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| Preface | |
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| Fundamentals of General Mathematics | |
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| Whole Numbers | |
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| Place Value | |
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| Expanding Whole Numbers | |
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| Estimating (Approximating) | |
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| Addition of Whole Numbers | |
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| Subtraction of Whole Numbers | |
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| Problem Solving-Word Problem Practical Applications | |
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| Adding and Subtracting Whole Numbers in Practical Applications | |
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| Multiplication of Whole Numbers | |
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| Division of Whole Numbers | |
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| Multiplying and Dividing Whole Numbers in Practical Applications | |
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| Combined Operations of Whole Numbers | |
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| Combined Operations of Whole Numbers in Practical Applications | |
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| Unit Exercise and Problem Review | |
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| Computing with a Calculator: Whole Numbers | |
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| Common Fractions | |
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| Definitions | |
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| Fractional Parts | |
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| A Fraction as an Indicated Division | |
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| Equivalent Fractions | |
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| Expressing Fractions in Lowest Terms | |
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| Expressing Mixed Numbers as Improper Fractions | |
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| Expressing Improper Fractions as Mixed Numbers | |
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| Division of Whole Numbers; Quotients as Mixed Numbers | |
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| Use of Common Fractions in Practical Applications | |
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| Addition of Common Fractions | |
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| Subtraction of Common Fractions | |
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| Adding and Subtracting Common Fractions in Practical Applications | |
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| Multiplication of Common Fractions | |
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| Multiplying Common Fractions in Practical Applications | |
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| Division of Common Fractions | |
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| Dividing Common Fractions in Practical Applications | |
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| Combined Operations with Common Fractions | |
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| Combined Operations of Common Fractions in Practical Applications | |
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| Unit Exercise and Problem Review | |
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| Computing with a Calculator: Fractions and Mixed Numbers | |
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| Decimal Fractions | |
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| Meaning of Fractional Parts | |
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| Reading Decimal Fractions | |
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| Simplified Method of Reading Decimal Fractions | |
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| Writing Decimal Fractions | |
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| Rounding Decimal Fractions | |
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| Expressing Common Fractions as Decimal Fractions | |
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| Expressing Decimal Fractions as Common Fractions | |
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| Expressing Decimal Fractions in Practical Applications | |
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| Adding Decimal Fractions | |
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| Subtracting Decimal Fractions | |
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| Adding and Subtracting Decimal Fractions in Practical Applications | |
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| Multiplying Decimal Fractions | |
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| Multiplying Decimal Fractions in Practical Applications | |
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| Dividing Decimal Fractions | |
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| Dividing Decimal Fractions in Practical Applications | |
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| Powers and Roots of Decimal Fractions | |
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| Decimal Fraction Powers and Roots in Practical Applications | |
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| Table of Decimal Equivalents | |
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| Combined Operations of Decimal Fractions | |
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| Combined Operations of Decimal Fractions in Practical Applications | |
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| Unit Exercise and Problem Review | |
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| Computing with a Calculator: Decimals | |
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| Ratio and Proportion | |
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| Description of Ratios | |
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| Order of Terms of Ratios | |
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| Description of Proportions | |
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| Direct Proportions | |
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| Inverse Proportions | |
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| Unit Exercise and Problem Review | |
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| Percents | |
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| Definition of Percent | |
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| Expressing Decimal Fractions as Percents | |
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| Expressing Common Fractions and Mixed Numbers as Percents | |
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| Expressing Percents as Decimal Fractions | |
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| Expressing Percents as Common Fractions | |
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| Types of Simple Percent Problems | |
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| Finding Percentage in Practical Applications | |
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| Finding Percent (Rate) in Practical Applications | |
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| Finding the Base in Practical Applications | |
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| More Complex Percentage Practical Applications | |
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| Unit Exercise and Problem Review | |
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| Signed Numbers | |
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| Meaning of Signed Numbers | |
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| The Number Line | |
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| Operations Using Signed Numbers | |
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| Absolute Value | |
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| Addition of Signed Numbers | |
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| Subtraction of Signed Numbers | |
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| Multiplication of Signed Numbers | |
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| Division of Signed Numbers | |
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| Powers of Signed Numbers | |
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| Roots of Signed Numbers | |
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| Combined Operations of Signed Numbers | |
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| Scientific Notation | |
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| Engineering Notation | |
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| Unit Exercise and Problem Review | |
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| Measurement | |
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| Precision, Accuracy, and Tolerance | |
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| Exact and Approximate (Measurement) Numbers | |
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| Degree of Precision of Measuring Instruments | |
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| Common Linear Measuring Instruments | |
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| Degree of Precision of a Measurement Number | |
