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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