Last edited by Edward D Laughbaum
June 5, 2011 | History
Learning Algebra II (Intermediate Algebra) is made simpler by using pedagogical and curricular techniques based on basic brain function and the mathematical notion of function behaviors and function representation. Long-term memory, recall, and understanding of the algebra are accomplished through neural responses to the use of daily connections, early use of visualizations, meaning added through contextual situations, and pattern-building to a generalization.
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Book Details
Table of Contents
CHAPTER ONE
NUMBERS
1.0 Introduction and Numbers 1
1.1 Properties of Numbers, Equality, and Inequality 5
1.2 Data Analysis 20
Basic Brain Function – A Beginning 26
1.3 Describing Sets of Numbers with Interval Notation 27
Basic Brain Function – Connections 38
1.4 Notation for Big and Little Numbers 39
Chapter Test 47
CHAPTER TWO
REPRESENTATION AND BEHAVIOR OF FUNCTIONS
2.0 Introduction 49
Basic Brain Function – Can Algebra be Simple? 52
2.1 Data Relationships Represented Numerically and Graphically 53
2.2 Data Relationships Represented Symbolically 61
Basic Brain Function – What’s with the Prefrontal Lobes Stuff? 74
2.3 Geometric Behaviors of Data Relationships 75
Basic Brain Function – Visualizations I 90
2.4 Functions Represented Graphically 91
Chapter Test 100
CHAPTER THREE
COMMON BEHAVIORS OF FUNCTIONS
3.0 Introduction to Geometric Behaviors of Functions 101
3.1 An Introduction to the Analysis of the Linear Function 102
3.2 An Introduction to the Analysis of the Quadratic Function 115
3.3 An Introduction to the Analysis of the Absolute Value Function 128
Basic Brain Function – Generalizing 138
3.4 An Introduction to the Analysis of the Square Root Function 139
3.5 An Introduction to the Analysis of the Exponential Function 149
Chapter Test 155
CHAPTER FOUR
FUNCTIONS: NOTATION AND OPERATIONS
4.0 Introduction 156
4.1 Definition of a Function, Again 158
4.2 Addition and Subtraction of Polynomial Functions 171
4.3 Multiplication of Polynomial Functions 180
Basic Brain Function – Visualizations II 193
4.4 Factoring: Common Factors, Grouping, and Difference of Squares 194
4.5 Factoring the Trinomial 205
Basic Brain Function – Unconscious Processing 214
4.6 Function Operations from a Graphical Perspective 215
Chapter Test 224
CHAPTER FIVE
ADVANCED ANALYSIS OF THE LINEAR FUNCTION
5.0 Introduction and Review of the Function 225
5.1 Rate of Change, Initial Condition, and the Zero --
Slope and Intercepts of the Linear Function 228
Basic Brain Function – Distributed Learning 239
5.2 Slope-Intercept Method of Graphing 240
5.3 Point-Slope Form: 245
5.4 The Linear Function as a Mathematical Model 256
Chapter Test 267
CHAPTER SIX
EQUATIONS AND INEQUALITIES
6.0 Introduction 269
6.1 Solving Equations Containing the Linear Function 271
Basic Brain Function – Connections Revisited 284
6.2 Solving Inequalities Containing the Linear Function 285
6.3 Solving Inequalities and Equations Containing the Absolute Value Function 294
6.4 Formulas and Direct Variation 309
Chapter Test 321
Basic Brain Function – Learning 322
CHAPTER SEVEN
ADVANCED ANALYSIS OF THE EXPONENTIAL FUNCTION
7.0 Introduction 323
7.1 The Exponential Function 325
7.2 Simplifying Symbols in Exponential Functions 342
7.3 Equations and Inequalities Containing the Exponential Function 352
Basic Brain Function – Enriched Environment 360
7.4 The Exponential Function as a Mathematical Model 361
Chapter Test 372
CHAPTER EIGHT
ANALYSIS OF THE RATIONAL FUNCTION
8.0 Introduction 373
8.1 Rational Functions 375
8.2 The Fundamental Property of Rational Functions 390
8.3 Multiplication and Division of Rational Functions 398
8.4 Addition and Subtraction of Rational Functions and Simplification
of Complex Rational Functions 405
8.5 Solving Equations and Inequalities Containing the Rational Function and
Inverse Variation 419
Chapter Test 434
CHAPTER NINE
ADVANCED ANALYSIS OF THE SQUARE ROOT FUNCTION
9.0 Introduction 435
9.1 The Square Root Function 437
9.2 Properties of Irrational Expressions 449
9.3 Operations with Irrational Expressions 458
9.4 Fractional Exponents 466
9.5 Solving Equations Containing the Square Root Function 472
9.6 The Square Root Function as a Mathematical Model 483
Basic Brain Function – Graphing Technology 492
Chapter Test 493
CHAPTER TEN
ADVANCED ANALYSIS OF THE QUADRATIC FUNCTION
10.0 Introduction 494
10.1 The Quadratic Function 496
Basic Brain Function – Attention 508
10.2 Solving Quadratic Equations of the Form (ax + b)(cx + d) = 0 509
10.3 Solving Quadratic Equations by the Completing-the-Square Method 514
10.4 Solving Quadratic Equations with the Quadratic Formula 522
10.5 The Quadratic Function as a Mathematical Model 533
Chapter Test 540
CHAPTER ELEVEN
BASIC GEOMETRY
11.0 Introduction 541
11.1 The Distance and Midpoint Formulas 542
11.2 Triangles 552
11.3 Parallelograms 562
11.4 Circles 568
Chapter Test 577
CHAPTER TWELVE
BASIC TRIGONOMETRY
12.0 Introduction 578
12.1 Conversions between Degrees and Radians 580
12.2 Trigonometric Definitions 590
12.3 Solving Right Triangles 601
12.4 Trigonometric Functions as Mathematical Models 609
Basic Brain Function – Practice Practice Practice 615
Chapter Test 616
CHAPTER THIRTEEN
SYSTEMS OF EQUATIONS AND INEQUALITIES
13.0 Introduction to Systems of Equations 617
Basic Brain Function – The Role of Dopamine 618
13.1 Solving Systems Graphically 619
13.2 Solving Systems by the Addition and Substitution Methods 629
13.3 Solving Systems Using Cramer's Rule and Matrices 639
13.4 Modeling with Systems of Equations 656
Chapter Test 670
CHAPTER FOURTEEN
INTRODUCTION TO THE ANALYSIS OF THE LOGARITHMIC FUNCTION
14.0 Introduction 671
14.1 The Logarithmic Function 673
14.2 Properties of Logarithms 685
14.3 Solving Logarithmic and Exponential Equations 697
Basic Brain Function – Meaning and Understanding 704
14.4 The Logarithmic Function as a Mathematical Model 705
Chapter Test 718
Answers to selected odd exercises I
Index XIX
Edition Notes
The Physical Object
Edition Identifiers
Work Identifiers
Work Description
Algebra approached through function (instead of equation) to capitalize on basic brain function to enhance long-term memory, recall, and understanding of algebra.
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