Home Page Icon
Home Page
Table of Contents for
Algebraic Properties 11 (2/2)
Close
Algebraic Properties 11 (2/2)
by W. Michael Kelley
The Humongous Book of Algebra Problems
Contents iii (1/2)
Contents iii (2/2)
Chapter 1: Arithmetic Fundamentals 1
Number Classification 2
Expressions Containing Signed Numbers 5
Grouping Symbols 8
Algebraic Properties 11 (1/2)
Algebraic Properties 11 (2/2)
Chapter 2: Rational Numbers 17
Rational Number Notation 18
Simplifying Fractions 23
Combining Fractions 26 (1/3)
Combining Fractions 26 (2/3)
Combining Fractions 26 (3/3)
Chapter 3: Basic Algebraic Expressions 37
Translating Expressions 38
Exponential Expressions 40
Distributive Property 45
Order of Operations 48
Evaluating Expressions 51
Chapter 4: Linear Equations in One Variable 55
Adding and Subtracting to Solve an Equation 56
Multiplying and Dividing to Solve an Equation 59
Solving Equations Using Multiple Steps 61 (1/2)
Solving Equations Using Multiple Steps 61 (2/2)
Absolute Value Equations 70
Equations Containing Multiple Variables 73
Chapter 5: Graphing Linear Equations in Two Variables 77
Number Lines and the Coordinate Plane 78
Graphing with a Table of Values 83 (1/2)
Graphing with a Table of Values 83 (2/2)
Graphing Using Intercepts 90
Calculating Slope of a Line 93 (1/2)
Calculating Slope of a Line 93 (2/2)
Graphing Absolute Value Equations 100
Chapter 6: Linear Equations in Two Variables 105
Point-Slope Form of a Linear Equation 106
Slope-Intercept Form of a Linear Equation 110
Graphing Lines in Slope-Intercept Form 113
Standard Form of a Linear Equation 118
Creating Linear Equations 121 (1/2)
Creating Linear Equations 121 (2/2)
Chapter 7: Linear Inequalities 127
Inequalities in One Variable 128
Graphing Inequalities in One Variable 132
Compound Inequalities 135
Absolute Value Inequalities 137
Set Notation 140
Graphing Inequalities in Two Variables 142
Chapter 8: Systems of Linear Equations and Inequalities 147
Graphing Linear Systems 148
The Substitution Method 153 (1/2)
The Substitution Method 153 (2/2)
Variable Elimination 162 (1/2)
Variable Elimination 162 (2/2)
Systems of Inequalities 168
Linear Programming 173 (1/2)
Linear Programming 173 (2/2)
Chapter 9: Matrix Operations and Calculations 181
Anatomy of a Matrix 182
Adding and Subtracting Matrices 183
Multiplying Matrices 188
Calculating Determinants 192 (1/2)
Calculating Determinants 192 (2/2)
Cramer’s Rule 200 (1/2)
Cramer’s Rule 200 (2/2)
Chapter 10: Applications of Matrix Algebra 207
Augmented and Identity Matrices 208
Matrix Row Operations 211
Row and Reduced-Row Echelon Form 216 (1/3)
Row and Reduced-Row Echelon Form 216 (2/3)
Row and Reduced-Row Echelon Form 216 (3/3)
Inverse Matrices 228 (1/2)
Inverse Matrices 228 (2/2)
Chapter 11: Polynomials 237
Classifying Polynomials 238
Adding and Subtracting Polynomials 239
Multiplying Polynomials 244
Long Division of Polynomials 246
Synthetic Division of Polynomials 251 (1/2)
Synthetic Division of Polynomials 251 (2/2)
Chapter 12: Factoring Polynomials 257
Greatest Common Factors 258 (1/2)
Greatest Common Factors 258 (2/2)
Factoring by Grouping 265
Common Factor Patterns 267
Factoring Quadratic Trinomials 270
Chapter 13: Radical Expressions and Equations 275
Simplifying Radical Expressions 276
Rational Exponents 281
Radical Operations 283