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| Degrees of Precision in Adding and Subtracting Measurement Numbers | |
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| Significant Digits | |
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| Accuracy | |
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| Accuracy in Multiplying and Dividing Measurement Numbers | |
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| Absolute and Relative Error | |
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| Tolerance (Linear) | |
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| Unilateral and Bilateral Tolerance with Clearance and Interference Fits | |
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| Unit Exercise and Problem Review | |
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| Customary Measurement Units | |
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| Customary Linear Units | |
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| Expressing Equivalent Units of Measure | |
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| Arithmetic Operations with Compound Numbers | |
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| Customary Linear Measure Practical Applications | |
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| Customary Units of Surface Measure (Area) | |
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| Customary Area Measure Practical Applications | |
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| Customary Units of Volume (Cubic Measure) | |
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| Customary Volume Practical Applications | |
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| Customary Units of Capacity | |
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| Customary Capacity Practical Applications | |
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| Customary Units of Weight (Mass) | |
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| Customary Weight Practical Applications | |
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| Compound Units | |
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| Compound Units Practical Applications | |
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| Unit Exercise and Problem Review | |
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| Metric Measurement Units | |
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| Metric Units of Linear Measure | |
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| Expressing Equivalent Units within the Metric System | |
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| Arithmetic Operations with Metric Lengths | |
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| Metric Linear Measure Practical Applications | |
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| Metric Units of Surface Measure (Area) | |
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| Arithmetic Operations with Metric Area Units | |
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| Metric Area Measure Practical Applications | |
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| Metric Units of Volume (Cubic Measure) | |
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| Arithmetic Operations with Metric Volume Units | |
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| Metric Volume Practical Applications | |
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| Metric Units of Capacity | |
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| Metric Capacity Practical Applications | |
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| Metric Units of Weight (Mass) | |
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| Metric Weight Practical Applications | |
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| Compound Units | |
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| Compound Units Practical Applications | |
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| Metric Prefixes Applied to Very Large and Very Small Numbers | |
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| Conversion Between Metric and Customary Systems | |
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| Unit Exercise and Problem Review | |
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| Steel Rules and Vernier Calipers | |
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| Types of Steel Rules | |
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| Reading Fractional Measurements | |
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| Measurements that Do Not Fall on Rule Graduations | |
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| Reading Decimal-Inch Measurements | |
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| Reading Metric Measurements | |
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| Vernier Calipers: Types and Description | |
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| Reading Measurements on a Customary Vernier Caliper | |
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| Reading Measurements on a Metric Vernier Caliper | |
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| Unit Exercise and Problem Review | |
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| Micrometers | |
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| Description of a Customary Outside Micrometer | |
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| Reading a Customary Micrometer | |
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| The Customary Vernier Micrometer | |
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| Reading a Customary Vernier Micrometer | |
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| Description of a Metric Micrometer | |
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| Reading a Metric Micrometer | |
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| The Metric Vernier Micrometer | |
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| Reading a Metric Vernier Micrometer | |
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| Unit Exercise and Problem Review | |
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| Fundamentals of Algebra | |
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| Introduction to Algebra | |
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| Symbolism | |
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| Algebraic Expressions | |
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| Evaluation of Algebraic Expressions | |
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| Unit Exercise and Problem Review | |
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| Basic Algebraic Operations | |
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| Definitions | |
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| Addition | |
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| Subtraction | |
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| Multiplication | |
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| Division | |
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| Powers | |
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| Roots | |
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| Removal of Parentheses | |
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| Combined Operations | |
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| Basic Structure of the Binary Numeration System | |
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| Unit Exercise and Problem Review | |
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| Simple Equations | |
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| Expression of Equality | |
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| Writing Equations from Word Statements | |
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| Checking the Equation | |
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| Principles of Equality | |
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| Solution of Equations by the Subtraction Principle of Equality | |
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| Solution of Equations by the Addition Principle of Equality | |
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| Solution of Equations by the Division Principle of Equality | |
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| Solution of Equations by the Multiplication Principle of Equality | |
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| Solution of Equations by the Root Principle of Equality | |
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| Solution of Equations by the Power Principle of Equality | |
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| Unit Exercise and Problem Review | |
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| Complex Equations | |
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| Equations Consisting of Combined Operations | |
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| Solving for the Unknown in Formulas | |
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| Substituting Values Directly in Given Formulas | |
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| Rearranging Formulas | |
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| Unit Exercise and Problem Review | |
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| The Cartesian Coordinate System and Graphs of Linear Equations | |
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| Description of the Cartesian (Rectangular) Coordinate System | |
