Merrill Algebra 2 with Trigonometry : Applications and Connections

by Alan G. Foster, Berchie W. Gordon, Joan M. Gell, Leslie J. Winters

• ISBN13: 9780028242279
• ISBN10: 0028242270
• Format: Hardcover
• Copyright: 1995-12-01
• Publisher: Glencoe/McGraw-Hill School Pub

Table of Contents

Equations and Inequalities	6	(44)
Expressions and Formulas	8	(5)
Properties of Real Numbers	13	(5)
Solving Equations	18	(6)
Graphing Calculator Exploration: Evaluating Expressions	22	(2)
Applications of Equations	24	(5)
Mid-Chapter Review	28	(1)
Problem-Solving Strategy: List the Possibilities	29	(2)
Cooperative Learning Activity	30	(1)
Solving Absolute Value Equations	31	(5)
History Connection: Mileva Einstein	35	(1)
Solving Inequalities	36	(6)
Technology: Solving Equations and Inequalities	41	(1)
Solving Compound Sentences and Absolute Value Inequalities	42	(8)
Chapter Summary and Review	46	(3)
Chapter Test	49	(1)
Linear Relations and Functions	50	(52)
Relations and Functions	52	(8)
Graphing Calculator Exploration: Graphing Linear Equations	58	(2)
Linear Functions	60	(4)
Problem-Solving Strategy: Look for a Pattern	64	(2)
Cooperative Learning Activity	65	(1)
Slopes and Intercepts	66	(7)
Mid-Chapter Review	72	(1)
Writing Linear Equations	73	(7)
History Connection: Rene Descartes	79	(1)
Scatter Plots and Prediction Equations	80	(7)
Graphing Calculator Exploration: Lines of Regression	85	(2)
Special Functions	87	(5)
Technology: Median-Fit Lines	91	(1)
Graphing Linear Inequalities	92	(10)
Chapter Summary and Review	96	(3)
Chapter Test	99	(1)
College Entrance Exam Preview	100	(2)
Systems of Equations and Inequalities	102	(52)
Graphing Calculator Exploration: Graphing Systems of Equations	104	(4)
Graphing Systems of Equations	108	(4)
Solving Systems of Equations Algebraically	112	(6)
Technology: Solving Systems of Equations	117	(1)
Cramer's Rule	118	(4)
Graphing Systems of Inequalities	122	(4)
Mid-Chapter Review	125	(1)
Problem-Solving Strategy: Solve a Simpler Problem	126	(3)
Cooperative Learning Activity	128	(1)
Linear Programming	129	(5)
Applications of Linear Programming	134	(5)
Graphing Equations in Three Variables	139	(5)
Solving Systems of Equations in Three Variables	144	(10)
History Connection: Seki Kowa	149	(1)
Chapter Summary and Review	150	(3)
Chapter Test	153	(1)
Matrices	154	(54)
Problem-Solving Strategy: Using Matrix Logic	156	(5)
Cooperative Learning Activity	158	(1)
Graphing Calculator Exploration: Matrices	159	(2)
An Introduction to Matrices	161	(6)
Matrices and Determinants	167	(6)
Challenge	172	(1)
Multiplication of Matrices	173	(6)
History Connection: Chinese Matrix	178	(1)
Identity and Inverse Matrices	179	(5)
Mid-Chapter Review	183	(1)
Using Inverse Matrices	184	(6)
Using Cramer's Rule	190	(5)
Technology: Cramer's Rule	194	(1)
Using Augmented Matrices	195	(13)
Language Connection	200	(1)
Graphing Calculator Exploration: Matrix Row Operations	201	(1)
Chapter Summary and Review	202	(3)
Chapter Test	205	(1)
College Entrance Exam Preview	206	(2)
Polynomials	208	(42)
Monomials	210	(5)
Dividing Monomials	215	(5)
Problem-Solving Strategy: Draw a Diagram	220	(3)
Cooperative Learning Activity	222	(1)
Polynomials	223	(6)
Mid-Chapter Review	228	(1)
Factoring	229	(7)
Biology Connection: Genetics and Population Predictions	234	(1)
Technology: Factoring	235	(1)
Dividing Polynomials	236	(5)
History Connection: Prehistoric Counting	240	(1)
Synthetic Division	241	(9)
Chapter Summary and Review	246	(3)
Chapter Test	249	(1)
Irrational and Complex Numbers	250	(58)
Roots of Real Numbers	252	(6)
Language Connection	257	(1)
Products and Quotients of Radicals	258	(6)
Biology Connection	263	(1)
Computing with Radicals	264	(5)
Rational Exponents	269	(6)
Mid-Chapter Review	274	(1)
Problem-Solving Strategy: Identify Subgoals	275	(2)