Solving Radical Equations 288
Complex Numbers 290
Chapter 14: Quadratic Equations and Inequalities 295
Solving Quadratics by Factoring 296
Completing the Square 300
Quadratic Formula 305 (1/2)
Quadratic Formula 305 (2/2)
Applying the Discriminant 312
One-Variable Quadratic Inequalities 316 (1/2)
One-Variable Quadratic Inequalities 316 (2/2)
Chapter 15: Functions 323
Relations and Functions 324
Operations on Functions 326
Composition of Functions 330
Inverse Functions 335 (1/2)
Inverse Functions 335 (2/2)
Piecewise-Defined Functions 343
Chapter 16: Graphing Functions 347
Graphing with a Table of Values 348 (1/2)
Graphing with a Table of Values 348 (2/2)
Domain and Range of a Function 354 (1/2)
Domain and Range of a Function 354 (2/2)
Symmetry 360
Fundamental Function Graphs365
Graphing Functions Using Transformations 369
Absolute Value Functions 374
Chapter 17: Calculating Roots of Functions 379
Identifying Rational Roots 380
Leading Coefficient Test 384
Descartes’ Rule of Signs 388
Rational Root Test 390
Synthesizing Root Identification Strategies 394
Chapter 18: Logarithmic Functions 399
Evaluating Logarithmic Expressions 400
Graphs of Logarithmic Functions 402
Common and Natural Logarithms 406
Change of Base Formula 409
Logarithmic Properties 412
Chapter 19: Exponential Functions 417
Graphing Exponential Functions 418
Composing Exponential and Logarithmic Functions 423
Exponential and Logarithmic Equations 426 (1/2)
Exponential and Logarithmic Equations 426 (2/2)
Exponential Growth and Decay 433 (1/2)
Exponential Growth and Decay 433 (2/2)
Chapter 20: Rational Expressions 439
Simplifying Rational Expressions 440
Adding and Subtracting Rational Expressions 444 (1/2)
Adding and Subtracting Rational Expressions 444 (2/2)
Multiplying and Dividing Rational Expressions 452
Simplifying Complex Fractions 457
Graphing Rational Functions 459 (1/2)
Graphing Rational Functions 459 (2/2)
Chapter 21: Rational Equations and Inequalities 465
Proportions and Cross Multiplication 466
Solving Rational Equations 470
Direct and Indirect Variation 475
Solving Rational Inequalities 479 (1/2)
Solving Rational Inequalities 479 (2/2)
Chapter 22: Conic Sections 487
Parabolas 488 (1/2)
Parabolas 488 (2/2)
Circles 494
Ellipses 499 (1/2)
Ellipses 499 (2/2)
Hyperbolas 506 (1/2)
Hyperbolas 506 (2/2)
Chapter 23: Word Problems 515
Determining Unknown Values 516
Calculating Interest 521
Geometric Formulas 525
Speed and Distance 529
Mixture and Combination 534
Work 538 (1/2)
Work 538 (2/2)
Appendix A: Algebraic Properties 545
Appendix B: Important Graphs and Graph Transformations 547
Appendix C: Key Algebra Formulas 551
Index 555 (1/3)
Index 555 (2/3)
Index 555 (3/3)
Search in book...
Toggle Font Controls
Playlists
Add To
Create new playlist
Name your new playlist
Playlist description (optional)
Cancel
Create playlist
Sign In
Email address
Password
Forgot Password?
Create account
Login
or
Continue with Facebook
Continue with Google
Sign Up
Full Name
Email address
Confirm Email Address
Password
Login
Create account
or
Continue with Facebook
Continue with Google
Prev
Previous Chapter
Algebraic Properties 11 (1/2)
Next
Next Chapter
Chapter 2: Rational Numbers 17
Add Highlight
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click
here
login for view all page.
Day Mode
Cloud Mode
Night Mode
Reset