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| Graphing a Linear Equation | |
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| Slope of a Linear Equation | |
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| Slope Intercept Equation of a Straight Line | |
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| Point-Slope Equation of a Straight Line | |
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| Determining an Equation, Given Two Points | |
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| Describing a Straight Line | |
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| Unit Exercise and Problem Review | |
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| Systems of Equations | |
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| Graphical Method of Solving Systems of Equations | |
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| Substitution Method of Solving Systems of Equations | |
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| Addition or Subtraction Method of Solving Systems of Equations | |
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| Types of Systems of Equations | |
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| Determinants | |
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| Cramer's Rule | |
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| Writing and Solving Systems of Equations from Word Statements, Number Problems, and Practical Applications | |
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| Unit Exercise and Problem Review | |
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| Quadratic Equations | |
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| General or Standard Form of Quadratic Equations | |
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| Incomplete Quadratic Equations (ax[superscript 2] = c) | |
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| Complete Quadratic Equations | |
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| Practical Applications of Complete Quadratic Equations. Equations Given | |
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| Word Problems Involving Complete Quadratic Equations. Equations Not Given | |
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| Unit Exercise and Problem Review | |
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| Fundamentals of Plane Geometry | |
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| Introduction to Plane Geometry | |
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| Plane Geometry | |
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| Axioms and Postulates | |
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| Points and Lines | |
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| Unit Exercise and Problem Review | |
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| Angular Measure | |
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| Units of Angular Measure | |
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| Units of Angular Measure in Degrees, Minutes, and Seconds | |
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| Expressing Degrees, Minutes, and Seconds as Decimal Degrees | |
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| Expressing Decimal Degrees as Degrees, Minutes, and Seconds | |
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| Arithmetic Operations on Angular Measure in Degrees, Minutes, and Seconds | |
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| Simple Semicircular Protractor | |
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| Complements and Supplements of Scale Readings | |
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| Unit Exercise and Problem Review | |
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| Angular Geometric Principles | |
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| Naming Angles | |
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| Types of Angles | |
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| Angles Formed by a Transversal | |
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| Theorems and Corollaries | |
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| Unit Exercise and Problem Review | |
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| Triangles | |
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| Types of Triangles | |
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| Angles of a Triangle | |
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| Isosceles and Equilateral Triangles | |
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| Isosceles Triangle Practical Applications | |
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| Equilateral Triangle Practical Applications | |
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| The Pythagorean Theorem | |
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| Pythagorean Theorem Practical Applications | |
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| Unit Exercise and Problem Review | |
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| Congruent and Similar Figures | |
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| Congruent Figures | |
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| Similar Figures | |
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| Practical Applications of Similar Triangles | |
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| Unit Exercise and Problem Review | |
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| Polygons | |
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| Types of Polygons | |
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| Types of Quadrilaterals | |
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| Polygon Interior and Exterior Angles | |
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| Practical Applications of Polygon Interior and Exterior Angles | |
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| Practical Applications of Trapezoid Median | |
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| Unit Exercise and Problem Review | |
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| Circles | |
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| Definitions | |
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| Circumference Formula | |
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| Arc Length Formula | |
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| Radian Measure | |
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| Circle Postulates | |
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| Chords, Arcs, and Central Angles | |
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| Practical Applications of Circle Chord Bisector | |
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| Circle Tangents and Chord Segments | |
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| Practical Applications of Circle Tangent | |
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| Practical Applications of Tangents from a Common Point | |
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| Angles Formed Inside and on a Circle | |
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| Practical Applications of Inscribed Angles | |
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| Practical Applications of Tangent and Chord | |
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| Angles Outside a Circle | |
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| Internally and Externally Tangent Circles | |
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| Practical Applications of Internally Tangent Circles | |
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| Practical Applications of Externally Tangent Circles | |
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| Unit Exercise and Problem Review | |
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| Geometric Figures: Areas and Volumes | |
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| Areas of Common Polygons | |
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| Areas of Rectangles | |
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| Areas of Parallelograms | |
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| Areas of Trapezoids | |
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| Areas of Triangles Given the Base and Height | |
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| Areas of Triangles Given Three Sides | |
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| Unit Exercise and Problem Review | |
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| Areas of Circles, Sectors, Segments, and Ellipses | |
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| Areas of Circles | |
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| Ratio of Two Circles | |
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| Areas of Sectors | |
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| Areas of Segments | |
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| Areas of Ellipses | |
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| Unit Exercise and Problem Review | |
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| Prisms and Cylinders: Volumes, Surface Areas, and Weights | |
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| Prisms | |
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| Volumes of Prisms | |
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| Cylinders | |
