Developmental Mathematics: Basic Mathematics, Introductory Algebra, and Intermediate Algebra, 2nd edition

Mini-Mod 1 Whole Numbers

1.1 Whole Numbers

1.2 Rounding

1.3 Adding Whole Numbers; Estimation

1.4 Subtracting Whole Numbers

1.5 Basic Problem Solving

1.6 Multiplying Whole Numbers

1.7 Dividing Whole Numbers

1.8 More with Multiplying and Dividing

1.9 Exponents

1.10 Order of Operations and Whole Numbers

1.11 More Problem Solving

 

Mini-Mod 2 Factors and Fractions

2.1 Factors

2.2 Prime Factorization

2.3 Understanding Fractions

2.4 Simplifying Fractions - GCF and Factors Method

2.5 Simplifying Fractions - Prime Factors Method

2.6 Multiplying Fractions

2.7 Dividing Fractions

2.8 Applications of Multiplying and Dividing Fractions

 

Mini-Mod 3 LCM and Fractions

3.1 Finding the LCM - List Method

3.2 Finding the LCM - GCF Method

3.3 Finding the LCM - Prime Factor Method

3.4 Writing Fractions with an LCD

3.5 Adding and Subtracting Like Fractions

3.6 Adding and Subtracting Unlike Fractions

3.7 Order of Operations and Fractions

3.8 More Applications of Adding and Subtracting Fractions

 

Mini-Mod 4 Mixed Numbers

4.1 Changing a Mixed Number to an Improper Fraction

4.2 Changing an Improper Fraction to a Mixed Number

4.3 Multiplying Mixed Numbers

4.4 Dividing Mixed Numbers

4.5 Adding Mixed Numbers

4.6 Subtracting Mixed Numbers

4.7 Adding and Subtracting Mixed Numbers - Improper Fractions

4.8 Applications of Operations with Mixed Numbers

 

Mini-Mod 5 Operations with Decimals

5.1 Decimal Notation

5.2 Comparing Decimals

5.3 Rounding Decimals

5.4 Adding and Subtracting Decimals

5.5 Multiplying Decimals

5.6 Dividing Decimals

5.7 Order of Operations and Decimals

5.8 Converting Fractions to Decimals

5.9 Converting Decimals to Fractions

 

Mini-Mod 6 Ratios, Rates, and Percents

6.1 Ratios

6.2 Rates

6.3 Proportions

6.4 Percent Notation

6.5 Percent and Decimal Conversions

6.6 Percent and Fraction Conversions

6.7 The Percent Equation

6.8 The Percent Proportion

6.9 Percent Applications

 

Mini-Mod 7 U.S. and Metric Measurement

7.1 U.S. Length

7.2 U.S. Weight and Capacity

7.3 Metric Length

7.4 Metric Mass and Capacity

7.5 Converting between U.S. and Metric Units

7.6 Time and Temperature

 

Mini-Mod 8 Introduction to Geometry

8.1 Lines and Angles

8.2 Figures

8.3 Perimeter - Definitions and Units

8.4 Finding Perimeter

8.5 Area - Definitions and Units

8.6 Finding Area

8.7 Understanding Circles

8.8 Finding Circumference

8.9 Finding Area — Circles

 

Mini-Mod 9 More Geometry

9.1 Volume - Definitions and Units

9.2 Finding Volume

9.3 Square Roots

9.4 The Pythagorean Theorem

9.5 Similar Figures

9.6 Finding Missing Lengths

9.7 Congruent Triangles

9.8 Applications of Geometric Figures

 

Mini-Mod 10 Statistics

10.1 Bar Graphs and Histograms

10.2 Line Graphs

10.3 Circle Graphs

10.4 Mean

10.5 Median

10.6 Mode

10.7 Introduction to Probability

 

Mini-Mod 11 Real Numbers and Variables

11.1 Introduction to Real Numbers

11.2 Graphing Rational Numbers Using a Number Line

11.3 Translating Phrases into Algebraic Inequalities

11.4 Finding the Absolute Value of a Real Number

 

Mini-Mod 12 Adding and Subtracting with Real Numbers

12.1 Adding Real Numbers with the Same Sign

12.2 Adding Real Numbers with Different Signs

12.3 Finding the Opposite of a Real Number

12.4 Subtracting Real Numbers

12.5 Addition Properties of Real Numbers

12.6 Applications of Adding and Subtracting Real Numbers

 

