University of Chicago School Mathematics Project : Advanced Algebra

by Unknown

• ISBN13: 9780673459602
• ISBN10: 0673459608
• Edition: 2nd
• Format: Hardcover
• Copyright: 1998-01-01
• Publisher: Pearson Prentice Hall

Table of Contents

Acknowledgments	ii
The University of Chicago School Mathematics Project	iv
Table of Contents	vi
To the Student	1	(3)
Functions	4	(66)
The Language of Algebra	6	(6)
What Is a Function?	12	(7)
Grouping Symbols and Calculators	18	(1)
Function Notations	19	(5)
Graphs of Functions	24	(6)
Solving Equations	30	(6)
Rewriting Formulas	36	(6)
Patterns and Sequences	41	(1)
Explicit Formulas for Sequences	42	(6)
Recursive Formulas for Sequences	48	(7)
Notation for Recursive Formulas	55	(15)
Projects	61	(2)
Summary and Vocabulary	63	(1)
Progress Self-Test	64	(2)
Chapter Review	66	(4)
Variation and Graphs	70	(68)
Direct Variation	72	(6)
Inverse Variation	78	(6)
Functions of Variation	83	(1)
The Fundamental Theorem of Variation	84	(5)
The Graph of y = kx	89	(7)
Introduction to Automatic Graphers	94	(2)
The Graph of y = kx2	96	(8)
Automatic Graphers and Inverse Variation	103	(1)
The Graphs of y = k/x and y = k/x2	104	(6)
Fitting a Model to Data I	110	(6)
Fitting a Model to Data II	116	(6)
Combined and Joint Variation	122	(16)
Projects	128	(2)
Summary and Vocabulary	130	(2)
Progress Self-Test	132	(2)
Chapter Review	134	(4)
Linear Functions	138	(64)
Constant-Increase or Constant-Decrease Situations	140	(6)
The Graph of y = mx + b	146	(6)
Linear-Combination Situations	152	(5)
The Graph of Ax + By = C	157	(5)
Finding an Equation of a Line	162	(7)
Using Linear Models to Approximate Data	168	(1)
Fitting a Line to Data	169	(6)
Recursive Formulas for Arithmetic Sequences	175	(5)
Explicit Formulas for Arithmetic Sequences	180	(6)
Step Functions	186	(16)
Projects	192	(2)
Summary and Vocabulary	194	(1)
Progress Self-Test	195	(2)
Chapter Review	197	(5)
Matrices	202	(68)
Storing Data in Matrices	204	(5)
Matrix Addition	209	(5)
Matrix Multiplication	214	(7)
Size Changes	220	(1)
Matrices for Size Changes	221	(6)
Matrices for Scale Changes	227	(5)
Matrices for Reflections	232	(8)
Composites of Transformations	239	(1)
Transformations and Matrices	240	(6)
Matrices for Rotations	246	(5)
Rotations and Perpendicular Lines	251	(5)
Translations and Parallel Lines	256	(14)
Projects	261	(2)
Summary and Vocabulary	263	(2)
Progress Self-Test	265	(1)
Chapter Review	266	(4)
Systems	270	(74)
Inequalities and Compound Sentences	272	(7)
Solving Systems Using Tables or Graphs	279	(6)
Solving Systems by Substitution	285	(7)
Solving Systems Using Linear Combinations	292	(7)
Matrices and Inverses	298	(1)
Inverses of Matrices	299	(6)
Solving Systems Using Matrices	305	(7)
Graphing Inequalities in the Coordinate Plane	312	(7)
Systems of Linear Inequalities	319	(6)
Linear Programming I	325	(6)
Linear Programming II	331	(13)
Projects	336	(2)
Summary and Vocabulary	338	(1)
Progress Self-Test	339	(1)
Chapter Review	340	(4)
Quadratic Functions	344	(72)
Quadratic Expressions, Rectangles, and Squares	346	(5)
Absolute Value, Square Roots, and Quadratic Equations	351	(6)
Graphs and Translations	356	(1)
The Graph-Translation Theorem	357	(6)
Graphing y = ax2 + bx + c	363	(7)
Completing the Square	370	(6)
Fitting a Quadratic Model to Data	376	(6)
The Quadratic Formula	382	(6)
Imaginary Numbers	388	(5)
Complex Numbers	393	(7)
Predicting the Number of Real Solutions to a Quadratic Equation	399	(1)
Analyzing Solutions to Quadratic Equations	400	(16)
Projects	408	(2)
Summary and Vocabulary	410	(2)
Progress Self-Test	412	(1)
Chapter Review	413	(3)
Powers	416	(60)
Power Functions	418	(8)
Properties of Powers	426	(7)
Negative Integer Exponents	433	(5)
