Acknowledgments 

ii  
The University of Chicago School Mathematics Project 

iv  


vi  
To the Student 

1  (3) 


4  (76) 


6  (7) 


13  (8) 

Inclass Activity: Using a Statistics Utility to Enter and Analyze Data 


19  (2) 


21  (8) 

Quartiles, Percentiles, and Box Plots 


29  (10) 

Inclass Activity: Displaying Data with a Statistics Utility 


38  (1) 


39  (7) 


46  (8) 

Variance and Standard Deviation 


54  (8) 

Who Wrote The Federalist Papers? 


62  (18) 


68  (2) 


70  (1) 


71  (2) 


73  (7) 


80  (78) 

The Language of Functions 


82  (7) 

Inclass Activity: Linear Regression 


88  (1) 

Linear Models and Correlation 


89  (8) 


97  (8) 


105  (7) 


112  (8) 

Inclass Activity: Using Quadratic Regression 


119  (1) 


120  (8) 


128  (6) 


134  (7) 


141  (17) 


148  (2) 


150  (1) 


151  (1) 


152  (6) 

Transformations of Graphs and Data 


158  (72) 


160  (7) 

The GraphTranslation Theorem 


167  (6) 


173  (6) 


179  (8) 

Inclass Activity: Functions and Scale Changes 


186  (1) 

The Graph ScaleChange Theorem 


187  (7) 


194  (7) 


201  (7) 


208  (7) 


215  (15) 


220  (2) 


222  (2) 


224  (1) 


225  (5) 


230  (78) 

Measures of Angles and Rotations 


232  (7) 

Lengths of Arcs and Areas of Sectors 


239  (6) 

Inclass Activity: Introducing Sines, Cosines, and Tangents 


244  (1) 

Sines, Cosines, and Tangents 


245  (6) 

Basic Identities Involving Sines, Cosines, and Tangents 


251  (6) 

Exact Values of Sines, Cosines, and Tangents 


257  (8) 

Inclass Activity: Graphing Circular Functions 


263  (2) 

The Sine, Cosine, and Tangent Functions 


265  (7) 

ScaleChange Images of Circular Functions 


272  (6) 

Translation Images of Circular Functions 


278  (7) 

The GraphStandardization Theorem 


285  (8) 

Inclass Activity: Daylight in Seattle 


292  (1) 

Modeling with Circular Functions 


293  (15) 


299  (2) 


301  (1) 


302  (1) 


303  (5) 


308  (60) 

Trigonometric Ratios in Right Triangles 


310  (6) 


316  (5) 

The Inverse Cosine Function 


321  (6) 


327  (7) 

The Inverse Sine Function 


334  (6) 

The Inverse Tangent Function 


340  (6) 

Inclass Activity: Solving Trigonometric Equations Graphically 


345  (1) 

General Solutions to Trigonometric Equations 


346  (7) 

From Washington to Beijing 


353  (15) 


360  (2) 


362  (1) 


363  (1) 


364  (4) 

Root, Power, and Logarithm Functions 


368  (56) 


370  (6) 


376  (7) 


383  (7) 

Inclass Activity: The Number e 


389  (1) 


390  (8) 

Inclass Activity: Sums, Differences, and Logarithms 


397  (1) 


398  (5) 

Solving Exponential Equations 


403  (6) 

Linearizing Data to Find Models 


409  (15) 


416  (2) 


418  (1) 


419  (1) 


420  (4) 

Probability and Simulation 


424  (62) 

Basic Principles of Probability 


426  (7) 

Addition Counting Principles 


433  (7) 

Multiplication Counting Principles 


440  (5) 


445  (5) 


450  (7) 

Probability Distributions 


457  (8) 

Inclass Activity: The Monty Hall Problem 


464  (1) 


465  (6) 

Simulations with Technology 


471  (15) 


478  (2) 


480  (1) 


481  (1) 


482  (4) 

Sequences, Series, and Combinations 


486  (68) 


488  (8) 


496  (7) 


503  (6) 


509  (7) 

Inclass Activity: Exploring Infinite Series 


515  (1) 


516  (7) 


523  (6) 


529  (6) 


535  (5) 


540  (14) 


546  (2) 


548  (2) 


550  (1) 


551  (3) 


554  (72) 


556  (8) 

Inclass Activity: Finding Some Key Points of a Polynomial Function 


563  (1) 

Graphs of Polynomial Functions 


564  (6) 

Finding Polynomial Models 


570  (7) 

Division and the Remainder Theorem 


577  (7) 


584  (6) 


590  (6) 

The Fundamental Theorem of Algebra 


596  (7) 

Factoring Sums and Differences of Powers 


603  (5) 

Advanced Factoring Techniques 


608  (4) 

Roots and Coefficients of Polynomials 


612  (14) 


617  (2) 


619  (2) 


621  (1) 


622  (4) 

Binomial and Normal Distributions 


626  (70) 

Binomial Probability Distributions 


628  (6) 

Mean and Standard Deviation of a Binomial Distribution 


634  (7) 


641  (8) 

Inclass Activity: The Graph of y = ex2 


648  (1) 


649  (5) 

Finding Probabilities Using the Standard Normal Distribution 


654  (8) 

Other Normal Distributions 


662  (9) 

Inclass Activity: The Sampling Distribution of the Mean 


670  (1) 

Sampling Distributions and the Central Limit Theorem 


671  (9) 

Confidence and Cautions in Statistical Reasoning 


680  (16) 


687  (2) 


689  (2) 


691  (1) 


692  (4) 

Matrices and Trigonometry 


696  (56) 


698  (6) 

Matrices for Transformations 


704  (6) 

Matrices for Composites of Transformations 


710  (6) 

The General Rotation Matrix 


716  (5) 

Formulas for cos (α + β) and sin (α + β) 


721  (5) 

Formulas for cos 2&thetas; and sin 2&thetas; 


726  (5) 

Inverses of 2 x 2 Matrices 


731  (7) 

Matrices in Computer Graphics 


738  (14) 


745  (2) 


747  (1) 


748  (1) 


749  (3) 


752  (52) 

The Geometry of the Ellipse 


754  (6) 

The Algebra of the Ellipse 


760  (8) 


768  (8) 


776  (8) 

The General Quadratic Equation 


784  (8) 

It's All Done with Mirrors 


792  (12) 


797  (2) 


799  (2) 


801  (1) 


802  (2) 

Further Work with Trigonometry 


804  (62) 

The Secant, Cosecant, and Cotangent Functions 


806  (5) 

Proving Trigonometric Identities 


811  (5) 

Restrictions on Identities 


816  (4) 


820  (7) 


827  (6) 

The Geometry of Complex Numbers 


833  (6) 

Inclass Activity: Geometric Transformations Using Complex Multiplication 


838  (1) 

Trigonometric Form of Complex Numbers 


839  (7) 


846  (6) 


852  (14) 


858  (2) 


860  (2) 


862  (1) 


863  (3) 
Appendix A: Parent Functions and Graphs 

866  (5) 
Appendix B: Programming Languages 

871  (3) 
Appendix C: Random Number Table 

874  (1) 
Appendix D: Standard Normal Distribution Table 

875  (1) 
Selected Answers 

876  (35) 
Glossary 

911  (13) 
Index 

924  (10) 
List of Symbols 

934  (1) 
Photo Acknowledgments 

935  