Algebra and Trigonometry Structure and Method Book 2 (Student Version)

by Brown, Richard G.

• ISBN13: 9780395771181
• ISBN10: 0395771188
• Format: Hardcover
• Copyright: 1996-03-01
• Publisher: Houghton Mifflin College Div

Table of Contents

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	(24)
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	(21)
Appendix
A-1 Common Logrithms: Notation and Interpolation	856	(2)
A-2 Common Logrithms: Computation	858	(4)
A-3 Discrete Mathematics	862	(2)
A-4 Preparing for College Entrance Exams	864	(5)
Glossary	869	(10)
Index	879