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