Fundamental Operations with Numbers | p. 1 |

Four Operations | p. 1 |

System of Real Numbers | p. 2 |

Graphical Representation of Real Numbers | p. 2 |

Properties of Addition and Multiplication of Real Numbers | p. 3 |

Rules of Signs | p. 3 |

Exponents and Powers | p. 4 |

Operations with Fractions | p. 4 |

Fundamental Operations with Algebraic Expressions | p. 12 |

Algebraic Expressions | p. 12 |

Terms | p. 12 |

Degree | p. 13 |

Grouping | p. 13 |

Computation with Algebraic Expressions | p. 13 |

Properties of Numbers | p. 22 |

Sets of Numbers | p. 22 |

Properties | p. 22 |

Additional Properties | p. 23 |

Special Products | p. 27 |

Special Products | p. 27 |

Products Yielding Answers of the Form a[superscript n plus or minus]b[superscript n] | p. 28 |

Factoring | p. 32 |

Factoring | p. 32 |

Factorization Procedures | p. 33 |

Greatest Common Factor | p. 34 |

Least Common Multiple | p. 34 |

Fractions | p. 41 |

Rational Algebraic Fractions | p. 41 |

Operations with Algebraic Fractions | p. 42 |

Complex Fractions | p. 43 |

Exponents | p. 48 |

Positive Integral Exponent | p. 48 |

Negative Integral Exponent | p. 48 |

Roots | p. 48 |

Rational Exponents | p. 49 |

General Laws of Exponents | p. 49 |

Scientific Notation | p. 50 |

Radicals | p. 58 |

Radical Expressions | p. 58 |

Laws for Radicals | p. 58 |

Simplifying Radicals | p. 58 |

Operations with Radicals | p. 59 |

Rationalizing Binomial Denominators | p. 60 |

Simple Operations with Complex Numbers | p. 67 |

Complex Numbers | p. 67 |

Graphical Representation of Complex Numbers | p. 67 |

Algebraic Operations with Complex Numbers | p. 68 |

Equations in General | p. 73 |

Equations | p. 73 |

Operations Used in Transforming Equations | p. 73 |

Equivalent Equations | p. 74 |

Formulas | p. 74 |

Polynomial Equations | p. 75 |

Ratio, Proportion, and Variation | p. 81 |

Ratio | p. 81 |

Proportion | p. 81 |

Variation | p. 81 |

Unit Price | p. 82 |

Best Buy | p. 82 |

Functions and Graphs | p. 89 |

Variables | p. 89 |

Relations | p. 89 |

Functions | p. 89 |

Function Notation | p. 90 |

Rectangular Coordinate System | p. 90 |

Function of Two Variables | p. 91 |

Symmetry | p. 91 |

Shifts | p. 92 |

Scaling | p. 93 |

Using a Graphing Calculator | p. 93 |

Linear Equations in One Variable | p. 114 |

Linear Equations | p. 114 |

Literal Equations | p. 114 |

Word Problems | p. 115 |

Equations of Lines | p. 128 |

Slope of a Line | p. 128 |

Parallel and Perpendicular Lines | p. 129 |

Slope-Intercept form of Equation of a Line | p. 130 |

Slope-Point Form of Equation of a Line | p. 130 |

Two-point Form of Equation of a Line | p. 130 |

Intercept Form of Equation of a Line | p. 131 |

Simultaneous Linear Equations | p. 137 |

Systems of Two Linear Equations | p. 137 |

Systems of Three Linear Equations | p. 138 |

Quadratic Equations in One Variable | p. 150 |

Quadratic Equations | p. 150 |

Methods of Solving Quadratic Equations | p. 150 |

Sum and Product of the Roots | p. 152 |

Nature of the Roots | p. 152 |

Radical Equations | p. 152 |

Quadratic-type Equations | p. 153 |

Conic Sections | p. 169 |

General Quadratic Equations | p. 169 |

Conic Sections | p. 170 |

Circles | p. 170 |

Parabolas | p. 171 |

