Algebra 2 : And Trigonometry

by Dolciann

• ISBN13: 9780395535929
• ISBN10: 0395535921
• Format: Hardcover
• Copyright: 1991-05-01
• Publisher: Houghton Mifflin Harcourt School

Table of Contents

Review of Essentials	1	(40)
Basic Properties
Sets and Symbols	1	(2)
Open Sentences and Graphs	3	(3)
Axioms for the Real Numbers	6	(6)
Properties of Operations in R
Theorems and Proof: Addition	12	(5)
Properties of Products	17	(5)
Properties of Differences	22	(2)
Properties of Quotients	24	(17)
Review of Essentials	41	(42)
Solving and Applying Equations
Sums and Differences of Polynomials	41	(4)
Transforming Equations	45	(5)
Solving Problems Using Linear Equations	50	(6)
Order in the Set of Real Numbers
Properties of Order	56	(4)
Compound Sentences	60	(5)
Additional Properties of Order	65	(4)
Absolute Value and Order	69	(14)
Linear Functions and Relations	83	(40)
Specifying Functions and Relations
Relations and Functions	83	(5)
Graphing Functions and Relations	88	(4)
Graphs of Linear Equations and Inequalities
The Graph of a Linear Equation	92	(3)
The Graph of a Linear Inequality	95	(3)
Lines and Their Equations
The Slope of a Line	98	(5)
Finding an Equation of a Line	103	(5)
Applications of Linear Relations
Direct Variation	108	(15)
Systems of Linear Equations or Inequalities	123	(38)
Systems of Equations in Two Variables
Graphing a System of Equations	123	(5)
Solving a System of Equations	128	(5)
Determinants	133	(5)
Using Two Variables to Solve Problems	138	(7)
Systems of Inequalities in Two Variables
Graphing a System of Linear Inequalities	145	(2)
Linear Programming	147	(14)
Graphs in Space; Determinants	161	(38)
Systems of Equations in Three Variables
Coordinates in Space	161	(4)
Graphs of Linear Equations in Three Variables	165	(6)
Systems of Linear Equations in Three Variables	171	(5)
Determinants
Third-order Determinants	176	(4)
Solving Problems with Three Variables	180	(3)
Properties of Determinants	183	(16)
Polynomials and Rational Expressions	199	(48)
Polynomials and Their Factors
Laws of Exponents	199	(6)
Multiplying Polynomials	205	(2)
Factoring a Polynomial	207	(6)
Applications of Factoring
Solving Equations by Factoring	213	(5)
Solving Inequalities by Factoring	218	(3)
Rational Algebraic Expressions
Simplifying Rational Expressions	221	(2)
Dividing One Polynomial by Another	223	(3)
Multiplying and Dividing Rational Expressions	226	(2)
Adding and Subtracting Rational Expressions	228	(3)
Using Polynomials with Rational Coefficients	231	(3)
Fractional Equations	234	(13)
Radicals and Irrational Numbers	247	(46)
Power Functions, Roots, and Radicals
Power Functions and Variation	247	(4)
The Real nth Roots of a Number	251	(3)
Roots of Polynomial Equation	254	(3)
Rational and Irrational Numbers
Standard Notation	257	(4)
Decimal Numerals for Real Numbers	261	(6)
Operating with Radicals
Properties of Radicals	267	(3)
Operations with Radicals	270	(3)
Equations Involving Radicals	273	(3)
The Set of Complex Numbers
The Number i	276	(3)
Complex Numbers; Addition and Subtraction	279	(3)
Complex Numbers; Multiplication and Division	282	(11)
Sequences and Series	293	(48)
Arithmetic Sequences and Series
Sequences	293	(3)
Arithmetic Sequences and Arithmetic Means	296	(4)
Arithmetic Series	300	(6)
Geometric Sequences and Series
Geometric Sequences	306	(6)
Geometric Means	312	(4)
Geometric Series	316	(5)
Infinite Sequences and Series
Limit of a Sequence	321	(3)
Infinite Geometric Series	324	(17)
Polynomial Functions	341	(52)
Solving Quadratic Equations
Completing the Square and the Quadratic Formula	341	(6)
The Discriminant	347	(3)
Roots and Coefficients of a Quadratic Equation	350	(4)
Quadratic Functions and Their Graphs
The Graph of y = a(x - h)2 + k	354	(3)
The Graph of a Quadratic Function	357	(5)
Quadratic Inequalities	362	(3)
Polynomial Functions and Equations
