The Dow's Schoolroom

Review of the Saxon Math Program

Preface

Lesson 1

Geometry Review

Lesson 2

More on Area

Cylinders and Prisms

Cones and Pyramids

Spheres

Lesson 3

Pythagorean Theorem

Triangle Inequalities (1)

Similar Polygons

Similar Triangles

Lesson 4

Construction

Lesson 5

Exponents and Radicals

Complex Numbers

Areas of Similar Geometric Figures

Diagonals of Rectangular Solids

Lesson 6

Fractional Equations

Radical Equations

Systems of Three Linear Equations

Lesson 7

Inductive and Deductive Reasoning

Logic

The Contrapositive

Converse and Inverse

Lesson 8

Statements of Similarity

Proportional Segments

Angle Bisectors and Side Ratios

Lesson 9

Congruent Figures

Proof Outlines

Lesson 10

Equation of a Line

Rational Denominators

Completing the Square

Lesson 11

Circles

Properties of Circles

The Quadratic Formula

Lesson 12

Angles and Diagonals in Polygons

Proof of the Chord-Tangent Theorem

Lesson 13

Intersecting Secants

Intersecting Secants and Tangents

Products of Chord Segments

Products of Secant and Tangent Segments

Lesson 1 4

Sine, Cosine, and Tangent

Angles of Elevation and Depression

Rectangular and Polar Coordinates

Coordinate Conversion

Lesson 15

Assumptions

Proofs

Lesson 16

Complex Fractions

Abstract Equations

Division of Polynomials

Lesson 17

Proofs of the Pythagorean Theorem

Proofs of Similarity

Lesson 18

Advanced Word Problems

Lesson 19

Nonlinear Systems

Factoring Exponentials

Sum and Difference of Two Cubes

Lesson 20

Two Special Triangles

Lesson 21

Evaluating Functions

Domain and Range

Types of Functions

Tests for Functions

Lesson 22

Absolute Value

Reciprocal Functions

Lesson 23

The Exponential Function

Sketching Exponentials

Lesson 24

Sums of Trigonometric Functions

Combining Functions

Lesson 25

Age Problems

Rate Problems

Lesson 26

The Logarithmic Form of the Exponential

Logarithmic Equations

Lesson 27

Related Angles

Signs of Trigonometric Functions

Lesson 28

Factorial Notation

Abstract Rate Problems

Lesson 29

The Unit Circle

Very Large and Very Small Fractions

Quadrantal Angles

Lesson 30

Addition of Vectors

Overlapping Triangles

Lesson 31

Symmetry

Reflections

Translations

Lesson 32

Inverse Functions

Four Quadrant Signs

Inverse Trigonometric Functions

Lesson 33

Quadrilaterals

Properties of Parallelograms

Types of Parallelograms

Conditions for Parallelograms

Trapezoids

Lesson 34

Summation Notation

Linear Regression

Decomposing Functions

Lesson 35

Change in Coordinates

The Name of a Number

The Distance Formula

Lesson 36

Angles Greater Than 360°

Sums of Trigonometric Functions

Boat-in-the-River Problems

Lesson 37

The Line as a Locus

The Midpoint Formula

Lesson 38

Fundamental Counting Principle and Permutations

Designated Roots

Overall Average Rate Radian Measure of Angles

Forms of Linear Equations

Lesson 40

The Argument in Mathematics

The Laws of Logarithms

Properties of Inverse Functions

Lesson 41

Reciprocal Trigonometric Functions

Permutation Notation

Lesson 42

Conic Sections

Circles

Constants in Exponential Functions

Lesson 43

Periodic Functions

Graphs of Sin and Cos

Lesson 44

Abstract Rate Problems

Lesson 45

Conditional Permutations

Two-Variable Analysis Using a Graphing Calculator

Lesson 46

Complex Roots

Factoring Over the Complex Numbers

Lesson 47

Vertical Sinusoid Translations

Arctan

Lesson 48

Powers of Trigonometric Functions

Perpendicular Bisectors

Lesson 49

The Logarithmic Function

Development of the Rules for Logarithms

Lesson 50

Trigonometric Equations

Lesson 51

Common Logarithms and Natural Logarithms

Lesson 52

The Inviolable Argument

Arguments in Trigonometric Equations

Lesson 53

Review of Unit Multipliers

Angular Velocity

Lesson 54

Parabolas

Lesson 55

Circular Permutations

Distinguishable Permutations

Lesson 56

Triangular Areas

Areas of Segments

Systems of Inequalities

Lesson 57

Phase Shifts in Sinusoids

Period of a Sinusoid

Lesson 58

Distance from a Point to a Line

