Preface 

xv  
SECTION I Fundamentals of General Mathematics 

1  (164) 


2  (29) 


2  (1) 


3  (1) 

Estimating (Approximating) 


4  (1) 

Addition of Whole Numbers 


5  (1) 

Subtraction of Whole Numbers 


6  (2) 

Problem SolvingWord Problem Practical Applications 


8  (1) 

Adding and Subtracting Whole Numbers in Practical Applications 


8  (2) 

Multiplication of Whole Numbers 


10  (3) 

Division of Whole Numbers 


13  (3) 

Multiplying and Dividing Whole Numbers in Practical Applications 


16  (3) 

Combined Operations of Whole Numbers 


19  (1) 

Combined Operations of Whole Numbers in Practical Applications 


20  (7) 

Unit Exercise and Problem Review 


23  (4) 

Computing with a Calculator: Whole Numbers 


27  (4) 


31  (46) 


31  (1) 


32  (1) 

A Fraction as an Indicated Division 


33  (1) 


33  (1) 

Expressing Fractions in Lowest Terms 


33  (1) 

Expressing Mixed Numbers as Improper Fractions 


34  (1) 

Expressing Improper Fractions as Mixed Numbers 


35  (1) 

Use of Common Fractions in Practical Applications 


36  (2) 

Addition of Common Fractions 


38  (4) 

Subtraction of Common Fractions 


42  (3) 

Adding and Subtracting Common Fractions in Practical Applications 


45  (4) 

Multiplication of Common Fractions 


49  (4) 

Multiplying Common Fractions in Practical Applications 


53  (3) 

Division of Common Fractions 


56  (3) 

Dividing Common Fractions in Practical Applications 


59  (2) 

Combined Operations With Common Fractions 


61  (2) 

Combined Operations of Common Fractions in Practical Applications 


63  (8) 

Unit Exercise and Problem Review 


66  (5) 

Computing with a Calculator: Fractions and Mixed Numbers 


71  (6) 


77  (48) 

Meaning of Fractional Parts 


78  (1) 

Reading Decimal Fractions 


78  (1) 

Simplified Method of Reading Decimal Fractions 


79  (1) 

Writing Decimal Fractions 


79  (1) 

Rounding Decimal Fractions 


80  (1) 

Expressing Common Fractions as Decimal Fractions 


80  (1) 

Expressing Decimal Fractions as Common Fractions 


81  (1) 

Decimal Fractions in Practical Applications 


82  (1) 


83  (1) 

Subtracting Decimal Fractions 


84  (1) 

Adding and Subtracting Decimal Fractions in Practical Applications 


85  (3) 

Multiplying Decimal Fractions 


88  (2) 

Multiplying Decimal Fractions in Practical Applications 


90  (3) 

Dividing Decimal Fractions 


93  (2) 

Dividing Decimal Fractions in Practical Applications 


95  (3) 

Powers and Roots of Decimal Fractions 


98  (3) 

Decimal Fraction Powers and Roots in Practical Applications 


101  (4) 

Table of Decimal Equivalents 


105  (2) 

Combined Operations of Decimal Fractions 


107  (2) 

Combined Operations of Decimal Fractions in Practical Applications 


109  (10) 

Unit Exercise and Problem Review 


112  (7) 

Computing with a Calculator: Decimals 


119  (6) 


125  (16) 


125  (1) 

Expressing Decimal Fractions as Percents 


126  (1) 

Expressing Common Fractions and Mixed Numbers as Percents 


126  (1) 

Expressing Percents as Decimal Fractions 


127  (1) 

Expressing Percents as Common Fractions 


128  (1) 

Types of Simple Percentage Problems 


128  (2) 

Finding Percentage in Practical Applications 


130  (2) 

Finding Percent (Rate) in Practical Applications 


132  (2) 

Finding the Base in Practical Applications 


134  (1) 

More Complex Percentage Practical Applications 


135  (6) 

Unit Exercise and Problem Review 


138  (3) 


141  (24) 

Types and Structure of Graphs 


141  (1) 


142  (4) 


146  (2) 


148  (1) 


149  (1) 

Reading CombinedData Line Graphs 


150  (5) 


155  (1) 

Drawing BrokenLine Graphs 


155  (2) 

Drawing StraightLine Graphs 


157  (1) 

Drawing CurvedLine Graphs 


158  (7) 

Unit Exercise and Problem Review 


160  (5) 
SECTION II Measurement 

165  (82) 

Precision, Accuracy, and Tolerance 


166  (16) 

Exact and Approximate (Measurement) Numbers 


166  (1) 