Ellipses | p. 173 |

Hyperbolas | p. 177 |

Graphing Conic Sections with a Calculator | p. 180 |

Systems of Equations Involving Quadratics | p. 191 |

Graphical Solution | p. 191 |

Algebraic Solution | p. 191 |

Inequalities | p. 199 |

Definitions | p. 199 |

Principles of Inequalities | p. 199 |

Absolute Value Inequalities | p. 200 |

Higher Degree Inequalities | p. 200 |

Linear Inequalities in Two Variables | p. 202 |

Systems of Linear Inequalities | p. 202 |

Linear Programming | p. 203 |

Polynomial Functions | p. 214 |

Polynomial Equations | p. 214 |

Zeros of Polynomial Equations | p. 214 |

Solving Polynomial Equations | p. 216 |

Approximating Real Zeros | p. 218 |

Rational Functions | p. 235 |

Rational Functions | p. 235 |

Vertical Asymptotes | p. 235 |

Horizontal Asymptotes | p. 235 |

Graphing Rational Functions | p. 236 |

Graphing Rational Functions using a Graphing Calculator | p. 238 |

Sequences and Series | p. 245 |

Sequences | p. 245 |

Arithmetic Sequences | p. 245 |

Geometric Sequences | p. 245 |

Infinite Geometric Series | p. 246 |

Harmonic Sequences | p. 246 |

Means | p. 246 |

Logarithms | p. 263 |

Definition of a Logarithm | p. 263 |

Laws of Logarithms | p. 263 |

Common Logarithms | p. 264 |

Using a Common Logarithm Table | p. 264 |

Natural Logarithms | p. 265 |

Using a Natural Logarithm Table | p. 265 |

Finding Logarithms Using a Calculator | p. 266 |

Applications of Logarithms and Exponents | p. 276 |

Introduction | p. 276 |

Simple Interest | p. 276 |

Compound Interest | p. 277 |

Applications of Logarithms | p. 278 |

Applications of Exponents | p. 280 |

Permutations and Combinations | p. 288 |

Fundamental Counting Principle | p. 288 |

Permutations | p. 288 |

Combinations | p. 289 |

Using a Calculator | p. 290 |

The Binomial Theorem | p. 303 |

Combinatorial Notation | p. 303 |

Expansion of (a + x)[superscript n] | p. 303 |

Probability | p. 310 |

Simple Probability | p. 310 |

Compound Probability | p. 310 |

Mathematical Expectation | p. 311 |

Binomial Probability | p. 311 |

Conditional Probability | p. 311 |

Determinants | p. 323 |

Determinants of Second Order | p. 323 |

Cramer's Rule | p. 323 |

Determinants of Third Order | p. 324 |

Determinants of Order n | p. 326 |

Properties of Determinants | p. 327 |

Minors | p. 328 |

Value of a Determinant of Order n | p. 328 |

Cramer's Rule for Determinants of Order n | p. 328 |

Homogeneous Linear Equations | p. 329 |

Matrices | p. 349 |

Definition of a Matrix | p. 349 |

Operations With Matrices | p. 349 |

Elementary Row Operations | p. 351 |

Inverse of a Matrix | p. 352 |

Matrix Equations | p. 353 |

Matrix Solution of a System of Equations | p. 354 |

Mathematical Induction | p. 362 |

Principle of Mathematical Induction | p. 362 |

Proof by Mathematical Induction | p. 362 |

Partial Fractions | p. 368 |

Rational Fractions | p. 368 |

Proper Fractions | p. 368 |

Partial Fractions | p. 368 |

Identically Equal Polynomials | p. 369 |

Fundamental Theorem | p. 369 |

Finding the Partial Fraction Decomposition | p. 370 |

Table of Common Logarithms | p. 375 |

Table of Natural Logarithms | p. 379 |

Index | p. 383 |

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