operations
Topic 6: Simplifying and Evaluating Algebraic
Expressions
1 Combine like terms with integer coefficients
2 Evaluate algebraic expressions with integers
3 Use the distributive property with integers
4 Solve applied problems with integers
Module 3: Introduction to Equations
Topic 1: Equations of the form x + a = c and x
–a=c
1 Use the additive inverse property
2 Solve equations—the addition principle of
equality
3 Solve applied problems involving angles
Topic 2: Equations of the form ax = c
1 Solve equations—the division principle of
equality
2 Translate English statements into equations
3 Solve applied problems
Topic 3: Equations and Geometric Formulas
1 Solve equations involving perimeter
2 Solve equations involving area
3 Solve equations involving volume
4 Solve applied geometry problems
Topic 4: Performing Operations with Exponents
1 Use the product rule for exponents
2 Multiply algebraic expressions with exponents
3 Multiply a binomial by a monomial
4 Simplify geometric formulas
Module 4: Fractions, Ratios, and Proportions
Topic 1: Factoring Whole Numbers
1 Use the divisibility tests
2 Identify prime and composite numbers
3 Find the prime factors of whole numbers
Topic 2: Understanding Fractions
1 Understand fractions
2 Identify fractions and mixed numbers
3 Write improper fractions as mixed numbers
4 Write mixed numbers as improper fractions
Topic 3: Simplifying Fractional Expressions
1 Find equivalent fractions
2 Reduce fractions to lowest terms
3 Simplify fractions containing variables
4 Solve applied problems involving fractions
Topic 4: Simplifying Fractional Expressions with
Exponents
1 Use the quotient rule for exponents
2 Raise a power to a power
Topic 5: Ratios and Rates
1 Write two quantities as a ratio
2 Write two quantities as a unit rate
3 Solve applied problems involving rates
Topic 6: Proportions and Applications
1 Write proportions
2 Determine if statements are proportions
3 Find the missing number in proportions
4 Solve applied problems involving proportions
Module 5: Operations on Fractional
Expressions
Topic 1: Multiplying and Dividing Fractional
Expressions
1 Multiply fractions
2 Divide fractions
3 Solve applied problems involving fractions
Topic 2: Least Common Multiples of Algebraic
Expressions
1 Find multiples of algebraic expressions
2 Find the LCM of numerical or algebraic expressions
3 Solve applied problems involving the LCM
Mathematics and Statistics
To request an examination copy, for more information, or to locate your Pearson representative,