Degree of Precision of Measuring Instruments 


167  (1) 

Common Linear Measuring Instruments 


167  (1) 

Degree of Precision of a Measurement Number 


168  (1) 

Degrees of Precision in Adding and Subtracting Measurement Numbers 


169  (1) 


170  (1) 


171  (1) 

Accuracy in Multiplying and Dividing Measurement Numbers 


171  (1) 

Absolute and Relative Error 


172  (1) 


173  (1) 

Unilateral and Bilateral Tolerance with Clearance and Interference Fits 


174  (8) 

Unit Exercise and Problem Review 


177  (5) 


182  (40) 


183  (1) 

Expressing Equivalent Units of Measure 


183  (3) 

Arithmetic Operations with Compound Numbers 


186  (4) 

Customary Linear Measure Practical Applications 


190  (3) 

Metric Units of Linear Measure 


193  (1) 

Expressing Equivalent Units within the Metric System 


194  (2) 

Arithmetic Operations with Metric Lengths 


196  (1) 

Metric Linear Measure Practical Applications 


196  (2) 

Customary Units of Surface Measure (Area) 


198  (1) 

Customary Area Measure Practical Applications 


199  (1) 

Metric Units of Surface Measure (Area) 


200  (2) 

Arithmetic Operations with Metric Area Units 


202  (1) 

Metric Area Measure Practical Applications 


202  (1) 

Customary Units of Volume (Cubic Measure) 


203  (1) 

Customary Volume Practical Applications 


204  (1) 

Metric Units of Volume (Cubic Measure) 


205  (2) 

Arithmetic Operations with Metric Volume Units 


207  (1) 

Metric Volume Practical Applications 


207  (1) 

Customary and Metric Units of Capacity 


208  (1) 

Customary and Metric Capacity Practical Applications 


209  (1) 

Customary and Metric Units of Weight (Mass) 


210  (2) 

Customary and Metric Weight Practical Applications 


212  (1) 


212  (2) 

Compound Units Practical Applications 


214  (8) 

Unit Exercise and Problem Review 


216  (6) 

Steel Rules and Vernier Calipers 


222  (13) 


222  (1) 

Reading Fractional Measurements 


222  (2) 

Measurements that do not Fall on Rule Graduations 


224  (1) 

Reading DecimalInch Measurements 


225  (1) 

Reading Metric Measurements 


226  (1) 

Vernier Calipers: Types and Description 


227  (2) 

Reading Measurements on a Customary Vernier Caliper 


229  (2) 

Reading Measurements on a Metric Vernier Caliper 


231  (4) 

Unit Exercise and Problem Review 


233  (2) 


235  (12) 

Description of a Customary Outside Micrometer 


235  (1) 

Reading a Customary Micrometer 


236  (1) 

The Customary Vernier Micrometer 


237  (1) 

Reading a Customary Vernier Micrometer 


238  (2) 

Description of a Metric Micrometer 


240  (1) 

Reading a Metric Micrometer 


240  (1) 

The Metric Vernier Micrometer 


241  (1) 

Reading a Metric Vernier Micrometer 


242  (5) 

Unit Exercise and Problem Review 


244  (3) 
SECTION III Fundamentals of Algebra 

247  (168) 


248  (11) 


248  (1) 


248  (3) 

Evaluation of Algebraic Expressions 


251  (8) 

Unit Exercise and Problem Review 


256  (3) 


259  (21) 

Meaning of Signed Numbers 


259  (1) 


260  (2) 

Operations Using Signed Numbers 


262  (1) 


262  (1) 

Addition of Signed Numbers 


263  (3) 

Subtraction of Signed Numbers 


266  (1) 

Multiplication of Signed Numbers 


267  (1) 

Division of Signed Numbers 


268  (1) 


269  (3) 


272  (2) 

Combined Operations of Signed Numbers 


274  (6) 

Unit Exercise and Problem Review 


276  (4) 

Basic Algebraic Operations 


280  (39) 


280  (1) 


281  (2) 


283  (3) 


286  (3) 


289  (4) 


293  (2) 


295  (3) 


298  (1) 


298  (2) 


300  (5) 

Metric Prefixes Applied to Very Large and Very Small Numbers 


305  (3) 

Basic Structure of the Binary Numeration System 


308  (11) 

Unit Exercise and Problem Review 


312  (7) 


319  (23) 


319  (1) 

Writing Equations from Word Statements 


320  (2) 


322  (2) 


324  (1) 

Solution of Equations by the Subtraction Principle of Equality 


324  (3) 