"Narrow" and "Wide" Parabolas

Lesson 59

Advanced Logarithm Problems

The Color of the White House

Lesson 60

Factorable Trigonometric Equations

Loss of Solutions Caused by Division

Lesson 61

Single-Variable Analysis

The Normal Distribution

Box-and-Whisker Plots

Lesson 62

Abstract Coefficients

Linear Variation

Lesson 63

Circles and Completing the Square

Lesson 64

The Complex Plane

Polar Form of a Complex Number

Sums and Products of Complex Numbers

Lesson 65

Radicals in Trigonometric Equations

Graphs of Logarithmic Functions

Lesson 66

Formulas for Systems of Equations

Phase Shifts and Period Changes

Lesson 67

Antilogarithms

Lesson 68

Locus Definition of a Parabola

Translated Parabolas

Applications

Derivation

Lesson 69

Matrices

Determinants

Lesson 70

Percentiles and z Scores

Lesson 71

The Ellipse (1)

Lesson 72

One Side Plus Two Other Parts

Law of Sines

Lesson 73

Regular Polygons

Lesson 74

Cramer's Rule

Lesson 75

Combinations

Lesson 76

Functions of (-x)

Functions of the Other Angle

Trigonometric Identities (1)

Rules of the Game

Lesson 77

Binomial Expansions (1)

Lesson 78

The Hyperbola

Lesson 79

De Moivre's Theorem

Roots of Complex Numbers

Lesson 80

Trigonometric Identities (2)

Lesson 81

Law of Cosines

Lesson 82

Taking the Logarithm of

Exponential Equations

Lesson 83

Simple Probability

Independent Events

Replacement

Lesson 84

Factorable Expressions

Sketching Sinusoids

Lesson 85

Advanced Trigonometric Equations

Clock Problems

Lesson 86

Arithmetic Progressions and Arithmetic Means

Lesson 87

Sum and Difference Identities

Tangent Identities

Lesson 88

Exponential Functions (Growth and Decay)

Lesson 89

The Ellipse (2)

Lesson 90

Double-Angle Identities

Half-Angle Identities

Lesson 91

Geometric Progressions

Lesson 92

Probability of Either

Notations for Permutations and Combinations

Lesson 93

Advanced Trigonometric Identities

Triangle Inequalities (2)

Lesson 94

Graphs of Secant and Cosecant

Graphs of Tangent and Cotangent

Lesson 95

Advanced Complex Roots

Lesson 96

More Double-Angle Identities

Triangle Area Formula

Proof of the Law of Sines

Equal Angles Imply Proportional Sides

Lesson 97

The Ambiguous Case

Lesson 98

Change of Base

Contrived Logarithm Problems

Lesson 99

Sequence Notations

Advanced Sequence Problems

The Arithmetic and Geometric Means

Lesson 100

Product Identities

More Sum and Difference Identities

Lesson 101

Zero Determinants

3 x 3 Determinants

Determinant Solutions of 3 x 3 Systems

Independent Equations

Lesson 102

Binomial Expansions (2)

Lesson 103

Calculations with Logarithms

Power of the Hydrogen

Lesson 104

Arithmetic Series

Geometric Series

Lesson 105

Cofactors

Expansion by Cofactors

Lesson 106

Translations of Conic Sections

Equations of the Ellipse

Equations of the Hyperbola

Lesson 107

Convergent Geometric Series

Lesson 108

Matrix Addition and Multiplication

Lesson 109

Rational Numbers

Lesson 110

Graphs of arcsine and arccosine

Graphs of arcsecant and arccosecant

Graphs of arctangent and arccotangent

Lesson 111

Logarithmic Inequalities: Base Greater Than 1

Logarithmic Inequalities: Base Less Than 1

Lesson 112

Binomial Theorem

Lesson 113

Synthetic Division

Zeros and Roots

Lesson 114

Graphs of Factored Polynomial Functions

Lesson 115

The Remainder Theorem

Lesson 116

The Region of Interest

Lesson 117

Prime and Relatively Prime Numbers

Rational Roots Theorem

Lesson 118

Roots of Polynomial Equations

Lesson 119

Descartes' Rule of Signs

Upper and Lower Bound Theorem

Irrational Roots

Lesson 120

Matrix Algebra

Finding Inverse Matrices

Lesson 121

Piecewise Functions

Greatest Integer Function

Lesson 122

Graphs of Rational Functions

Graphs that Contain Holes

Lesson 123

The General Conic Equation

Lesson 124

Point of Division Formulas

Lesson 125

Using the Graphing Calculator to Graph

Solutions of Systems of Equations Using the Graphing Calculator

Roots

Appendix

Proofs

Answers

Index

Return to Saxon Advanced Math