Cooperative Learning Activity	276	(1)
Simplifying Expressions with Rational Exponents	277	(4)
Solving Equations Containing Radicals	281	(7)
History Connection: Johann Kepler	286	(1)
Technology: Solving Radical Equations	287	(1)
Pure Imaginary Numbers	288	(4)
Complex Numbers	292	(5)
Technology Connection: Benoit Mendelbroit	296	(1)
Simplifying Expressions Containing Complex Numbers	297	(11)
Chapter Summary and Review	302	(3)
Chapter Test	305	(1)
College Entrance Exam Preview	306	(2)
Quadratic Equations	308	(40)
Problem-Solving Strategy: Guess-and-Check	310	(6)
Cooperative Learning Activity	311	(1)
Graphing Calculator Exploration: Quadratic Equations	312	(4)
Solving Quadratic Equations	316	(6)
Completing the Square	322	(5)
Mid-Chapter Review	326	(1)
The Quadratic Formula and the Discriminant	327	(6)
Technology: Discriminants and Roots	332	(1)
Sum and Product of Roots	333	(6)
History Connection: Babylonians	338	(1)
Quadratic Techniques to Solve Polynomial Equations	339	(9)
Chapter Summary and Review	344	(3)
Chapter Test	347	(1)
Quadratic Relations and Functions	348	(46)
Graphing Calculator Exploration: Families of Parabolas	350	(3)
Quadratic Functions	353	(3)
Problem-Solving Strategy: Make a Table	356	(4)
Cooperative Learning Activity	358	(1)
Graphing Calculator Exploration: Locating the Vertex of a Parabola	359	(1)
Graphing Quadratic Functions	360	(6)
Analyzing Graphs of Quadratic Functions	366	(7)
Mid-Chapter Review	372	(1)
Applications of Quadratic Equations	373	(6)
Graphing Quadratic Inequalities	379	(4)
History Connection: Hypatia	382	(1)
Solving Quadratic Inequalities	383	(11)
Chapter Summary and Review	388	(3)
Chapter Test	391	(1)
College Entrance Exam Preview	392	(2)
Conics	394	(54)
The Distance and Midpoint Formulas	396	(4)
Parabolas	400	(5)
Circles	405	(4)
History Connection: The Dogon of Mali	408	(1)
Ellipses	409	(7)
Mid-Chapter Review	415	(1)
Hyperbolas	416	(7)
Applications in Architecture	422	(1)
Problem-Solving Strategy: Use a Model	423	(4)
Cooperative Learning Activity	424	(1)
Graphing Calculator Exploration: Conic Sections	425	(2)
Conic Sections	427	(5)
Technology: Conic Sections	431	(1)
Graphing Quadratic Systems	432	(7)
Graphing Calculator Exploration: Solving Quadratic Systems	437	(2)
Solving Quadratic Systems	439	(9)
Chapter Summary and Review	444	(3)
Chapter Test	447	(1)
Polynomial Functions	448	(54)
Polynomial Functions	450	(9)
History Connection: Carl Friedrich Gauss	456	(1)
Graphing Calculator Exploration: Graphing Polynomial Equations	457	(2)
The Remainder and Factor Theorems	459	(6)
Problem-Solving Strategy: Combining Strategies	465	(3)
Cooperative Learning Activity	467	(1)
Roots and Zeros	468	(7)
Mid-Chapter Review	474	(1)
Rational Zero Theorem	475	(6)
Language Connection	480	(1)
Graphing Polynomials and Approximating Zeros	481	(6)
Technology: Zeros of Polynomial Functions	486	(1)
Composition of Functions	487	(4)
Inverse Functions and Relations	491	(11)
Chapter Summary and Review	496	(3)
Chapter Test	499	(1)
College Entrance Exam Preview	500	(2)
Rational Polynomial Expressions	502	(42)
Graphing Calculator Exploration: Graphing Rational Functions	504	(2)
Graphing Rational Functions	506	(4)
Direct, Inverse, and Joint Variation	510	(6)
Fine Arts Connection	515	(1)
Multiplying and Dividing Rational Expressions	516	(6)
Mid-Chapter Review	521	(1)
Adding and Subracting Rational Expressions	522	(5)
Solving Rational Equations	527	(5)
Technology: Rational Expressions	531	(1)
Problem-Solving Strategy: Organizing Data	532	(8)
Cooperative Learning Activity	534	(6)
Applications of Rational Equations	540	(4)
Chapter Summary and Review	540	(3)
Chapter Test	543	(1)
Exponential and Logarithmic Functions	544	(48)
Real Exponents and Exponential Functions	546	(7)