Solution of Equations by the Addition Principle of Equality 


327  (3) 

Solution of Equations by the Division Principle of Equality 


330  (2) 

Solution of Equations by the Multiplication Principle of Equality 


332  (3) 

Solution of Equations by the Root Principle of Equality 


335  (2) 

Solution of Equations by the Power Principle of Equality 


337  (5) 

Unit Exercise and Problem Review 


339  (3) 


342  (14) 

Equations Consisting of Combined Operations 


342  (4) 

Solving for the Unknown in Formulas 


346  (1) 

Substituting Values Directly in Given Formulas 


346  (3) 


349  (7) 

Unit Exercise and Problem Review 


353  (3) 


356  (16) 


356  (1) 


357  (2) 

Description of Proportions 


359  (4) 


363  (2) 


365  (7) 

Unit Exercise and Problem Review 


368  (4) 

The Cartesian Coordinate System and Graphs of Linear Equations 


372  (9) 

Description of the Cartesian (Rectangular) Coordinate System 


372  (1) 

Graphing a Linear Equation 


373  (2) 

Slope of a Linear Equation 


375  (1) 

Slope Intercept Equation of a Straight Line 


376  (1) 

Determining an Equation, Given Two Points 


377  (1) 

Describing a Straight Line 


378  (3) 

Unit Exercise and Problem Review 


379  (2) 


381  (16) 

Graphical Method of Solving Systems of Equations 


381  (2) 

Substitution Method of Solving Systems of Equations 


383  (1) 

Addition or Subtraction Method of Solving Systems of Equations 


384  (4) 

Types of Systems of Equations 


388  (1) 

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


389  (8) 

Unit Exercise and Problem Review 


395  (2) 


397  (18) 

General or Standard Form of Quadratic Equations 


397  (1) 

Incomplete Quadratic Equations 


398  (4) 

Complete Quadratic Equations 


402  (2) 

Practical Applications of Complete Quadratic Equations 


404  (5) 

Word Problems Involving Complete Quadratic Equations. Equations Not Given 


409  (6) 

Unit Exercise and Problem Review 


413  (2) 
SECTION IV Fundamentals of Plane Geometry 

415  (120) 

Introduction to Plane Geometry 


416  (6) 


416  (1) 


417  (3) 


420  (2) 


421  (1) 


422  (20) 


422  (1) 

Units of Angular Measure in Degrees, Minutes, and Seconds 


423  (1) 

Expressing Degrees, Minutes, and Seconds as Decimal Degrees 


424  (1) 

Expressing Decimal Degrees as Degrees, Minutes, and Seconds 


424  (2) 

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


426  (8) 

Simple Semicircular Protractor 


434  (1) 


435  (3) 

Complements and Supplements of Scale Readings 


438  (4) 

Unit Exercise and Problem Review 


439  (3) 

Angular Geometric Principles 


442  (13) 


442  (1) 


442  (1) 

Angles Formed by a Transversal 


443  (2) 


445  (10) 

Unit Exercise and Problem Review 


452  (3) 


455  (16) 


456  (2) 


458  (4) 

Isosceles and Equilateral Triangles 


462  (1) 

Isosceles Triangle Practical Application 


462  (1) 

Equilateral Triangle Practical Application 


463  (1) 


464  (1) 

Pythagorean Theorem Practical Applications 


464  (7) 

Unit Exercise and Problem Review 


467  (4) 

Congruent and Similar Figures 


471  (14) 


471  (2) 


473  (3) 

Similar Triangles Practical Applications 


476  (9) 

Unit Exercise and Problem Review 


481  (4) 


485  (14) 


485  (2) 


487  (2) 

Polygon Interior and Exterior Angles 


489  (1) 

Polygon Interior and Exterior Angles Practical Applications 


489  (5) 

Trapezoid Median Practical Applications 


494  (5) 

Unit Exercise and Problem Review 


496  (3) 


499  (36) 


499  (2) 


501  (1) 


502  (2) 


504  (2) 


506  (1) 

Chords, Arcs, and Central Angles 


507  (1) 

Circle Chord Bisector Practical Application 


508  (3) 

Circle Tangents and Chord Segments 


511  (1) 

Circle Tangent Practical Application 


512  (1) 

Tangents From a Common Point Practical Application 


513  (3) 

Angles Formed Inside and on a Circle 


516  (1) 

Inscribed Angles Practical Application 


516  (1) 

Tangent and Chord Practical Application 


517  (3) 


520  (1) 

Internally and Externally Tangent Circles 


521  (1) 

