| |
| |
| Introduction | |
| |
| |
| |
| Preliminaries and Basic Operations | |
| |
| |
| Preliminaries | |
| |
| |
| Groups of numbers | |
| |
| |
| Ways to show multiplication | |
| |
| |
| Common math symbols | |
| |
| |
| Properties of Basic Mathematical Operations | |
| |
| |
| Some properties (axioms) of addition | |
| |
| |
| Some properties (axioms) of multiplication | |
| |
| |
| A property of two operations | |
| |
| |
| Multiplying and Dividing Using Zero | |
| |
| |
| Powers and Exponents | |
| |
| |
| Squares and cubes | |
| |
| |
| Operations with powers and exponents | |
| |
| |
| Square Roots and Cube Roots | |
| |
| |
| Cube roots | |
| |
| |
| Approximating square roots | |
| |
| |
| Simplifying square roots | |
| |
| |
| Grouping Symbols | |
| |
| |
| Parentheses () | |
| |
| |
| Brackets [] and braces [] | |
| |
| |
| Order of operations | |
| |
| |
| Divisibility Rules | |
| |
| |
| |
| Signed Numbers, Fractions, and Percents | |
| |
| |
| Signed Numbers (Positive Numbers and Negative Numbers) | |
| |
| |
| Number lines | |
| |
| |
| Addition of signed numbers | |
| |
| |
| Subtraction of signed numbers | |
| |
| |
| Minus preceding parenthesis | |
| |
| |
| Multiplying and dividing signed numbers | |
| |
| |
| Fractions | |
| |
| |
| Negative fractions | |
| |
| |
| Adding positive and negative fractions | |
| |
| |
| Subtracting positive and negative fractions | |
| |
| |
| Multiplying fractions | |
| |
| |
| Canceling | |
| |
| |
| Multiplying mixed numbers | |
| |
| |
| Dividing fractions | |
| |
| |
| Dividing complex fractions | |
| |
| |
| Dividing mixed numbers | |
| |
| |
| Simplifying Fractions and Complex Fractions | |
| |
| |
| Decimals | |
| |
| |
| Changing terminating decimals to fractions | |
| |
| |
| Changing fractions to decimals | |
| |
| |
| Changing infinite repeating decimals to fractions | |
| |
| |
| Important equivalents that can save you time | |
| |
| |
| Percent | |
| |
| |
| Changing decimals to percents | |
| |
| |
| Changing percents to decimals | |
| |
| |
| Changing fractions to percents | |
| |
| |
| Changing percents to fractions | |
| |
| |
| Finding the percent of a number | |
| |
| |
| Other applications of percent | |
| |
| |
| Percent--proportion method | |
| |
| |
| Scientific Notation | |
| |
| |
| Multiplication in scientific notation | |
| |
| |
| Division in scientific notation | |
| |
| |
| |
| Terminology, Sets, and Expressions | |
| |
| |
| Some Basic Language | |
| |
| |
| Understood multiplication | |
| |
| |
| Letters to be aware of | |
| |
| |
| Set Theory | |
| |
| |
| Special sets | |
| |
| |
| Describing sets | |
| |
| |
| Types of sets | |
| |
| |
| Comparing sets | |
| |
| |
| Operations with sets | |
| |
| |
| Variables and Algebraic Expressions | |
| |
| |
| Evaluating Expressions | |
| |
| |
| |
| Equations, Ratios, and Proportions | |
| |
| |
| Equations | |
| |
| |
| Axioms of equality | |
| |
| |
| Solving equations | |
| |
| |
| Literal equations | |
| |
| |
| Ratios and Proportions | |
| |
| |
| Ratios | |
| |
| |
| Proportions | |
| |
| |
| Solving proportions for value | |
| |
| |
| |
| Equations with Two Variables | |
| |
| |
| Solving Systems of Equations (Simultaneous Equations) | |
| |
| |
| Addition/subtraction method | |
| |
| |
| Substitution method | |
| |
| |
| Graphing method | |
| |
| |
| |
| Monomials, Polynomials, and Factoring | |
| |
| |