Compound Interest	438	(6)
Geometric Sequences	444	(6)
nth Roots	450	(8)
Noninteger Power Functions	457	(1)
Positive Rational Exponents	458	(6)
Negative Rational Exponents	464	(12)
Projects	469	(2)
Summary and Vocabulary	471	(1)
Progress Self-Test	472	(1)
Chapter Review	473	(3)
Inverses and Radicals	476	(54)
Composition of Functions	478	(6)
Inverses of Relations	484	(6)
Properties of Inverse Functions	490	(5)
Radical Notation for nth Roots	495	(5)
Products with Radicals	500	(6)
Quotients with Radicals	506	(5)
Graphs of Radical Functions	510	(1)
Powers and Roots of Negative Numbers	511	(6)
Solving Equations with Radicals	517	(13)
Projects	522	(2)
Summary and Vocabulary	524	(2)
Progress Self-Test	526	(1)
Chapter Review	527	(3)
Exponential and Logarithmic Functions	530	(72)
Exponential Growth	532	(7)
Exponential Decay	539	(8)
The Number e	546	(1)
Continuous Growth or Decay	547	(5)
Fitting Exponential Models to Data	552	(5)
Common Logarithms	557	(6)
Logarithmic Scales	563	(7)
Logarithms to Bases Other Than 10	570	(6)
Properties of Logarithms	576	(7)
Natural Logarithms	583	(5)
Using Logarithms to Solve Exponential Equations	588	(14)
Projects	593	(2)
Summary and Vocabulary	595	(2)
Progress Self-Test	597	(2)
Chapter Review	599	(3)
Trigonometry	602	(70)
Three Trigonometric Functions	604	(7)
More Right-Triangle Trigonometry	611	(5)
Properties of Trigonometric Ratios	616	(7)
Rotations, Sines, and Cosines	622	(1)
Trigonometry and the Unit Circle	623	(5)
Cosines and Sines in Quadrants II-IV	628	(5)
The Law of Cosines	633	(6)
The Law of Sines	639	(8)
Graphing y = cos θ	646	(1)
The Cosine and Sine Functions	647	(6)
The Law of Sines when SSA Is Given	652	(1)
Solving sin θ = k	653	(5)
Radian Measure	658	(14)
Projects	664	(2)
Summary and Vocabulary	666	(2)
Progress Self-Test	668	(1)
Chapter Review	669	(3)
Polynomials	672	(74)
Introduction to Polynomials	674	(6)
Polynomials and Geometry	680	(6)
Factoring Special Cases	686	(6)
Estimating Solutions to Polynomial Equations	692	(7)
Factors and Graphs	698	(1)
The Factor Theorem	699	(7)
Factoring Quadratic Trinomials and Related Polynomials	706	(5)
The Rational-Zero Theorem	711	(6)
Solving All Polynomial Equations	717	(8)
Examining Difference Patterns for Polynomial Functions	723	(2)
Finite Differences	725	(5)
Modeling Data with Polynomials	730	(16)
Projects	737	(2)
Summary and Vocabulary	739	(1)
Progress Self-Test	740	(1)
Chapter Review	741	(5)
Quadratic Relations	746	(62)
Parabolas	748	(6)
Circles	754	(5)
Semicircles, Interiors, and Exteriors of Circles	759	(6)
Drawing an Ellipse	764	(1)
Ellipses	765	(6)
Relationships Between Ellipses and Circles	771	(6)
Drawing a Hyperbola	776	(1)
Equations for Some Hyperbolas	777	(7)
Equations for More Hyperbolas	784	(5)
Quadratic-Linear Systems	789	(5)
Quadratic-Quadratic Systems	794	(14)
Projects	799	(2)
Summary and Vocabulary	801	(2)
Progress Self-Test	803	(1)
Chapter Review	804	(4)
Series and Combinations	808	(76)
Arithmetic Series	810	(7)
Geometric Series	817	(6)
The Σ and ! Symbols	823	(7)
Descriptive Statistics	830	(5)
Pascal's Triangle	835	(6)
The Binomial Theorem	841	(4)
Subsets and Combinations	845	(6)
Probabilities and Combinations	851	(6)
Lotteries	857	(5)
Binomial and Normal Distributions	862	(6)
Polls and Sampling	868	(16)
Projects	875	(2)
Summary and Vocabulary	877	(2)
Progress Self-Test	879	(1)
Chapter Review	880	(4)
Appendix A: Algebra Properties from Earlier Courses	884	(2)
Appendix B: Geometry Properties from Earlier Courses	886	(4)
Appendix C: Theorems of UCSMP Advanced Algebra	890	(5)
Appendix D: Programming Languages	895	(2)
Selected Answers	897	(32)
Glossary	929	(10)
Index	939	(10)
List of Symbols	949	(1)
Photo Acknowledgments	950