Mini-Mod 13 Multiplying and Dividing with Real Numbers

13.1 Multiplying Real Numbers

13.2 Finding the Reciprocal of a Real Number

13.3 Dividing Real Numbers

13.4 Exponents and the Order of Operations

13.5 The Distributive Property

13.6 Multiplication Properties of Real Numbers

13.7 Applications of Multiplying and Dividing Real Numbers

 

Mini-Mod 14 Variables and Expressions

14.1 Introduction to Expressions

14.2 Evaluating Algebraic Expressions

14.3 Simplifying Expressions

14.4 Simplifying Expressions with Parentheses

14.5 Translating Words into Symbols

 

Mini-Mod 15 Introduction to Solving Linear Equations

15.1 Translating Words into Equations

15.2 Linear Equations and Solutions

15.3 Using the Addition Property of Equality

15.4 Using the Multiplication Property of Equality

15.5 Using the Addition and Multiplication Properties Together

 

Mini-Mod 16 Solving More Linear Equations and Inequalities

16.1 Solving Equations with Variables on Both Sides  

16.2 Solving Equations with Parentheses

16.3 Solving Equations with Fractions

16.4 Solving a Variety of Equations

16.5 Solving Equations and Formulas for a Variable

16.6 Solving and Graphing Linear Inequalities

16.7 Applications of Linear Equations and Inequalities

 

Mini-Mod 17 Introduction to Graphing Linear Equations

17.1 The Rectangular Coordinate System  

17.2 Graphing Linear Equations by Plotting Points

17.3 Graphing Linear Equations Using Intercepts

17.4 Graphing Linear Equations of the Form x=a, y=b, and y=mx

17.5 Applications of Graphing Linear Equations

 

Mini-Mod 18 Slope and the Equation of a Line

18.1 The Slope of a Line

18.2 Slope-Intercept Form

18.3 Graphing Lines Using the Slope and y-Intercept

18.4 Writing Equations of Lines Using a Point and Slope

18.5 Writing Equations of Lines Using Two Points

18.6 Writing Equations of Parallel and Perpendicular Lines

18.7 Graphing Linear Inequalities in Two Variables

18.8 Applications of Linear Equations and Slope

 

Mini-Mod 19 Introduction to Functions

19.1 Relations and Functions

19.2 The Vertical Line Test

19.3 Function Notation

19.4 Evaluating Functions

19.5 Applications of Functions

 

Mini-Mod 20 Solving Systems of Linear Equations

20.1 Introduction to Systems of Linear Equations  

20.2 Solving by the Graphing Method

20.3 Solving by the Substitution Method

20.4 Solving by the Elimination Method

20.5 Solving a System in Three Variables by the Elimination Method

20.6 Applications of Systems of Linear Equations

 

Mini-Mod 21 Introduction to Polynomials and Exponent Rules

21.1 Introduction to Polynomials

21.2 Addition of Polynomials

21.3 Subtraction of Polynomials

21.4 Product Rule for Exponents

21.5 Power Rule for Exponents

 

Mini-Mod 22 Multiplying Polynomials

22.1 Multiplying by a Monomial

22.2 Multiplying Binomials

22.3 Multiplying Polynomials

22.4 Multiplying the Sum and Difference of Two Terms

22.5 Squaring Binomials

 

Mini-Mod 23 Dividing Polynomials and More Exponent Rules

23.1 The Quotient Rule

23.2 Integer Exponents

23.3 Scientific Notation

23.4 Dividing a Polynomial by a Monomial

23.5 Dividing a Polynomial by a Binomial

 

Mini-Mod 24 Factoring Polynomials

24.1 Greatest Common Factor

24.2 Factoring by Grouping

24.3 Factoring Trinomials of the Form x²+bx+c

24.4 Factoring Trinomials of the Form ax²+bx+c

24.5 More Factoring of Trinomials by the Reverse FOIL Method

24.6 Factoring Trinomials by Grouping Numbers (the ac-Method)

 

Mini-Mod 25 More Factoring and Quadratic Equations

25.1 Special Cases of Factoring

25.2 Factoring Polynomials

25.3 Factor the Sum and Difference of Cubes

25.4 Solving Quadratic Equations by Factoring

25.5 Applications of Quadratic Equations

 

Mini-Mod 26 Introduction to Rational Expressions

26.1 Undefined Rational Expressions

26.2 Simplifying Rational Expressions

26.3 Multiplying Rational Expressions

26.4 Dividing Rational Expressions

 

Mini-Mod 27 Adding and Subtracting Rational Expressions

27.1 Adding Like Rational Expressions

27.2 Subtracting Like Rational Expressions

27.3 Finding the Least Common Denominator for Rational Expressions

27.4 Adding and Subtracting Unlike Rational Expressions

 

