Preface 

xvii  

SECTION I Fundamentals of General Mathematics 


1  (196) 


2  (31) 


2  (1) 


3  (1) 

Estimating (Approximating) 


4  (1) 

Addition of Whole Numbers 


5  (2) 

Subtraction of Whole Numbers 


7  (1) 

Problem SolvingWord Problem Practical Applications 


8  (1) 

Adding and Subtracting Whole Numbers in Practical Applications 


9  (2) 

Multiplication of Whole Numbers 


11  (4) 

Division of Whole Numbers 


15  (3) 

Multiplying and Dividing Whole Numbers in Practical Applications 


18  (2) 

Combined Operations of Whole Numbers 


20  (2) 

Combined Operations of Whole Numbers in Practical Applications 


22  (7) 

Unit Exercise and Problem Review 


25  (4) 

Computing with a Calculator: Whole Numbers 


29  (4) 


33  (48) 


33  (1) 


34  (1) 

A Fraction as an Indicated Division 


35  (1) 


35  (1) 

Expressing Fractions in Lowest Terms 


36  (1) 

Expressing Mixed Numbers as Improper Fractions 


36  (1) 

Expressing Improper Fractions as Mixed Numbers 


37  (1) 

Division of Whole Numbers; Quotients as Mixed Numbers 


38  (1) 

Use of Common Fractions in Practical Applications 


38  (2) 

Addition of Common Fractions 


40  (5) 

Subtraction of Common Fractions 


45  (3) 

Adding and Subtracting Common Fractions in Practical Applications 


48  (4) 

Multiplication of Common Fractions 


52  (4) 

Multiplying Common Fractions in Practical Applications 


56  (3) 

Division of Common Fractions 


59  (3) 

Dividing Common Fractions in Practical Applications 


62  (3) 

Combined Operations with Common Fractions 


65  (2) 

Combined Operations of Common Fractions in Practical Applications 


67  (7) 

Unit Exercise and Problem Review 


69  (5) 

Computing with a Calculator: Fractions and Mixed Numbers 


74  (7) 


81  (50) 

Meaning of Fractional Parts 


82  (1) 

Reading Decimal Fractions 


82  (1) 

Simplified Method of Reading Decimal Fractions 


83  (1) 

Writing Decimal Fractions 


83  (1) 

Rounding Decimal Fractions 


84  (1) 

Expressing Common Fractions as Decimal Fractions 


84  (1) 

Expressing Decimal Fractions as Common Fractions 


85  (1) 

Expressing Decimal Fractions in Practical Applications 


86  (2) 


88  (1) 

Subtracting Decimal Fractions 


88  (1) 

Adding and Subtracting Decimal Fractions in Practical Applications 


89  (3) 

Multiplying Decimal Fractions 


92  (3) 

Multiplying Decimal Fractions in Practical Applications 


95  (2) 

Dividing Decimal Fractions 


97  (3) 

Dividing Decimal Fractions in Practical Applications 


100  (3) 

Powers and Roots of Decimal Fractions 


103  (3) 

Decimal Fraction Powers and Roots in Practical Applications 


106  (3) 

Table of Decimal Equivalents 


109  (3) 

Combined Operations of Decimal Fractions 


112  (2) 

Combined Operations of Decimal Fractions in Practical Applications 


114  (11) 

Unit Exercise and Problem Review 


118  (7) 

Computing with a Calculator: Decimals 


125  (6) 


131  (15) 


131  (1) 


132  (2) 

Description of Proportions 


134  (3) 


137  (2) 


139  (7) 

Unit Exercise and Problem Review 


142  (4) 


146  (18) 


146  (1) 

Expressing Decimal Fractions as Percents 


147  (1) 

Expressing Common Fractions and Mixed Numbers as Percents 


147  (1) 

Expressing Percents as Decimal Fractions 


148  (1) 

Expressing Percents as Common Fractions 


149  (1) 

Types of Simple Percent Problems 


149  (3) 

Finding Percentage in Practical Applications 


152  (2) 

Finding Percent (Rate) in Practical Applications 


154  (2) 

Finding the Base in Practical Applications 


156  (1) 