| Monomials | |
| |
| |
| Adding and subtracting monomials | |
| |
| |
| Multiplying monomials | |
| |
| |
| Dividing monomials | |
| |
| |
| Working with negative exponents | |
| |
| |
| Polynomials | |
| |
| |
| Adding and subtracting polynomials | |
| |
| |
| Multiplying polynomials | |
| |
| |
| Dividing polynomials by monomials | |
| |
| |
| Dividing polynomials by polynomials | |
| |
| |
| Factoring | |
| |
| |
| Factoring out a common factor | |
| |
| |
| Factoring the difference between two squares | |
| |
| |
| Factoring polynomials having three terms of the form ax[superscript 2] + bx + c | |
| |
| |
| Factoring by grouping | |
| |
| |
| |
| Algebraic Fractions | |
| |
| |
| Operations with Algebraic Fractions | |
| |
| |
| Reducing algebraic fractions | |
| |
| |
| Multiplying algebraic fractions | |
| |
| |
| Dividing algebraic fractions | |
| |
| |
| Adding or subtracting algebraic fractions | |
| |
| |
| |
| Inequalities, Graphing, and Absolute Value | |
| |
| |
| Inequalities | |
| |
| |
| Axioms and properties of inequalities | |
| |
| |
| Solving inequalities | |
| |
| |
| Graphing on a Number Line | |
| |
| |
| Graphing inequalities | |
| |
| |
| Intervals | |
| |
| |
| Absolute Value | |
| |
| |
| Solving equations containing absolute value | |
| |
| |
| Solving inequalities containing absolute value and graphing | |
| |
| |
| |
| Coordinate Geometry | |
| |
| |
| Coordinate Graphs | |
| |
| |
| Graphing equations on the coordinate plane | |
| |
| |
| Slope and intercept of linear equations | |
| |
| |
| Graphing linear equations using slope and intercept | |
| |
| |
| Finding the equation of a line | |
| |
| |
| Linear Inequalities and Half-Planes | |
| |
| |
| Open half-plane | |
| |
| |
| Closed half-plane | |
| |
| |
| |
| Functions and Variations | |
| |
| |
| Functions | |
| |
| |
| Relations | |
| |
| |
| Domain and range | |
| |
| |
| Defining a function | |
| |
| |
| Graphs of functions | |
| |
| |
| Graphs of relationships that are not functions | |
| |
| |
| Determining domain, range, and if the relation is a function | |
| |
| |
| Finding the values of functions | |
| |
| |
| Variations | |
| |
| |
| Direct variation | |
| |
| |
| Inverse variation (indirect variation) | |
| |
| |
| |
| Roots and Radicals | |
| |
| |
| Simplifying Square Roots | |
| |
| |
| Operations with Square Roots | |
| |
| |
| Under a single radical sign | |
| |
| |
| When radical values are alike | |
| |
| |
| When radical values are different | |
| |
| |
| Addition and subtraction of square roots after simplifying | |
| |
| |
| Products of nonnegative roots | |
| |
| |
| Quotients of nonnegative roots | |
| |
| |
| |
| Quadratic Equations | |
| |
| |
| Solving Quadratic Equations | |
| |
| |
| Factoring | |
| |
| |
| The quadratic formula | |
| |
| |
| Completing the square | |
| |
| |
| |
| Word Problems | |
| |
| |
| Solving Technique | |
| |
| |
| Key Words and Phrases | |
| |
| |
| Simple Interest | |
| |
| |
| Compound Interest | |
| |
| |
| Ratio and Proportion | |
| |
| |
| Percent | |
| |
| |
| Percent Change | |
| |
| |
| Number Problems | |
| |
| |
| Age Problems | |
| |
| |
| Motion Problems | |
| |
| |
| Coin Problems | |
| |
| |
| Mixture Problems | |
| |
| |
| Work Problems | |
| |
| |
| Number Problems with Two Variables | |
| |
| |
| CQR Review | |
| |
| |
| CQR Resource Center | |
| |
| |
| Glossary | |
| |
| |
| Index | |