Internally Tangent Circles Practical Application 


522  (2) 

Externally Tangent Circles Practical Application 


524  (11) 

Unit Exercise and Problem Review 


528  (7) 
SECTION V Geometric Figures: Areas and Volumes 

535  (76) 


536  (22) 


536  (3) 


539  (4) 


543  (4) 

Areas of Triangles Given the Base and Height 


547  (2) 

Areas of Triangles Given Three Sides 


549  (9) 

Unit Exercise and Problem Review 


553  (5) 

Areas of Circles, Sectors, Segments, and Ellipses 


558  (14) 


558  (1) 


559  (3) 


562  (2) 


564  (2) 


566  (6) 

Unit Exercise and Problem Review 


568  (4) 

Prisms and Cylinders: Volumes, Surface Areas, and Weights 


572  (13) 


572  (1) 


572  (3) 


575  (1) 


576  (2) 

Computing Heights and Bases of Prisms and Cylinders 


578  (2) 

Lateral Areas and Surface Areas of Right Prisms and Cylinders 


580  (5) 

Unit Exercise and Problem Review 


583  (2) 

Pyramids and Cones: Volumes, Surface Areas, and Weights 


585  (16) 


585  (1) 


586  (1) 

Volumes of Regular Pyramids and Right Circular Cones 


586  (2) 

Computing Heights and Bases of Regular Pyramids and Right Circular Cones 


588  (1) 

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


589  (3) 

Frustums of Pyramids and Cones 


592  (1) 

Volumes of Frustums of Regular Pyramids and Right Circular Cones 


593  (2) 

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


595  (6) 

Unit Exercise and Problem Review 


599  (2) 

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


601  (10) 


601  (1) 


602  (1) 


602  (2) 

Volumes and Surface Areas of Composite Solid Figures 


604  (7) 

Unit Exercise and Problem Review 


609  (2) 
SECTION VI Fundamentals of Trigonometry 

611  (108) 

Introduction to Trigonometric Functions 


612  (10) 

Ratio of Right Triangle Sides 


612  (1) 

Identifying Right Triangle Sides by Name 


613  (1) 

Trigonometric Functions: Ratio Method 


614  (2) 

Customary and Metric Units of Angular Measure 


616  (1) 

Determining Functions of Given Angles and Determining Angles of Given Functions 


616  (6) 

Unit Exercise and Problem Review 


620  (2) 

Trigonometric Functions with Right Triangles 


622  (12) 


622  (2) 

Functions of Complementary Angles 


624  (2) 

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


626  (2) 

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


628  (6) 

Unit Exercise and Problem Review 


632  (2) 

Practical Applications with Right Triangles 


634  (28) 

Solving Problems Stated in Word Form 


634  (5) 

Solving Problems Given in Picture Form that Require Auxiliary Lines 


639  (9) 

Solving Complex Problems that Require Auxiliary Lines 


648  (14) 

Unit Exercise and Problem Review 


657  (5) 

Functions of Any Angle, Oblique Triangles 


662  (35) 

Cartesian (Rectangular) Coordinate System 


662  (1) 

Determining Functions of Angles in Any Quadrant 


663  (3) 

Alternating Current Applications 


666  (3) 

Determining Functions of Angles Greater Than 360° 


669  (1) 

Instantaneous Voltage Related to Time Application 


670  (1) 

Solving Oblique Triangles 


671  (1) 


671  (1) 

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


672  (2) 

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


674  (4) 

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


678  (1) 

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


678  (3) 

Law of Cosines (Given Three Sides) 


681  (1) 

Solving Problems Given Three Sides, Using the Law of Cosines 


682  (3) 

Practical Applications of Oblique Trigonometry 


685  (12) 

Unit Exercise and Problem Review 


692  (5) 


697  (22) 

Scalar and Vector Quantities 


697  (1) 

Description and Naming Vectors 


697  (1) 

Vector Ordered Pair Notation 


698  (1) 

Vector Length and Angle Notation 


699  (1) 


699  (2) 

Graphic Addition of Vectors 


701  (4) 

Addition of Vectors Using Trigonometry 


705  (6) 

General (Component Vector) Procedure for Vectors Using Trigonometry 


711  (8) 

Unit Exercise and Problem Review 


716  (3) 
Appendix A United States Customary and Metric Units of Measure 

719  (2) 
Appendix B Formulas for Areas (A) of Plane Figures 

721  (1) 
Appendix C Formulas for Volumes and Areas of Solid Figures 

722  (1) 
Appendix D Answers to OddNumbered Exercises 

723  (32) 
Index 

755  