More Complex Percentage Practical Applications 


157  (7) 

Unit Exercise and Problem Review 


160  (4) 


164  (33) 

Meaning of Signed Numbers 


164  (2) 


166  (1) 

Operations Using Signed Numbers 


167  (1) 


167  (1) 

Addition of Signed Numbers 


168  (3) 

Subtraction of Signed Numbers 


171  (1) 

Multiplication of Signed Numbers 


172  (2) 

Division of Signed Numbers 


174  (1) 


175  (2) 


177  (3) 

Combined Operations of Signed Numbers 


180  (2) 


182  (6) 


188  (9) 

Unit Exercise and Problem Review 


191  (6) 


197  (96) 

Precision, Accuracy, and Tolerance 


198  (16) 

Exact and Approximate (Measurement) Numbers 


198  (1) 

Degree of Precision of Measuring Instruments 


199  (1) 

Common Linear Measuring Instruments 


199  (1) 

Degree of Precision of a Measurement Number 


200  (1) 

Degrees of Precision in Adding and Subtracting Measurement Numbers 


201  (1) 


202  (1) 


203  (1) 

Accuracy in Multiplying and Dividing Measurement Numbers 


204  (1) 

Absolute and Relative Error 


204  (1) 


205  (2) 

Unilateral and Bilateral Tolerance with Clearance and Interference Fits 


207  (7) 

Unit Exercise and Problem Review 


209  (5) 

Customary Measurement Units 


214  (26) 


214  (1) 

Expressing Equivalent Units of Measure 


215  (3) 

Arithmetic Operations with Compound Numbers 


218  (4) 

Customary Linear Measure Practical Applications 


222  (3) 

Customary Units of Surface Measure (Area) 


225  (2) 

Customary Area Measure Practical Applications 


227  (1) 

Customary Units of Volume (Cubic Measure) 


228  (1) 

Customary Volume Practical Applications 


229  (1) 

Customary Units of Capacity 


230  (1) 

Customary Capacity Practical Applications 


231  (1) 

Customary Units of Weight (Mass) 


232  (1) 

Customary Weight Practical Applications 


233  (1) 


233  (2) 

Compound Units Practical Applications 


235  (5) 

Unit Exercise and Problem Review 


237  (3) 


240  (28) 

Metric Units of Linear Measure 


240  (2) 

Expressing Equivalent Units within the Metric System 


242  (2) 

Arithmetic Operations with Metric Lengths 


244  (1) 

Metric Linear Measure Practical Applications 


244  (2) 

Metric Units of Surface Measure (Area) 


246  (1) 

Arithmetic Operations with Metric Area Units 


247  (1) 

Metric Area Measure Practical Applications 


248  (1) 

Metric Units of Volume (Cubic Measure) 


248  (2) 

Arithmetic Operations with Metric Volume Units 


250  (1) 

Metric Volume Practical Applications 


250  (1) 


251  (1) 

Metric Capacity Practical Applications 


252  (1) 

Metric Units of Weight (Mass) 


253  (1) 

Metric Weight Practical Applications 


254  (1) 


254  (2) 

Compound Units Practical Applications 


256  (1) 

Metric Prefixes Applied to Very Large and Very Small Numbers 


257  (4) 

Conversion Between Metric and Customary Systems 


261  (7) 

Unit Exercise and Problem Review 


264  (4) 

Steel Rules and Vernier Calipers 


268  (13) 


268  (1) 

Reading Fractional Measurements 


268  (2) 

Measurements that Do Not Fall on Rule Graduations 


270  (1) 

Reading DecimalInch Measurements 


271  (1) 

Reading Metric Measurements 


272  (1) 

Vernier Calipers: Types and Description 


273  (2) 

Reading Measurements on a Customary Vernier Caliper 


275  (2) 

Reading Measurements on a Metric Vernier Caliper 


277  (4) 

Unit Exercise and Problem Review 


279  (2) 


281  (12) 

Description of a Customary Outside Micrometer 


281  (1) 

Reading a Customary Micrometer 


282  (1) 

The Customary Vernier Micrometer 


283  (1) 