please visit us at www.pearsonhighered.com/math
MyMathLab eCourse for Developmental Mathematics
John Tobey
Jeffrey Slater
Jamie Blair
Jennifer Crawford
Topic 3: Adding and Subtracting Fractional
Expressions
1 Add and subtract fractions—common
denominator
2 Add and subtract fractions—different
denominators
Topic 4: Operations with Mixed Numbers
1 Add and subtract mixed numbers
2 Multiply and divide mixed numbers
3 Solve applied problems involving mixed
numbers
Topic 5: Order of Operations and Complex
Fractions
1 Follow the order of operations with fractions
2 Simplify complex fractions
3 Solve applied problems involving complex
fractions
Topic 6: Solve Applied Problems Involving
Fractions
1 Solve applied problems involving fractions
Topic 7: The Multiplication Principle of
Equality
1 Use the multiplication principle of equality
Module 6: Decimals and Percents
Topic 1: Understanding Decimal Fractions
1 Write word names for decimal fractions
2 Convert between decimals and fractions
3 Compare and order decimals
4 Round decimals
Topic 2: Adding and Subtracting Decimal
Expressions
1 Add and subtract decimal expressions
2 Combine like terms
3 Evaluate algebraic expressions involving
decimals
4 Estimate sums and differences
5 Solve applied problems involving decimals
Topic 3: Multiplying and Dividing Decimal
Expressions
1 Multiply decimals
2 Multiply a decimal by a power of 10
3 Divide a decimal by a whole number
4 Divide a decimal by a decimal
5 Change a fraction to a decimal
Topic 4: Estimating with Percents
1 Estimate a percentage of a number
2 Solve applied problems by estimating
percentages
Topic 5: Percents
1 Understand the meaning of percent
2 Change between decimals and percents
3 Change between fractions, decimals, and
percents
Topic 6: Solving Percent Problems Using
Equations
1 Translate and solve percent problems
2 Solve applied percent problems using
equations
Topic 7: Solving Percent Problems Using
Proportions
1 Identify the parts of a percent proportion
2 Use the percent proportion
3 Solve applied percent problems using
proportions
Topic 8: Solving Applied Problems
Involving Percents
1 Solve commission problems
2 Solve percent increase/decrease, discount
problems
3 Solve simple interest problems
Module 7: Measurement and
Geometric Figures
Topic 1: Using Unit Fractions with U.S. and
Metric Units
1 Use unit fractions to convert between U.S.
units
2 Solve applied problems involving U.S. units
3 Convert between metric units
4 Solve applied problems involving metric units
Topic 2: Converting Between the U.S. and
Metric Systems
1 Convert units between the metric and U.S.
systems
2 Convert Fahrenheit and Celsius temperatures
Topic 3: Angles
1 Understand angles
2 Find the complement and supplement of an
angle
3 Identify adjacent and vertical angles
4 Use alternate interior and corresponding
Mathematics and Statistics
To request an examination copy, for more information, or to locate your Pearson representative,
please visit us at www.pearsonhighered.com/math
MyMathLab eCourse for Developmental Mathematics
John Tobey
Jeffrey Slater
Jamie Blair
Jennifer Crawford
Topic 4: The Circle
1 Find the circumference of circles
2 Find the area of circles
3 Solve area problems involving circles
Topic 5: Volume
1 Find the volumes of cylinders and spheres
2 Find the volume of cones
3 Find the volume of pyramids
Topic 6: Similar Geometric Figures
1 Find the corresponding parts of similar triangles
2 Find the corresponding parts of similar figures
Module 8: Introduction to Polynomials
Topic 1: Adding and Subtracting Polynomials
1 Identify the terms of a polynomial
2 Add polynomials
3 Find the opposite of a polynomial
4 Subtract polynomials
Topic 2: Multiplying Polynomials
1 Multiply a monomial times a polynomial
2 Multiply a binomial times a trinomial
3 Multiply binomials using FOIL
Topic 3: Translate from English to Algebra
1 Translate from English to Algebra
2 Write algebraic expressions to compare
quantities
Topic 4: Factoring Using the Greatest
Common Factor
1 Find the greatest common factor (GCF)
2 Factor out the GCF from a polynomial
Module 9: Equations, Inequalities, and
Applications
Topic 1: Addition and Multiplication
Principles of Equality
1 Use the addition principle of equality
2 Use the multiplication principle of equality
3 Use the division principle of equality
Topic 2: Using Both Principles of Equality
Together
1 Solve equations using both principles
2 Solve equations when the variable is on both
sides
3 Solve equations with parentheses
Topic 3: Solving Equations with Fractions
1 Solve equations with fractions
Topic 4: Formulas
1 Solve a formula for a specified variable
Topic 5: Using Equations to Solve Word
Problems
1 Solve number problems
2 Apply the Mathematics Blueprint of Problem
Solving
Topic 6: Solving Word Problems Involving
Money and Percents
1 Solve problems involving periodic rate charges
2 Solve percent problems
3 Solve investment problems
4 Solve coin problems
Topic 7: Solving Inequalities in One Variable
1 Interpret inequality statements
2 Graph an inequality on a number line
3 Translate from English to Algebra
4 Solve and graph an inequality
Module 10: Graphing and Functions
Topic 1: The Rectangular Coordinate System
1 Plot a point, given the coordinates
2 Determine the coordinates of a plotted point
3 Find ordered pairs for a given linear equation
Topic 2: Graphing Linear Equations
1 Graph a linear equation by plotting three points
2 Graph a straight line by plotting its intercepts
3 Graph horizontal and vertical lines
