Intermediate Algebra

Slice 1 Fundamentals 1.1 Integer and Rational Numbers 1.2 Integer, Rational, and Irrational Numbers 1.3 Evaluation of a Linear Expression in Two Variables 1.4 Evaluation of a Polynomial in One Variable 1.5 Writing a Linear Equation 1.6 Writing an Inequality 1.7 Writing a Compound Inequality 1.8 Properties of Addition 1.9 Properties of Real Numbers Slice 2 Solving Linear Equations 2.1 Addition Property of Equality: Problem Type 1 2.2 Addition Property of Equality: Problem Type 2 2.3 Addition Property of Equality: Problem Type 3 2.4 Multiplication Property of Equality: Problem Type 1 2.5 Multiplication Property of Equality: Problem Type 2 2.6 Solving a Linear Equation: Problem Type 1 2.7 Solving a Linear Equation: Problem Type 2 2.8 Solving a Linear Equation: Problem Type 3 2.9 Solving a Linear Equation with Several Occurrences of the Variable: Problem Type 1 2.10 Solving a Linear Equation with Several Occurrences of the Variable: Problem Type 2 2.11 Solving a Linear Equation with Several Occurrences of the Variable: Problem Type 3 2.12 Solving a Linear Equation with Several Occurrences of the Variable: Problem Type 4 2.13 Solving a Linear Equation with Several Occurrences of the Variable: Problem Type 5 2.14 Word Problem on Linear Equations: Problem Type 1 2.15 Word Problem on Linear Equations: Problem Type 2 2.16 Solving a Linear Equality: Problem Type 1 2.17 Solving a Linear Equality: Problem Type 2 2.18 Solving a Linear Equality: Problem Type 3 2.19 Solving a Linear Equality: Problem Type 4 2.20 Graphing a Linear Inequality on a Number Line 2.21 Graphing a Compound Linear Inequality on a Number Line 2.22 Word Problem with Linear Inequalities 2.23 Solving a Linear Equation with Absolute Value: Problem Type 1 2.24 Solving a Linear Equation with Absolute Value: Problem Type 2 2.25 Solving a Linear Inequality with Absolute Value 2.26 Graphing a Linear Inequality with Absolute Value on a Number Line 2.27 Word Problem on Proportions: Problem Type 1 2.28 Word Problem on Proportions: Problem Type 2 2.29 Word Problem with Percent and Money: Problem Type 1 2.30 Word Problem with Percent and Money: Problem Type 2 2.31 Solving a System of Linear Equations 2.32 Inconsistent System of Linear Equations 2.33 Word Problem on Systems of Linear Equations: Problem Type 1 2.34 Word Problem on Systems of Linear Equations: Problem Type 2 2.35 Word Problem on Systems of Linear Equations: Problem Type 3 2.36 Word Problem on Systems of Linear Equations: Problem Type 4 Slice 3 Graphing Linear Equations 3.1 Reading a Point in the Coordinate Plane 3.2 Marking a Point in the Coordinate Plane 3.3 Midpoint of a Line Segment in the Plane 3.4 Solutions to a Linear Equation in Two Variables: Problem Type 1 3.5 Solutions to a Linear Equation in Two Variables: Problem Type 2 3.6 Graphing a Line Given the X- and Y-Intercepts 3.7 Graphing a Line Given the Equation in Slope-Intercept Form 3.8 Graphing a Line Given the Equation in Standard Form 3.9 Graphing the Line through a Given Point with a Given Slope 3.10 Graphing a Vertical or Horizontal Line 3.11 Y-Intercept of a Line 3.12 X- and Y-Intercepts of a Line Given the Equation in Standard Form 3.13 Writing the Equation of a Line Given the Slope and the Y-Intercept 3.14 Writing the Equation of a Line Given the Slope and a Point 3.15 Writing the Equation of the Line through Two Given Points 3.16 Writing the Equation of Vertical and Horizontal Lines through a Given Point 3.17 Writing the Equation of the Line through a Given Point and Parallel to a Given Line 3.18 Writing the Equation of the Line through a Given Point and Perpindicular to a Given Line 3.19 Graphing a Linear Inequality in the Plane: Problem Type 1 3.20 Graphing a Linear Inequality in the Plane: Problem Type 2 3.21 Graphing a Linear Equation with Absolute Value in