Reading a Customary Vernier Micrometer 


284  (2) 

Description of a Metric Micrometer 


286  (1) 

Reading a Metric Micrometer 


286  (1) 

The Metric Vernier Micrometer 


287  (1) 

Reading a Metric Vernier Micrometer 


288  (5) 

Unit Exercise and Problem Review 


290  (3) 

SECTION III Fundamentals of Algebra 


293  (130) 


294  (11) 


294  (1) 


294  (3) 

Evaluation of Algebraic Expressions 


297  (8) 

Unit Exercise and Problem Review 


302  (3) 

Basic Algebraic Operations 


305  (31) 


305  (1) 


306  (2) 


308  (3) 


311  (3) 


314  (4) 


318  (3) 


321  (3) 


324  (1) 


325  (1) 

Basic Structure of the Binary Numeration System 


326  (10) 

Unit Exercise and Problem Review 


330  (6) 


336  (23) 


336  (1) 

Writing Equations from Word Statements 


337  (2) 


339  (2) 


341  (1) 

Solution of Equations by the Subtraction Principle of Equality 


341  (3) 

Solution of Equations by the Addition Principle of Equality 


344  (3) 

Solution of Equations by the Division Principle of Equality 


347  (2) 

Solution of Equations by the Multiplication Principle of Equality 


349  (3) 

Solution of Equations by the Root Principle of Equality 


352  (2) 

Solution of Equations by the Power Principle of Equality 


354  (5) 

Unit Exercise and Problem Review 


356  (3) 


359  (14) 

Equations Consisting of Combined Operations 


359  (4) 

Solving for the Unknown in Formulas 


363  (1) 

Substituting Values Directly in Given Formulas 


363  (3) 


366  (7) 

Unit Exercise and Problem Review 


370  (3) 

The Cartesian Coordinate System and Graphs of Linear Equations 


373  (12) 

Description of the Cartesian (Rectangular) Coordinate System 


373  (1) 

Graphing a Linear Equation 


374  (3) 

Slope of a Linear Equation 


377  (1) 

Slope Intercept Equation of a Straight Line 


378  (1) 

PointSlope Equation of a Straight Line 


378  (1) 

Determining an Equation, Given Two Points 


379  (1) 

Describing a Straight Line 


380  (5) 

Unit Exercise and Problem Review 


383  (2) 


385  (18) 

Graphical Method of Solving Systems of Equations 


385  (2) 

Substitution Method of Solving Systems of Equations 


387  (1) 

Addition or Subtraction Method of Solving Systems of Equations 


388  (4) 

Types of Systems of Equations 


392  (1) 


393  (1) 


394  (1) 

Writing and Solving Systems of Equations from Word Statements, Number Problems, and Practical Applications 


395  (8) 

Unit Exercise and Problem Review 


401  (2) 


403  (20) 

General or Standard Form of Quadratic Equations 


403  (1) 

Incomplete Quadratic Equations (αx2 = c) 


404  (4) 

Complete Quadratic Equations 


408  (3) 

Practical Applications of Complete Quadratic Equations, Equations Given 


411  (6) 

Word Problems Involving Complete Quadratic Equations. Equations Not Given 


417  (6) 

Unit Exercise and Problem Review 


421  (2) 

SECTION IV Fundamentals of Plane Geometry 


423  (118) 

Introduction to Plane Geometry 


424  (6) 


424  (1) 


425  (3) 


428  (2) 

Unit Exercise and Problem Review 


429  (1) 


430  (18) 


430  (1) 

Units of Angular Measure in Degrees, Minutes, and Seconds 


431  (1) 

Expressing Degrees, Minutes, and Seconds as Decimal Degrees 


432  (1) 

Expressing Decimal Degrees as Degrees, Minutes, and Seconds 


432  (3) 

Arithmetic Operations on Angular Measure in Degrees, Minutes, and Seconds 


435  (6) 

Simple Semicircular Protractor 


441  (4) 

Complements and Supplements of Scale Readings 


445  (3) 

Unit Exercise and Problem Review 


445  (3) 

Angular Geometric Principles 


448  (13) 


