MyMathLab ecourse for Developmental Mathematics

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1 MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, 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 1 Use symbols and key words for addition 2 Use properties of addition to rewrite 3 Evaluate algebraic (addition) 4 Add whole numbers when carrying is needed 5 Find the perimeters of geometric figures Topic 3: Subtracting Whole Number 1 Understand subtraction of whole numbers 2 Use symbols and key words for subtraction 3 Evaluate algebraic (subtraction) 4 Subtract whole numbers with two or more digits 5 Solve applied problems involving subtraction Topic 4: Multiplying Whole Number 1 Understand multiplication of whole numbers 2 Use symbols and key words for multiplication 3 Use the multiplication properties with 4 Multiply two several-digit numbers 5 Solve applied problems involving multiplication Topic 5: Dividing Whole Number 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 in exponent form 3 Use symbols and key words for expressing exponents 4 Follow the order of operations Topic 7: More on Algebraic 1 Use key words for expressing algebraic 2 Evaluate algebraic (multiply, divide) 3 Use the distributive property with Topic 8: Introduction to Solving Linear 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

2 Topic 2: Adding Integers 1 Add integers with the same sign 2 Add integers with different signs 3 Evaluate algebraic 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 1 Combine like terms with integer coefficients 2 Evaluate algebraic with integers 3 Use the distributive property with integers 4 Solve applied problems with integers Module 3: Introduction to Topic 1: 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: 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: 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 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 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 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 Topic 1: Multiplying and Dividing Fractional 1 Multiply fractions 2 Divide fractions 3 Solve applied problems involving fractions Topic 2: Least Common Multiples of Algebraic 1 Find multiples of algebraic 2 Find the LCM of numerical or algebraic 3 Solve applied problems involving the LCM

3 Topic 3: Adding and Subtracting Fractional 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 1 Add and subtract decimal 2 Combine like terms 3 Evaluate algebraic involving decimals 4 Estimate sums and differences 5 Solve applied problems involving decimals Topic 3: Multiplying and Dividing Decimal 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 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

4 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 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:, 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 with Fractions 1 Solve equations with fractions Topic 4: Formulas 1 Solve a formula for a specified variable Topic 5: Using 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 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 y- intercept 4 Graph a line using the slope and y-intercept 5 Find slopes of parallel and perpendicular lines

5 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 5: Graphing Linear Inequalities 1 Graph linear inequalities in two variables 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 and Inequalities Topic 1: Systems of Linear 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 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 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 Module 12: Exponents and Polynomials Topic 1: The Rules of Exponents 1 Use the product rule with exponential 2 Use the quotient rule with exponential 3 Raise exponential to a power Topic 2: Negative Exponents and Scientific Notation 1 Use negative exponents 2 Use scientific notation 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 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 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 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 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

6 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 by Factoring 1 Solve quadratic equations by factoring 2 Use quadratic equations to solve applied problems Module 14: Rational and Topic 1: Simplifying Rational 1 Simplify rational by factoring Topic 2: Multiplying and Dividing Rational 1 Multiply rational 2 Divide rational Topic 3: Adding and Subtracting Rational 1 Add and subtract like rational 2 Find the LCD for rational 3 Add and subtract unlike rational Topic 4: Simplifying Complex Rational 1 Simplify complex rational 2 Simplify complex rational with the LCD Topic 5: Solving Involving Rational 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 4 Solve work problems Module 15: Rational Exponents and Radicals Topic 1: Rational Exponents 1 Simplify with rational exponents 2 Add with rational exponents 3 Factor with rational exponents Topic 2: Radical and Functions 1 Evaluate radical and functions 2 Change radicals to rational-exponent 3 Change rational-exponent to radicals 4 Evaluate higher-order radical 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 2 Divide radical 3 Simplify radicals by rationalizing the denominator Topic 5: Radical 1 Solve a radical equation by squaring once 2 Solve a radical equation by squaring twice Topic 6: Complex Numbers 1 Simplify 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 Topic 1: Quadratic 1 Solve quadratic equations square root property 2 Solve quadratic equations completing the square

7 Topic 3: Solving 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 Module 17: The Conic Sections 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 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 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 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 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 19: Logarithmic and Exponential Functions 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 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 1 Solve logarithmic equations 2 Solve exponential equations 3 Apply exponential and logarithmic equations

8 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 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 Using Matrices Appendix G Sets

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