Advanced Mathematics

, by Saxon, John H., Jr.

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ISBN: 9781565770393 | 1565770390
Cover: Hardcover
Copyright: 6/1/1996

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Supplemental Materials

Preface

Geometry Review

(13)

More on Area

(12)

Cylinders and Prisms

Cones and Pyramids

Spheres

Pythagorean Theorem

(10)

Triangle Inequalities (1)

Similar Polygons

Similar Triangles

Construction

(7)

Exponents and Radicals

(6)

Complex Numbers

Areas of Similar Geometric Figures

Diagonals of Rectangular Solids

Fractional Equations

(5)

Radical Equations

Systems of Three Linear Equations

Inductive and Deductive Reasoning

(7)

Logic

The Contrapositive

Converse and Inverse

Statements of Similarity

(6)

Proportional Segments

Angle Bisectors and Side Ratios

Congruent Figures

(7)

Proof Outlines

Equation of a Line

(9)

Rational Denominators

Completing the Square

Circles

(7)

Properties of Circles

The Quadratic Formula

Angles and Diagonals in Polygons

(7)

Proof of the Chord-Tangent Theorem

Intersecting Secants

(11)

Intersecting Secants and Tangents

Products of Chord Segments

Products of Secant and Tangent Segments

Sine, Cosine, and Tangent

108

(7)

Angles of Elevation and Depression

Rectangular and Polar Coordinates

Coordinate Conversion

Assumptions

115

(7)

Proofs

Complex Fractions

122

(5)

Abstract Equations

Division of Polynomials

Proofs of the Pythagorean Theorem

127

(6)

Proofs of Similarity

Advanced Word Problems

133

(5)

Nonlinear Systems

138

(7)

Factoring Exponentials

Sum and Difference of Two Cubes

Two Special Triangles

145

(5)

Evaluating Functions

150

(10)

Domain and Range

Types of Functions

Tests for Functions

Absolute Value

160

(6)

Reciprocal Functions

The Exponential Function

166

(6)

Sketching Exponentials

Sums of Trigonometric Functions

172

(6)

Combining Functions

Age Problems

178

(5)

Rate Problems

The Logarithmic Form of the Exponential

183

(5)

Logarithmic Equations

Related Angles

188

(5)

Signs of Trigonometric Functions

Factorial Notation

193

(4)

Abstract Rate Problems

The Unit Circle

197

(8)

Very Large and Very Small Fractions

Quadrantal Angles

Addition of Vectors

205

(6)

Overlapping Triangles

Symmetry

211

(8)

Reflections

Translations

Inverse Functions

219

(14)

Four Quadrant Signs

Inverse Trigonometric Functions

Quadrilaterals

233

(9)

Properties of Parallelograms

Types of Parallelograms

Conditions for Parallelograms

Trapezoids

Summation Notation

242

(7)

Linear Regression

Decomposing Functions

Change in Coordinates

249

(7)

The Name of a Number

The Distance Formula

Angles Greater Than 360°

256

(6)

Sums of Trigonometric Functions

Boat-in-the-River Problems

The Line as a Locus

262

(7)

The Midpoint Formula

Fundamental Counting Principle and Permutations

269

(8)

Designated Roots

Overall Average Rate

Radian Measure of Angles

277

(9)

Forms of Linear Equations

The Argument in Mathematics

286

(7)

The Laws of Logarithms

Properties of Inverse Functions

Reciprocal Trigonometric Functions

293

(8)

Permutation Notation

Conic Sections

301

(7)

Circles

Constants in Exponential Functions

Periodic Functions

308

(7)

Graphs of Sin θ and Cos θ

Abstract Rate Problems

315

(4)

Conditional Permutations

319

(5)

Two-Variable Analysis Using a Graphing Calculator

Complex Roots

324

(4)

Factoring Over the Complex Numbers

Vertical Sinusoid Translations

328

(5)

Arctan

Powers of Trigonometric Functions

333

(5)

Perpendicular Bisectors

The Logarithmic Function

338

(4)

Development of the Rules for Logarithms

Trigonometric Equations

342

(4)

Common Logarithms and Natural Logarithms

346

(3)

The Inviolable Argument

349

(4)

Arguments in Trigonometric Equations

Review of Unit Multipliers

353

(5)

Angular Velocity

Parabolas

358

(5)

Circular Permutations

363

(4)

Distinguishable Permutations

Triangular Areas

367

(8)

Areas of Segments

Systems of Inequalities

Phase Shifts in Sinusoids

375

(6)

Period of a Sinusoid

Distance from a Point to a Line

381

(6)