Mini-Mod 28 Complex Rational Expressions and Rational Equations

28.1 Simplifying Complex Rational Expressions by Adding and Subtracting

28.2 Simplifying Complex Rational Expressions by Multiplying by the LCD

28.3 Solving Rational Equations

28.4 Applications of Rational Equations: Solving Formulas for a Variable

28.5 Applications of Rational Equations: Work Problems

28.6 Applications of Rational Equations: D = RT

 

Mini-Mod 29 Variation

29.1 Direct Variation

29.2 Inverse Variation

29.3 Joint and Combined Variation

29.4 Applications of Variation

 

Mini-Mod 30 Roots and Radicals

30.1 Square Roots

30.2 Higher-Order Roots

30.3 Simplifying Radical Expressions

30.4 Rational Exponents

30.5 More on The Pythagorean Theorem

30.6 The Distance Formula

 

Mini-Mod 31 Operations of Radical Expressions

31.1 Introduction to Radical Functions

31.2 Adding and Subtracting Radical Expressions

31.3 Multiplying Radical Expressions

31.4 Dividing Radical Expressions

31.5 Rationalizing the Denominator

31.6 Solving Radical Equations

 

Mini-Mod 32 Solving Quadratic Equations

32.1 Introduction to Solving Quadratic Equations

32.2 Solving Quadratic Equations by Factoring

32.3 Solving Quadratic Equations using the Square Root Property

32.4 Solving Quadratic Equations by Completing the Square

32.5 Solving Quadratic Equations using the Quadratic Formula

32.6 Applications with Quadratic Equations

 

Mini-Mod 33 Complex Numbers and More Quadratic Equations

33.1 Complex Numbers

33.2 The Discriminant in the Quadratic Formula

33.3 Solving Quadratic Equations with Real or Complex Number Solutions

33.4 Solving Equations Quadratic in Form

33.5 Complex and Quadratic Applications

 

Mini-Mod 34 Graphing Quadratic Functions

34.1 Introduction to Graphing Quadratic Functions

34.2 Finding the Vertex of a Quadratic Function

34.3 Finding the Intercepts of a Quadratic Function

34.4 Graphing Quadratic Functions Summary

34.5 Applications with Quadratic Functions

 

Mini-Mod 35 Compound and Non-Linear Inequalities

35.1 Interval Notation

35.2 Graphing Compound Inequalities

35.3 Solving Compound Inequalities

35.4 Solving Quadratic Inequalities

35.5 Solving Rational Inequalities

 

Mini-Mod 36 Absolute Value Equations and Inequalities

36.1 Introduction to Absolute Value Equations

36.2 Solving Basic Absolute Value Equations

36.3 Solving Multiple Absolute Value Equations

36.4 Solving Absolute Value Inequalities

 

Mini-Mod 37 Conic Sections

37.1 Introduction to Conic Sections

37.2 The Circle

37.3 The Parabola

37.4 The Ellipse

37.5 The Hyperbola

 

Mini-Mod 38 Logarithmic and Exponential Functions

38.1 Composite Functions

38.2 Inverse Functions

38.3 Evaluating Exponential and Logarithmic Expressions

38.4 Graphing Exponential Functions

38.5 Converting Between Exponential and Logarithmic Forms

38.6 Graphing Logarithmic Functions

 

Mini-Mod 39 Solving Logarithmic and Exponential Equations

39.1 Properties of Logarithms

39.2 Common and Natural Logarithms

39.3 Change of Base of Logarithms

39.4 Solving Simple Exponential Equations and Applications

39.5 Solving Exponential Equations and Applications

39.6 Solving Simple Logarithmic Equations

39.7 Solving Logarithmic Equations and Applications

 

Appendix A: More on Functions

A.1 Using a Graphing Calculator

A.2 Algebra of Functions

A.3 Transformations of Functions

A.4 Piecewise Functions

A.5 Graphing Piecewise Functions

 

Appendix B: More on Systems

B.1 Systems of Linear Inequalities

B.2 Systems of Non-Linear Equations

B.3 Matrices and Determinants

B.4 Solving Systems of Linear Equations Using Matrices

B.5 Cramer’s Rule

 

Appendix C: Additional Topics

C.1 Sets

C.2 The Midpoint Formula

C.3 Surface Area

C.4 Synthetic Division

C.5 Balancing a Checking Account

C.6 Determining the Best Deal when Purchasing a Vehicle