448  (1) 


448  (1) 

Angles Formed by a Transversal 


449  (2) 


451  (10) 

Unit Exercise and Problem Review 


458  (3) 


461  (16) 


462  (2) 


464  (4) 

Isosceles and Equilateral Triangles 


468  (1) 

Isosceles Triangle Practical Applications 


468  (1) 

Equilateral Triangle Practical Applications 


469  (1) 


470  (1) 

Pythagorean Theorem Practical Applications 


470  (7) 

Unit Exercise and Problem Review 


473  (4) 

Congruent and Similar Figures 


477  (14) 


477  (2) 


479  (3) 

Practical Applications of Similar Triangles 


482  (9) 

Unit Exercise and Problem Review 


488  (3) 


491  (14) 


491  (2) 


493  (2) 

Polygon Interior and Exterior Angles 


495  (1) 

Practical Applications of Polygon Interior and Exterior Angles 


495  (5) 

Practical Applications of Trapezoid Median 


500  (5) 

Unit Exercise and Problem Review 


502  (3) 


505  (36) 


505  (2) 


507  (1) 


508  (2) 


510  (2) 


512  (1) 

Chords, Arcs, and Central Angles 


513  (2) 

Practical Applications of Circle Chord Bisector 


515  (3) 

Circle Tangents and Chord Segments 


518  (1) 

Practical Applications of Circle Tangent 


518  (1) 

Practical Applications of Tangents from a Common Point 


519  (3) 

Angles Formed Inside and on a Circle 


522  (1) 

Practical Applications of Inscribed Angles 


523  (1) 

Practical Applications of Tangent and Chord 


524  (2) 


526  (2) 

Internally and Externally Tangent Circles 


528  (1) 

Practical Applications of Internally Tangent Circles 


529  (1) 

Practical Applications of Externally Tangent Circles 


530  (11) 

Unit Exercise and Problem Review 


534  (7) 

SECTION V Geometric Figures: Areas and Volumes 


541  (76) 


542  (22) 


542  (4) 


546  (4) 


550  (3) 

Areas of Triangles Given the Base and Height 


553  (2) 

Areas of Triangles Given Three Sides 


555  (9) 

Unit Exercise and Problem Review 


559  (5) 

Areas of Circles, Sectors, Segments, and Ellipses 


564  (14) 


564  (1) 


565  (3) 


568  (2) 


570  (2) 


572  (6) 

Unit Exercise and Problem Review 


574  (4) 

Prisms and Cylinders: Volumes, Surface Areas, and Weights 


578  (13) 


578  (1) 


578  (4) 


582  (1) 


582  (2) 

Computing Heights and Bases of Prisms and Cylinders 


584  (2) 

Lateral Areas and Surface Areas of Right Prisms and Cylinders 


586  (5) 

Unit Exercise and Problem Review 


589  (2) 

Pyramids and Cones: Volumes, Surface Areas, and Weights 


591  (16) 


591  (1) 


592  (1) 

Volumes of Regular Pyramids and Right Circular Cones 


592  (2) 

Computing Heights and Bases of Regular Pyramids and Right Circular Cones 


594  (1) 

Lateral Areas and Surface Areas of Regular Pyramids and Right Circular Cones 


595  (3) 

Frustums of Pyramids and Cones 


598  (1) 

Volumes of Frustums of Regular Pyramids and Right Circular Cones 


599  (2) 

Lateral Areas and Surface Areas of Frustums of Regular Pyramids and Right Circular Cones 


601  (6) 

Unit Exercise and Problem Review 


605  (2) 

Spheres and Composite Figures: Volumes, Surface Areas, and Weights 


607  (10) 


607  (1) 


608  (1) 


608  (2) 

Volumes and Surface Areas of Composite Solid Figures 


610  (7) 

Unit Exercise and Problem Review 


615  (2) 

SECTION VI Basic Statistics 


617  (70) 

Graphs: Bar, Circle, and Line 


618  (39) 

Types and Structure of Graphs 


618  (1) 


619  (5) 


624  (2) 

Drawing Bar Graphs with a Spreadsheet 


626  (5) 


