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Tables of Contents for Algebra and Trigonometry Structure and Method
Chapter/Section Title
Page #
Page Count
Basic Concepts of Algebra
The Language of Algebra
Real Numbers and Their Graphs
1
5
Simplifying Expressions
6
8
Operating with Real Numbers
Basic Properties of Real Numbers
14
7
Sums and Differences
21
6
Products
27
6
Quotients
33
4
Solving Equations and Solving Problems
Solving Equations in One Variable
37
6
Words into Symbols
43
6
Problem Solving with Equations
49
10
Inequalities and Proof
Working with Inequalities
Solving Inequalities in One Variable
59
6
Solving Combined Inequalities
65
4
Problem Solving Using Inequalities
69
4
Working with Absolute Value
Absolute Value in Open Sentences
73
3
Solving Absolute Value Sentences Graphically
76
5
Proving Theorems
Theorems and Proofs
81
7
Theorems about Order and Absolute Value
88
13
Linear Equations and Functions
Linear Equations and Their Graphs
Open Sentences in Two Variables
101
6
Graphs of Linear Equations in Two Variables
107
5
The Slope of a Line
112
6
Finding an Equation of a Line
118
6
Linear Systems
Systems of Linear Equations in Two Variables
124
7
Problem Solving: Using Systems
131
4
Linear Inequalities in Two Variables
135
6
Functions and Relations
Functions
141
5
Linear Functions
146
7
Relations
153
14
Products and Factors of Polynomials
Working with Polynomials
Polynomials
167
4
Using Laws of Exponents
171
3
Multiplying Polynomials
174
5
Factors of Polynomials
Using Prime Factorization
179
4
Factoring Polynomials
183
5
Factoring Quadratic Polynomials
188
6
Applications of Factoring
Solving Polynomial Equations
194
4
Problem Solving Using Polynomial Equations
198
4
Solving Polynomial Inequalities
202
9
Rational Expressions
Using the Laws of Exponents
Quotients of Monomials
211
5
Zero and Negative Exponents
216
5
Scientific Notation and Significant Digits
221
6
Rational Expressions
Rational Algebraic Expressions
227
5
Products and Quotients of Rational Expressions
232
3
Sums and Differences of Rational Expressions
235
3
Complex Fractions
238
4
Problem Solving Using Fractional Equations
Fractional Coefficients
242
5
Fractional Equations
247
12
Irrational and Complex Numbers
Roots and Radicals
Roots of Real Numbers
259
5
Properties of Radicals
264
6
Sums of Radicals
270
4
Binomials Containing Radicals
274
3
Equations Containing Radicals
277
6
Real Numbers and Complex Numbers
Rational and Irrational Numbers
283
5
The Imaginary Number i
288
4
The Complex Numbers
292
15
Quadratic Equations and Functions
Solving Quadratic Equations
Completing the Square
307
4
The Quadratic Formula
311
6
Roots of Quadratic Equations
The Discriminant
317
5
Equations in Quadratic Form
322
4
Quadratic Functions and Their Graphs
Graphing y - k = a(x-h)2
326
7
Quadratic Functions
333
5
Writing Quadratic Equations and Functions
338
13
Variation and Polynomial Equations
Variation and Proportion
Direct Variation and Proportion
351
7
Inverse and Joint Variation
358
6
Polynomial Equations
Dividing Polynomials
364
4
Synthetic Division
368
4
The Remainder and Factor Theorems
372
5
Some Useful Theorems
377
5
Solving Polynomial Equations
Finding Rational Roots
382
4
Approximating Irrational Roots
386
5
Linear Interpolation
391
10
Analytic Geometry
Conic Sections: Circles and Parabolas
Distance and Midpoint Formulas
401
6
Circles
407
5
Parabolas
412
6
Conic Sections: Ellipses and Hyperbolas
Ellipses
418
8
Hyperbolas
426
6
More on Central Conics
432
4
Systems of Equations
The Geometry of Quadratic Systems
436
3
Solving Quadratic Systems
439
5
Systems of Linear Equations in Three Variables
444
11
Exponential and Logarithmic Functions
Exponential Functions
Rational Exponents
455
4
Real Number Exponents
459
4
Composition and Inverses of Functions
463
5
Logarithmic Functions
Definition of Logarithms
468
5
Laws of Logarithms
473
5
Applications
Applications of Logarithms
478
5
Problem Solving: Exponential Growth and Decay
483
6
The Natural Logarithm Function
489
12
Sequences and Series
Sequences
Types of Sequences
501
6
Arithmetic Sequences
507
3
Geometric Sequences
510
8
Series
Series and Sigma Notation
518
7
Sums of Arithmetic and Geometric Series
525
6
Infinite Geometric Series
531
6
Binomial Expansions
Powers of Binomials
537
3
The General Binomial Expansion
540
9
Triangle Trigonometry
Trigonometric Functions
Angles and Degree Measure
549
6
Trigonometric Functions of Acute Angles
555
6
Trigonometric Functions of General Angles
561
7
Values of Trigonometric Functions
568
6
Triangle Trigonometry
Solving Right Triangles
574
6
The Law of Cosines
580
6
The Law of Sines
586
5
Solving General Triangles
591
6
Areas of Triangles
597
10
Trigonometric Graphs; Identities
Circular Functions and Their Graphs
Radian Measure
607
6
Circular Functions
613
6
Periodicity and Symmetry
619
5
Graphs of the Sine and Cosine
624
6
Graphs of the Other Functions
630
6
Trigonometric Identities
The Fundamental Identities
636
5
Trigonometric Addition Formulas
641
5
Double-Angle and Half-Angle Formulas
646
4
Formulas for the Tangent
650
9
Trigonometric Applications
Vectors
Vector Operations
659
7
Vectors in the Plane
666
9
Polar Coordinates and Complex Numbers
Polar Coordinates
675
5
The Geometry of Complex Numbers
680
5
De Moivre's Theorem
685
4
Inverse Functions
The Inverse Cosine and Inverse Sine
689
4
Other Inverse Functions
693
4
Trigonometric Equations
697
12
Statistics and Probability
Statistics
Presenting Statistical Data
709
4
Analyzing Statistical Data
713
6
The Normal Distribution
719
5
Correlation
724
6
Counting
Fundamental Counting Principles
730
4
Permutations
734
4
Combinations
738
5
Probability
Sample Spaces and Events
743
2
Probability
745
9
Mutually Exclusive and Independent Events
754
13
Matrices and Determinants
Matrices
Definition of Terms
767
3
Addition and Scalar Multiplication
770
4
Matrix Multiplication
774
5
Applications of Matrices
779
8
Inverses of Matrices
Determinants
787
3
Inverses of Matrices
790
4
Working with Determinants
Expansion of Determinants by Minors
794
4
Properties of Determinants
798
3
Cramer's Rule
801
9
Tables
810
22
Explorations
832
16
Portfolio Projects
848
20
Appendix
A-1 Common Logarithms: Notation and Interpolation
856
2
A-2 Common Logarithms: Computation
858
4
A-3 Discrete Mathematics
862
2
A-4 Preparing for College Entrance Exams
864
4
Glossary
868
10
Index
878
Answers to Selected Exercises