Graphing Calculator Exploration: Graphing Exponential and Logarithmic Functions	551	(2)
Logarithms and Logarithmic Functions	553	(5)
Properties of Logarithms	558	(5)
Common Logarithms	563	(4)
Mid-Chapter Review	566	(1)
Natural Logarithms	567	(4)
History Connection: Napier and Briggs	570	(1)
Problem-Solving Strategy: Using Estimation	571	(3)
Cooperative Learning Activity	573	(1)
Exponential Equations	574	(6)
Biology Connection	578	(1)
Technology: Compound Interest	579	(1)
Applications of Logarithms	580	(12)
Chapter Summary and Review	586	(3)
Chapter Test	589	(1)
College Entrance Exam Preview	590	(2)
Sequences and Series	592	(44)
Problem-Solving Strategy: Look for a Pattern	594	(2)
Cooperative Learning Activity	595	(1)
Arithmetic Sequences	596	(6)
Arithmetic Series	602	(6)
Mid-Chapter Review	607	(1)
Geometric Sequences	608	(7)
Fine Arts Connection	614	(1)
Geometric Series	615	(5)
Infinite Geometric Series	620	(5)
The Binomial Theorem	625	(11)
Technology: Amortization	631	(1)
Chapter Summary and Review	632	(3)
Chapter Test	635	(1)
Statistics	636	(44)
Problem-Solving Strategy: Make a Graph	638	(4)
Cooperative Learning Activity	641	(1)
Line Plots and Stem-and-Leaf Plots	642	(6)
Central Tendency: Median, Mode, and Mean	648	(5)
Variation: Range, Interquartile Range, and Outliers	653	(5)
Mid-Chapter Review	657	(1)
Box-and-Whisker Plots	658	(6)
Challenge	662	(1)
Technology: Statistical Graphs	663	(1)
Variation: Standard Deviation	664	(4)
The Normal Distribution	668	(12)
Application: Misleading Graphs	673	(1)
Chapter Summary and Review	674	(3)
Chapter Test	677	(1)
College Entrance Exam Preview	678	(2)
Probability	680	(50)
Problem-Solving Strategy: Using Models	682	(2)
Cooperative Learning Activity	683	(1)
The Counting Principle	684	(5)
History Connection: Games	688	(1)
Linear Permutations	689	(5)
Circular Permutations	694	(5)
Combinations	699	(6)
Mid-Chapter Review	704	(1)
Probability	705	(5)
Multiplying Probabilities	710	(5)
Adding Probabilities	715	(5)
Simulation and Binomial Experiments	720	(10)
TEchnology: Coin Toss Simulation	725	(1)
Chapter Summary and Review	726	(3)
Chapter Test	729	(1)
Trigonometric Functions	730	(56)
Angles and the Unit Circle	732	(5)
Challenge	736	(1)
Sine and Cosine Functions	737	(5)
Applications in Music	741	(1)
Other Trigonometric Functions	742	(4)
Applications in Optics	745	(1)
Inverse Trigonometric Functions	746	(5)
Finding Values for Trigonometric Functions	751	(5)
Mid-Chapter Review	755	(1)
Solving Right Triangles	756	(6)
Technology: Solving Triangles	761	(1)
Applications of Right Triangle	762	(5)
Law of Sines	767	(4)
Problem-Solving Strategy: Examine the Solution	771	(4)
Cooperative Learning Activity	774	(1)
Law of Cosines	775	(11)
Chapter Summary and Review	780	(3)
Chapter Test	783	(1)
College Entrance Exam Preview	784	(2)
Trigonometric Graphs, Identities, and Equations	786	(52)
Graphing Calculator Exploration: Graphing Trigonometric Functions	788	(2)
Graphs of Trigonometric Functions	790	(7)
Trigonometric Identities	797	(6)
Graphing Calculator Exploration: Verifying Trigonometric Identities	801	(2)
Verifying Trigonometric Identities	803	(4)
Problem-Solving Strategy: Working Backwards	807	(3)
Cooperative Learning Activity	809	(1)
Sum and Difference of Angles Formulas	810	(5)
Mid-Chapter Review	814	(1)
Double-Angle and Half-Angle Formulas	815	(7)
Graphing Calculator Exploration: Solving Trigonometric Equations	820	(2)
Solving Trigonometric Equations	822	(7)
Technology: Trigonometric Equations	828	(1)
Trigonometric Notation for Complex Numbers	829	(9)
Chapter Summary and Review	834	(3)
Chapter Test	837	(1)
Appendix	838	(3)
Common Logarithm Tables	841	(2)
Values for Trigonometric Functions Tables	843	(5)
Glossary	848	(9)
Selected Answers	857	(43)
Index	900	(11)
Photo Credits	911