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University of Chicago School Mathematics Project : Advanced Algebra,9780673459602

University of Chicago School Mathematics Project : Advanced Algebra

by Unknown
Edition:
2nd
ISBN13:

9780673459602

ISBN10:
0673459608
Format:
Hardcover
Pub. Date:
1/1/1998
Publisher(s):
Pearson Prentice Hall
List Price: $81.52

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This is the 2nd edition with a publication date of 1/1/1998.
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    University of Chicago School Mathematics Project, Adv Alg




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


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