the Plane 3.22 Graphing a System of Linear Equations 3.23 Graphing a System of Linear Inequalities 3.24 Distance between Two Points in the Plane Slice 4 Sets, Relations, and Functions 4.1 Definition of a Set by Extension and by a Property Satisfied by its Elements 4.2 Inclusion of Sets 4.3 Union of Sets 4.4 Intersection of Sets 4.5 Difference of Sets 4.6 Cartesian Product of Sets 4.7 Representation of a Cartesian Product in the Plane 4.8 Concept of Relation 4.9 Domain and Range of a Relation 4.10 Representation of a Relation in the Plane 4.11 Inverse of a Relation 4.12 Graph of the Inverse of a Relation 4.13 Concept of a Function 4.14 Domain of a Real Function 4.15 Range of a Real Function 4.16 One-to-One Functions 4.17 Inverse of a One-to-One Function 4.18 Sum of Two Linear Functions 4.19 Product of Two Linear Functions 4.20 Quotient of Two Linear Functions 4.21 Composition of Two Functions 4.22 Vertical Translation of the Graph of a Function 4.23 Horizontal Translation of the Graph of a Function Slice 5 Exponents and Rational Expressions 5.1 Restriction on the Variable in a Denominator 5.2 Ordering Fractions 5.3 Word Problem on Proportions: Problem Type 3 5.4 Additive Law of Exponents 5.5 Multiplicative Law of Exponents and negative Exponents 5.6 Substitution and Laws of Exponents: Problem Type 1 5.7 Substitution and Laws of Exponents: Problem Type 2 5.8 Additive Law of Exponents in a Multivariate Monomial 5.9 Multiplying Rational Expressions 5.10 Dividing Rational Expressions 5.11 Complex Fraction: Problem Type 1 5.12 Complex Fraction: Problem Type 2 5.13 Adding Rational Expressions with a Common Denominator 5.14 Adding Rational Expressions with Different Denominators 5.15 Adding Rational Expressions 5.16 Ratio of Multivariate Polynomials 5.17 Algebraic Symbol Manipulation 5.18 Solving a Simple Equation with Rational Expressions: Problem Type 1 5.19 Solving a Simple Equation with Rational Expressions: Problem Type 2 5.20 Solving a Simple Equation with Rational Expressions: Problem Type 3 5.21 Solving an Equation with Rational Expressions: Problem Type 1 5.22 Solving an Equation with Rational Expressions: Problem Type 2 5.23 Solving an Equation with Rational Expressions: Problem Type 3 5.24 Word Problem on Direct Variation 5.25 Word Problem on Inverse Variation Slice 6 Polynomials and Quadratic Equations 6.1 Addition of Polynomials 6.2 Multiplication of Monomials 6.3 Multiplication of Two Binomials 6.4 Squaring a Binomial 6.5 Multiplication of Polynomials 6.6 Degree of a Multivariate Polynomial 6.7 Division of a Polynomial by a Binomial with no Remainder 6.8 Division of a Polynomial by a Binomial with Remainder 6.9 Greatest Common Factor of Two Monomials 6.10 Least Common Multiple of Two Monomials 6.11 Factoring a Multivariate by Grouping: Problem Type 1 6.12 Factoring a Multivariate by Grouping: Problem Type 2 6.13 Factoring a Quadratic Trinomial with Leading Coefficient 1 6.14 Factoring a Quadratic Trinomial with Leading Coefficient Greater than 1 6.15 Factoring a Perfect Square 6.16 Completing the Square 6.17 Factoring the Product of a Quadratic Trinomial with a Monomial 6.18 Factoring the Difference of Two Squares 6.19 Factoring the Difference of Two Fourth Powers 6.20 Factoring the Sum and Difference of Two Cubes 6.21 Ratio of Quadratic Polynomials: Problem Type 1 6.22 Ratio of Quadratic Polynomials: Problem Type 2 6.23 Ratio of Quadratic Polynomials: Problem Type 3 6.24 Roots of a Quadratic Equation with Leading Coefficient 1 6.25 Roots of a Quadratic Equation with Leading Coefficient Greater than 1 6.26 Roots of a Product of Polynomials 6.27 Roots of a Sum of Polynomials 6.28 Even-Root Property 6.29 Odd-Root Property 6.30 Writing a Quadratic Equation GiBergman, Barry is the author of 'Intermediate Algebra' with ISBN 9780072530766 and ISBN 0072530766.