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| College Algebra Online |
MAT 105 (College Algebra)
By Kunio Mitsuma, Ph.D.
Please bookmark this page. It will expand as we progress.
| Chapter P | Chapter 1 | Chapter 2 | Chapter 3 | Chapter 5 |
| Chapter P Prerequisites |
| Section |
Topic |
Title |
| P.1 |
P.1.1 |
Number System |
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P.1.2 |
Inequalities and Interval Notations |
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P.1.3 |
Absolute Value |
| P.2 |
P.2.1 |
Exponents |
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P.2.2 |
Scientific Notation |
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P.2.3 |
Radicals |
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P.2.4 |
Simplifying Radicals |
| P.3 |
P.3.1 |
Polynomials and Special Products |
| P.4 |
P.4.1 |
Factoring Polynomials |
| P.5 |
P.5.1 |
Rational Expressions (Multiplication & Division) |
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P.5.2 |
Rational Expressions (Addition & Subtraction) |
| P.6 |
P.6.1 |
(NOT covered) Errors and the Algebra of Calculus |
| P.7 |
P.7.1 |
Quadrants of the xy-plane |
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P.7.2 |
The Distance Formula |
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P.7.3 |
The Midpoint Formula |
| Chapter P | Chapter 1 | Chapter 2 | Chapter 3 | Chapter 5 |
| Chapter 1 Equations, Inequalities, and Mathematical Modeling |
| Section |
Topic |
Title |
| 1.1 |
1.1.1 |
x-intercept, y-intercept |
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1.1.2 |
Circles |
| 1.2 |
1.2.1 |
Linear Equations in One Variable |
| 1.3 |
1.3.1 |
(NOT covered) Modeling with Linear Equations |
| 1.4 |
1.4.1 |
Quadratic Equations and Discriminant |
| 1.5 |
1.5.1 |
Complex Numbers |
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1.5.2 |
Complex Numbers—Division |
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1.5.3 |
Powers of i |
| 1.6 |
1.6.1 |
(NOT covered) Other Types of Equations |
| 1.7 |
1.7.1 |
(NOT covered) Linear Inequalities in One Variable |
| 1.8 |
1.8.1 |
(NOT covered) Other Types of Inequalities |
| Chapter P | Chapter 1 | Chapter 2 | Chapter 3 | Chapter 5 |
| Chapter 2 Functions and Their Graphs |
| Section |
Topic |
Title |
| 2.1 |
2.1.1 |
Intercepts |
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2.1.2 |
Slope of a Line |
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2.1.3 |
Types of Lines |
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2.1.4 |
Parallel & Perpendicular Lines |
| 2.2 |
2.2.1 |
Functions |
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2.2.2 |
Domain of a Function |
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2.2.3 |
Difference Quotient |
| 2.3 |
2.3.1 |
Vertical Line Test |
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2.3.2 |
Zeros of a Function |
| 2.4 |
2.4.1 |
A Library of Parent Functions (10 functions and their graphs to memorize) |
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2.4.2 |
Piecewise-Defined Functions |
| 2.5 |
2.5.1 |
Flip about the x-axis |
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2.5.2 |
Vertical Shifts |
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2.5.3 |
Horizontal Shifts |
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2.5.4 |
Sharpness of a Graph |
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2.5.5 |
A Combination of All Transformations |
| 2.6 |
2.6.1 |
Combinations of Functions: Composite Functions |
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2.6.2 |
Composite Functions |
| 2.7 |
2.7.1 |
Horizontal Line Test |
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2.7.2 |
How to Find the Inverse of a Function and How to Graph it |
| Chapter P | Chapter 1 | Chapter 2 | Chapter 3 | Chapter 5 |
| Chapter 3 Polynomial Functions |
| Section |
Topic |
Title |
| 3.1 |
3.1.1 |
Quadratic Functions—Three Forms |
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3.1.2 |
Quadratic Functions—General Form |
| 3.2 |
3.2.1 |
Polynomial Functions of Higher Degree |
| 3.3 |
3.3.1 |
Polynomial and Synthetic Division |
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3.3.2 |
Remainder & Factor Theorems |
| 3.4 |
3.4.1 |
Polynomials with Real Zeros (Rational Zero Test) |
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3.4.2 |
Polynomials with Complex Zeros (Complex Conjugate Revisited) |
| 3.5 |
3.5.1 |
(NOT covered) Mathematical Modeling and Variation |
| Chapter P | Chapter 1 | Chapter 2 | Chapter 3 | Chapter 5 |
| Chapter 5 Exponential and Logarithmic Functions |
| Section |
Topic |
Title |
| 5.1 |
5.1.1 |
Exponential Functions and Their Graphs (various bases) |
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5.1.2 |
Exponential Functions and Their Graphs (shifts) |
| 5.2 |
5.2.1 |
Logarithmic Functions and Their Graphs |
| 5.3 |
5.3.1 |
Properties of Logarithms |
| 5.4 |
5.4.1 |
Exponential Equations |
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5.4.2 |
Exponential Equations (Quadratic Form) |
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5.4.3 |
Logarithmic Equations |
| 5.5 |
5.5.5 |
(NOT covered) Exponential and Logarithmic Models |
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Disclaimer • Updated
September 4, 2008
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