Values of Polynomial Functions	365	(3)
Remainder and Factor Theorems	368	(6)
The Fundamental Theorem of Algebra	374	(2)
Estimating Real Roots
Locating Possible Real Roots	376	(4)
Estimates of Real Roots	380	(13)
Quadratic Relations and Systems	393	(48)
Coordinates and Distances in a Plane
Distance between Points	393	(4)
Perpendicular Lines	397	(4)
Graphing Quadratic Relations
Circles	401	(3)
Parabolas	404	(4)
Ellipses	408	(4)
Hyperbolas	412	(5)
Inverse and Other Kinds of Variation	417	(6)
Solving Quadratic Systems
Graphic Solutions of Systems	423	(1)
Linear-Quadratic Systems: Substitution	424	(6)
Quadratic-Quadratic Systems	430	(11)
Exponents and Logarithms	441	(42)
Extending the Laws of Exponents
Rational Exponents	441	(3)
Real-Number Exponents	444	(3)
From Exponents to Logarithms
The Inverse of a Function	447	(4)
The Logarithmic Function	451	(3)
Laws of Logarithms	454	(4)
Using Logarithms
Common Logarithms	458	(3)
Solving Exponential Equations	461	(3)
Exponential Growth and Decay	464	(4)
Natural Logarithms	468	(15)
Permutations, Combinations, and Probability	483	(44)
Permutations
Two Fundamental Counting Principles	483	(3)
Linear and Circular Permutations	486	(4)
Permutations with Repeated Elements	490	(2)
Combinations
Counting Subsets	492	(4)
Combinations and Products	496	(2)
Binomial Expansions
The Binomial Theorem	498	(4)
Pascal's Triangle	502	(3)
Probability
Sample Spaces and Events	505	(3)
Mathematical Probability	508	(3)
Mutually Exclusive Events	511	(3)
Conditional Probability	514	(13)
Matrices	527	(48)
Basic Properties of Matrices
Matrices and Their Sums	527	(5)
Properties of Matrix Addition	532	(3)
Product of a Scalar and a Matrix	535	(3)
Product of Two Matrices	538	(5)
Properties of Matrix Multiplication	543	(4)
Matrices and Linear Systems
Matrix Solution of a Linear System	547	(6)
Transformations of the Plane
Transformations by Matrix Addition	553	(5)
Transformations by Matrix Multiplication	558	(17)
Trigonometric and Circular Functions	575	(44)
Angles and Their Measurement
Rotations and Angles	575	(4)
Measurement of Angles	579	(5)
The Sine and Cosine Functions
The Sine and Cosine Functions	584	(5)
Special Values of Sine and Cosine	589	(3)
Reference Angles and Arcs	592	(3)
Graphs of Sine and Cosine I	595	(4)
Graphs of Sine and Cosine II	599	(3)
Other Trigonometric and Circular Functions and Applications
The Tangent, Cotangent, Secant, and Cosecant Functions	602	(5)
Solving Right Triangles	607	(12)
Trigonometric Identities	619	(42)
Identities
Fundamental Identities	619	(3)
Proving Identities	622	(3)
Functions: Sums and Differences
The Cosine of a Sum or a Difference	625	(6)
The Sine and Tangent of a Sum or a Difference	631	(6)
Double-Angle and Half-Angle Formulas	637	(5)
More on Identities	642	(2)
Solving General Triangles
The Law of Cosines	644	(4)
The Law of Sines	648	(13)
Inverses; Polar Coordinates; Vectors	661	(42)
Inverse Functions
Inverse Functions; Principal Values	661	(6)
Equations Involving Circular and Trigonometric Functions	667	(5)
Polar Coordinates
Polar Coordinates; Polar Graphs	672	(4)
Graphs of Complex Numbers	676	(4)
De Moivre's Theorem	680	(6)
Vectors
Vectors in the Plane	686	(6)
Applications of Vectors	692	(11)
Statistics	703	(43)
Organizing and Measuring Statistical Data
Representing Data; Measures of Central Tendency	703	(7)
Measures of Variation	710	(7)
Applying the Normal Distribution
The Normal Distribution	717	(9)
Statistical Inference	726	(6)
Examining Relationships between Sets of Data
Correlation	732	(14)
Tables	746	(22)
Appendix A: Computation with Common Logarithms	768	(4)
Appendix B: Programming in Pascal	772	(26)
Appendix C: Preparing for College Entrance Examinations	798	(3)
Appendix D: Discrete Mathematics	801	(6)
Appendix E: Graphing Calculator Explorations	807	(6)
Glossary	813	(6)
Index	819