``Narrow'' and ``Wide'' Parabolas

Advanced Logarithm Problems

387

(5)

The Color of the White House

Factorable Trigonometric Equations

392

(5)

Loss of Solutions Caused by Division

Single-Variable Analysis

397

(8)

The Normal Distribution

Box-and-Whisker Plots

Abstract Coefficients

405

(4)

Linear Variation

Circles and Completing the Square

409

(3)

The Complex Plane

412

(4)

Polar Form of a Complex Number

Sums and Products of Complex Numbers

Radicals in Trigonometric Equations

416

(6)

Graphs of Logarithmic Functions

Formulas for Systems of Equations

422

(4)

Phase Shifts and Period Changes

Antilogarithms

426

(4)

Locus Definition of a Parabola

430

(7)

Translated Parabolas

Applications

Derivation

Matrices

437

(4)

Determinants

Percentiles and z Scores

441

(4)

The Ellipse (1)

445

(5)

One Side Plus Two Other Parts

450

(5)

Law of Sines

Regular Polygons

455

(3)

Cramer's Rule

458

(3)

Combinations

461

(4)

Functions of (-x)

465

(7)

Functions of the Other Angle

Trigonometric Identities (1)

Rules of the Game

Binomial Expansions (1)

472

(3)

The Hyperbola

475

(5)

De Moivre's Theorem

480

(5)

Roots of Complex Numbers

Trigonometric Identities (2)

485

(4)

Law of Cosines

489

(6)

Taking the Logarithm of

495

(4)

Exponential Equations

Simple Probability

499

(5)

Independent Events

Replacement

Factorable Expressions

504

(4)

Sketching Sinusoids

Advanced Trigonometric Equations

508

(4)

Clock Problems

Arithmetic Progressions and Arithmetic Means

512

(4)

Sum and Difference Identities

516

(5)

Tangent Identities

Exponential Functions (Growth and Decay)

521

(5)

The Ellipse (2)

526

(5)

Double-Angle Identities

531

(4)

Half-Angle Identities

Geometric Progressions

535

(3)

Probability of Either

538

(4)

Notations for Permutations and Combinations

Advanced Trigonometric Identities

542

(4)

Triangle Inequalities (2)

Graphs of Secant and Cosecant

546

(5)

Graphs of Tangent and Cotangent

Advanced Complex Roots

551

(2)

More Double-Angle Identities

553

(4)

Triangle Area Formula

Proof of the Law of Sines

Equal Angles Imply Proportional Sides

The Ambiguous Case

557

(3)

Change of Base

560

(5)

Contrived Logarithm Problems

Sequence Notations

565

(5)

Advanced Sequence Problems

The Arithmetic and Geometric Means

Product Identities

570

(4)

More Sum and Difference Identities

Zero Determinants

574

(6)

3 x 3 Determinants

Determinant Solutions of 3 x 3 Systems

Independent Equations

Binomial Expansions (2)

580

(2)

Calculations with Logarithms

582

(4)

Power of the Hydrogen

Arithmetic Series

586

(4)

Geometric Series

Cofactors

590

(5)

Expansion by Cofactors

Translations of Conic Sections

595

(5)

Equations of the Ellipse

Equations of the Hyperbola

Convergent Geometric Series

600

(3)

Matrix Addition and Multiplication

603

(7)

Rational Numbers

610

(3)

Graphs of arcsine and arccosine

613

(5)

Graphs of arcsecant and arccosecant

Graphs of arctangent and arccotangent

Logarithmic Inequalities: Base Greater Than 1

618

(3)

Logarithmic Inequalities: Base Less Than 1

Binomial Theorem

621

(3)

Synthetic Division

624

(4)

Zeros and Roots

Graphs of Factored Polynomial Functions

628

(7)

The Remainder Theorem

635

(3)

The Region of Interest

638

(5)

Prime and Relatively Prime Numbers

643

(4)

Rational Roots Theorem

Roots of Polynomial Equations

647

(4)

Descartes' Rule of Signs

651

(5)

Upper and Lower Bound Theorem

Irrational Roots

Matrix Algebra

656

(6)

Finding Inverse Matrices

Piecewise Functions

662

(3)

Greatest Integer Function

Graphs of Rational Functions

665

(6)

Graphs that Contain Holes

The General Conic Equations

671

(4)

Point of Division Formulas

675

(4)

Using the Graphing Calculator to Graph

679

(6)

Solutions of Systems of Equations Using the Graphing Calculator

Roots

Appendix Proofs

685

(6)

Answers

691

(50)

Index

741

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Advanced Mathematics

Table of Contents

Supplemental Materials