Topic 3: The Slope of a Line
1 Find the slope of a line given two points
2 Find the slope and y-intercept of a line
3 Write the equation given the slope and yintercept
4 Graph a line using the slope and y-intercept
5 Find slopes of parallel and perpendicular lines
Mathematics and Statistics
To request an examination copy, for more information, or to locate your Pearson representative,
please visit us at www.pearsonhighered.com/math
MyMathLab eCourse for Developmental Mathematics
John Tobey
Jeffrey Slater
Jamie Blair
Jennifer Crawford
Topic 4: Writing the Equation of a Line
1 Write an equation given a point and the slope
2 Write an equation of a line given two points
3 Write an equation of a line given its graph
Topic 2: Negative Exponents and Scientific
Notation
1 Use negative exponents
2 Use scientific notation
Topic 5: Graphing Linear Inequalities
1 Graph linear inequalities in two variables
Topic 3: Fundamental Polynomial Operations
1 Recognize polynomials and determine their
degrees
2 Add polynomials
3 Subtract polynomials
4 Evaluate polynomials to predict a value
Topic 6: Functions
1 Understand the concepts of relation and function
2 Graph simple nonlinear equations
3 Determine whether a graph represents a function
4 Use function notation
Module 11: Systems of Linear Equations
and Inequalities
Topic 1: Systems of Linear Equations in Two
Variables
1 Identify ordered pair solutions to a system
2 Solve a system of two equations by graphing
3 Solve a system of two equations by substitution
4 Solve a system of two equations by addition
5 Identify systems with no unique solution
6 Choose a method for solving systems
Topic 2: Systems of Linear Equations in Three
Variables
1 Identify ordered triple solutions to a system
2 Solve systems with non-zero coefficients
3 Solve systems with zero coefficients
Topic 3: Applications of Systems of Linear
Equations
1 Solve applications with systems in two variables
2 Solve applications with systems in three variables
Topic 4: Systems of Linear Inequalities
1 Graph a system of linear inequalities
Topic 4: Multiplying Polynomials
1 Multiply a monomial by a polynomial
2 Multiply two binomials
Topic 5: Multiplication –Special Cases
1 Multiply the sum and difference of two terms
2 Square binomials
3 Multiply polynomials with more than two terms
Topic 6: Dividing Polynomials
1 Divide a polynomial by a monomial
2 Divide a polynomial by a binomial
Module 13: Factoring
Topic 1: Removing a Common Factor
1 Factor polynomials with a common factor
Topic 2: Factoring by Grouping
1 Factor expressions with four terms by grouping
Topic 3: Factoring Trinomials When a = 1
1 Factor trinomials when a = 1
2 Factor trinomials with a = 1 and a common
factor
Module 12: Exponents and Polynomials
Topic 4: Factoring Trinomials When a ≠ 1
1 Factor trinomials by the trial-and-error method
2 Factor trinomials with a ≠ 1 by grouping
3 Factor trinomials with a ≠ 1 and a common factor
Topic 1: The Rules of Exponents
1 Use the product rule with exponential expressions
2 Use the quotient rule with exponential
expressions
3 Raise exponential expressions to a power
Topic 5: Special Cases of Factoring
1 Factor the difference of two squares
2 Factor perfect square trinomials
3 Factor the sum and difference of two cubes
4 Factor out a common factor first
Mathematics and Statistics
To request an examination copy, for more information, or to locate your Pearson representative,
please visit us at www.pearsonhighered.com/math
MyMathLab eCourse for Developmental Mathematics
John Tobey
Jeffrey Slater
Jamie Blair
Jennifer Crawford
Topic 6: A Brief Review of Factoring
1 Identify and factor any factorable polynomial
2 Determine whether a polynomial is prime
Topic 7: Solving Quadratic Equations by
Factoring
1 Solve quadratic equations by factoring
2 Use quadratic equations to solve applied
problems
Module 14: Rational Expressions and
Equations
Topic 1: Simplifying Rational Expressions
1 Simplify rational expressions by factoring
Topic 2: Multiplying and Dividing Rational
Expressions
1 Multiply rational expressions
2 Divide rational expressions
Topic 3: Adding and Subtracting Rational
Expressions
1 Add and subtract like rational expressions
2 Find the LCD for rational expressions
3 Add and subtract unlike rational expressions
Topic 4: Simplifying Complex Rational
Expressions
1 Simplify complex rational expressions
2 Simplify complex rational expressions with the
LCD
Topic 5: Solving Equations Involving Rational
Expressions
1 Solve rational equations that have solutions
2 Determine if a rational equation has no solution
Topic 6: Ratio, Proportion, and Other Applied
Problems
1 Solve problems involving ratio and proportion
2 Solve problems involving similar triangles
3 Solve distance problems with rational
expressions
4 Solve work problems
Module 15: Rational Exponents and
Radicals
Topic 1: Rational Exponents
1 Simplify expressions with rational exponents
2 Add expressions with rational exponents
3 Factor expressions with rational exponents
Topic 2: Radical Expressions and Functions
1 Evaluate radical expressions and functions
2 Change radicals to rational-exponent expressions
3 Change rational-exponent expressions to radicals
4 Evaluate higher-order radical expressions
Topic 3: Simplifying, Adding, and Subtracting
Radicals
1 Simplify a radical by using the product rule
2 Add and subtract like radical terms
Topic 4: Multiplying and Dividing Radicals
1 Multiply radical expressions
2 Divide radical expressions