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| Volumes of Cylinders | |
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| Computing Heights and Bases of Prisms and Cylinders | |
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| Lateral Areas and Surface Areas of Right Prisms and Cylinders | |
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| Unit Exercise and Problem Review | |
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| Pyramids and Cones: Volumes, Surface Areas, and Weights | |
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| Pyramids | |
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| Cones | |
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| Volumes of Regular Pyramids and Right Circular Cones | |
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| Computing Heights and Bases of Regular Pyramids and Right Circular Cones | |
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| Lateral Areas and Surface Areas of Regular Pyramids and Right Circular Cones | |
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| Frustums of Pyramids and Cones | |
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| Volumes of Frustums of Regular Pyramids and Right Circular Cones | |
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| Lateral Areas and Surface Areas of Frustums of Regular Pyramids and Right Circular Cones | |
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| Unit Exercise and Problem Review | |
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| Spheres and Composite Figures: Volumes, Surface Areas, and Weights | |
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| Spheres | |
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| Surface Area of a Sphere | |
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| Volume of a Sphere | |
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| Volumes and Surface Areas of Composite Solid Figures | |
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| Unit Exercise and Problem Review | |
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| Basic Statistics | |
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| Graphs: Bar, Circle, and Line | |
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| Types and Structure of Graphs | |
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| Reading Bar Graphs | |
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| Drawing Bar Graphs | |
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| Drawing Bar Graphs with a Spreadsheet | |
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| Circle Graphs | |
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| Drawing Circle Graphs with a Spreadsheet | |
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| Line Graphs | |
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| Reading Line Graphs | |
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| Reading Combined-Data Line Graphs | |
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| Drawing Line Graphs | |
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| Drawing Broken-Line Graphs | |
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| Drawing Broken-Line Graphs with a Spreadsheet | |
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| Drawing Straight-Line Graphs | |
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| Drawing Curved-Line Graphs | |
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| Unit Exercise and Problem Review | |
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| Statistics | |
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| Probability | |
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| Independent Events | |
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| Mean Measurement | |
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| Other Average Measurements | |
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| Quartiles and Percentiles | |
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| Grouped Data | |
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| Variance and Standard Deviation | |
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| Statistical Process Control: X-Bar Charts | |
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| Statistical Process Control: R-Charts | |
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| Unit Exercise and Problem Review | |
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| Fundamentals of Trigonometry | |
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| Introduction to Trigonometric Functions | |
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| Ratio of Right Triangle Sides | |
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| Identifying Right Triangle Sides by Name | |
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| Trigonometric Functions: Ratio Method | |
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| Customary and Metric Units of Angular Measure | |
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| Determining Functions of Given Angles and Determining Angles of Given Functions | |
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| Unit Exercise and Problem Review | |
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| Trigonometric Functions with Right Triangles | |
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| Variation of Functions | |
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| Functions of Complementary Angles | |
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| Determining an Unknown Angle When Two Sides of a Right Triangle Are Known | |
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| Determining an Unknown Angle When an Acute Angle an One Side of a Right Triangle Are Known | |
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| Unit Exercise and Problem Review | |
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| Practical Applications with Right Triangles | |
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| Solving Problems Stated in Word Form | |
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| Solving Problems Given in Picture Form that Require Auxiliary Lines | |
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| Solving Complex Problems that Require Auxiliary Lines | |
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| Unit Exercise and Problem Review | |
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| Functions of Any Angle, Oblique Triangles | |
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| Cartesian (Rectangular) Coordinate System | |
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| Determining Functions of Angles in Any Quadrant | |
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| Alternating Current Applications | |
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| Determining Functions of Angles Greater Than 360[degree] | |
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| Instantaneous Voltage Related to Time Application | |
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| Solving Oblique Triangles | |
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| Law of Sines | |
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| Solving Problems Given Two Angles and a Side, Using the Law of Sines | |
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| Solving Problems Given Two Sides and an Angle Opposite One of the Given Sides, Using the Law of Sines | |
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| Law of Cosines (Given Two Sides and the Included Angle) | |
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| Solving Problems Given Two Sides and the Included Angle, Using the Law of Cosines | |
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| Law of Cosines (Given Three Sides) | |
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| Solving Problems Given Three Sides, Using the Law of Cosines | |
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| Practical Applications of Oblique Triangles | |
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| Unit Exercise and Problem Review | |
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| Vectors | |
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| Scalar and Vector Quantities | |
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| Description and Naming Vectors | |
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| Vector Ordered Pair Notation | |
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| Vector Length and Angle Notation | |
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| Adding Vectors | |
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| Graphic Addition of Vectors | |
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| Addition of Vectors Using Trigonometry | |
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| General (Component Vector) Procedure for Vectors Using Trigonometry | |
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| Unit Exercise and Problem Review | |
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| United States Customary and Metric Units of Measure | |
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| Formulas for Areas (A) of Plane Figures | |
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| Formulas for Volumes and Areas of Solid Figures | |
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| Answers to Odd-Numbered Exercises | |
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| Index | |