631  (4) 

Drawing Circle Graphs with a Spreadsheet 


635  (2) 


637  (1) 


638  (2) 

Reading CombinedData Line Graphs 


640  (4) 


644  (1) 

Drawing BrokenLine Graphs 


644  (2) 

Drawing BrokenLine Graphs with a Spreadsheet 


646  (2) 

Drawing StraightLine Graphs 


648  (1) 

Drawing CurvedLine Graphs 


649  (8) 

Unit Exercise and Problem Review 


653  (4) 


657  (30) 


657  (2) 


659  (2) 


661  (2) 

Other Average Measurements 


663  (1) 

Quartiles and Percentiles 


664  (3) 


667  (5) 

Variance and Standard Deviation 


672  (5) 

Statistical Process Control: XBar Charts 


677  (4) 

Statistical Process Control: RCharts 


681  (6) 

Unit Exercise and Problem Review 


685  (2) 

SECTION VII Fundamentals of Trigonometry 


687  (109) 

Introduction to Trigonometric Functions 


688  (11) 

Ratio of Right Triangle Sides 


688  (1) 

Identifying Right Triangle Sides by Name 


689  (1) 

Trigonometric Functions: Ratio Method 


690  (2) 

Customary and Metric Units of Angular Measure 


692  (1) 

Determining Functions of Given Angles and Determining Angles of Given Functions 


692  (7) 

Unit Exercise and Problem Review 


696  (3) 

Trigonometric Functions with Right Triangles 


699  (12) 


699  (2) 

Functions of Complementary Angles 


701  (2) 

Determining an Unknown Angle When Two Sides of a Right Triangle Are Known 


703  (2) 

Determining an Unknown Angle When an Acute Angle an One Side of a Right Triangle Are Known 


705  (6) 

Unit Exercise and Problem Review 


709  (2) 

Practical Applications with Right Triangles 


711  (28) 

Solving Problems Stated in Word Form 


711  (5) 

Solving Problems Given in Picture Form that Require Auxiliary Lines 


716  (9) 

Solving Complex Problems that Require Auxiliary Lines 


725  (14) 

Unit Exercise and Problem Review 


734  (5) 

Functions of Any Angle, Oblique Triangles 


739  (35) 

Cartesian (Rectangular) Coordinate System 


739  (1) 

Determining Functions of Angles in Any Quadrant 


740  (3) 

Alternating Current Applications 


743  (3) 

Determining Functions of Angles Greater Than 360° 


746  (1) 

Instantaneous Voltage Related to Time Application 


747  (1) 

Solving Oblique Triangles 


748  (1) 


748  (1) 

Solving Problems Given Two Angles and a Side, Using the Law of Sines 


749  (2) 

Solving Problems Given Two Sides and an Angle Opposite One of the Given Sides, Using the Law of Sines 


751  (4) 

Law of Cosines (Given Two Sides and the Included Angle) 


755  (1) 

Solving Problems Given Two Sides and the Included Angle, Using the Law of Cosines 


755  (3) 

Law of Cosines (Given Three Sides) 


758  (1) 

Solving Problems Given Three Sides, Using the Law of Cosines 


759  (3) 

Practical Applications of Oblique Triangles 


762  (7) 

Unit Exercise and Problem Review 


769  (5) 


774  (22) 

Scalar and Vector Quantities 


774  (1) 

Description and Naming Vectors 


774  (1) 

Vector Ordered Pair Notation 


775  (1) 

Vector Length and Angle Notation 


776  (1) 


776  (2) 

Graphic Addition of Vectors 


778  (4) 

Addition of Vectors Using Trigonometry 


782  (6) 

General (Component Vector) Procedure for Vectors Using Trigonometry 


788  (8) 

Unit Exercise and Problem Review 


793  (3) 
Appendix A United States Customary and Metric Units of Measure 

796  (2) 
Appendix B Formulas for Areas (A) of Plane Figures 

798  (1) 
Appendix C Formulas for Volumes and Areas of Solid Figures 

799  (1) 
Appendix D Answers to OddNumbered Exercises 

800  (45) 
Index 

845  