3 Simplify radicals by rationalizing the denominator
Topic 5: Radical Equations
1 Solve a radical equation by squaring once
2 Solve a radical equation by squaring twice
Topic 6: Complex Numbers
1 Simplify expressions involving complex numbers
2 Add and subtract complex numbers
3 Multiply complex numbers
4 Evaluate powers of i
5 Divide two complex numbers
Topic 7: Variation
1 Solve direct variation problems
2 Solve inverse variation problems
3 Solve joint and combined variation problems
Module 16: Quadratic Equations
Topic 1: Quadratic Equations
1 Solve quadratic equations—square root property
2 Solve quadratic equations—completing the
square
Mathematics and Statistics
To request an examination copy, for more information, or to locate your Pearson representative,
please visit us at www.pearsonhighered.com/math
MyMathLab eCourse for Developmental Mathematics
John Tobey
Jeffrey Slater
Jamie Blair
Jennifer Crawford
Topic 3: Solving Equations That Are Quadratic
in Form
1 Solve equations of degree greater than 2
2 Solve equations with fractional exponents
Topic 4: Formulas and Applications
1 Solve a quadratic equation with several variables
2 Solve problems using the Pythagorean Theorem
3 Solve applied problems using quadratic equations
Topic 3: Algebraic Operations on Functions
1 Perform operations on functions
2 Find the composition of two functions
Topic 4: Inverse of a Function
1 Determine if a function is a one-to-one function
2 Find the inverse function for a given function
3 Graph a function and its inverse function
Module 17: The Conic Sections
Module 19: Logarithmic and Exponential
Functions
Topic 1: The Distance Formula and the Circle
1 Find the distance between two points
2 Find the center, radius, and graph of a circle
3 Write the equation of a circle in standard form
4
Rewrite the equation of a circle in
standard form
Topic 1: The Exponential Function
1 Graph an exponential function
2 Solve elementary exponential equations
3 Solve applied problems using exponential
equations
Topic 2: The Parabola
1 Graph vertical parabolas
2 Graph horizontal parabolas
3 Write the equation of a parabola in standard
form
Topic 3: The Ellipse
1 Graph an ellipse whose center is at the origin
2 Graph an ellipse whose center is at (h, k)
Topic 4: The Hyperbola
1 Graph a hyperbola whose center is at the origin
2 Graph a hyperbola whose center is at (h, k)
Topic 5: Nonlinear Systems of Equations
1 Solve nonlinear systems by substitution
2 Solve nonlinear systems by addition
Module 18: Additional Properties of
Functions
Topic 1: Function Notation
1 Use function notation to evaluate expressions
2 Use function notation to solve applied problems
Topic 2: General Graphing Procedures for
Functions
1 Use the vertical line test—graphs of functions
2 Perform horizontal and vertical shifts
Topic 2: The Logarithmic Function
1 Write exponential equations in logarithmic form
2 Write logarithmic equations in exponential form
3 Solve elementary logarithmic equations
4 Graph a logarithmic function
Topic 3: Properties of Logarithms
1 Use the logarithm of a product property
2 Use the logarithm of a quotient property
3 Use the logarithm of a power property
4 Solve simple logarithmic equations
Topic 4: Common and Natural Logarithms;
Change of Base
1 Find common logarithms
2 Find the antilogarithm of a common logarithm
3 Find natural logarithms
4 Find the antilogarithm of a natural logarithm
5 Evaluate a logarithm to a base other than 10 or
e
Topic 5: Exponential and Logarithmic
Equations
1 Solve logarithmic equations
2 Solve exponential equations
3 Apply exponential and logarithmic equations
Mathematics and Statistics
To request an examination copy, for more information, or to locate your Pearson representative,
please visit us at www.pearsonhighered.com/math
MyMathLab eCourse for Developmental Mathematics
John Tobey
Jeffrey Slater
Jamie Blair
Jennifer Crawford
Module 20 Additional Topics
Topic 1: Quadratic Functions
1 Find vertex, intercepts of a quadratic function
2 Graph a quadratic function
Topic 2: Compound and Quadratic Inequalities
1 Graph compound inequalities that use and
2 Graph compound inequalities that use or
3 Solve compound inequalities and graph their
solutions.
4 Solve a factorable quadratic inequality in one
variable.
5 Solve a nonfactorable quadratic inequality in one
variable.
Topic 3: Absolute Value Equations and
Inequalities
1 Solve equations; absolute value isolated
2 Solve equations; absolute value not isolated
3 Solve equations; two absolute values
4 Solve absolute value inequalities; less than
5 Solve absolute value inequalities; greater than
Topic 4: Interpreting and Constructing Graphs
1 Read pictographs
2 Read circle graphs with percentage values
3 Read and interpret double-bar graphs
4 Read and interpret comparison line graphs
5 Construct double-bar and line graphs
Topic 5: Mean, Median, and Mode
1 Find the mean of a set of numbers
2 Find the median of a set of numbers
3 Find the mode of a set of numbers
Appendices
Appendix A Consumer Finance Applications
Appendix B Introduction to U.S. and Metric Units
of Measurement
Appendix C Additional Arithmetic Practice
Appendix D Foundations for Intermediate Algebra:
A Transition from Beginning to Intermediate
Appendix E Determinants and Cramer’s Rule
Appendix F Solving Systems of Linear Equations
Using Matrices
Appendix G Sets
Mathematics and Statistics
To request an examination copy, for more information, or to locate your Pearson representative,
please visit us at www.pearsonhighered.com/math