beginalgebra_contents

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Ch. 1 Introduction to Algebraic Expressions

1.1 Introduction to Algebra
1 Evaluate Algebraic Expression in One Variable
2 Evaluate Algebraic Expression in Two Variables
3 Solve Apps: Evaluate Algebraic Expression
4 Translate Verbal Exprn to Algebraic Exprn I
5 Translate Verbal Exprn to Algebraic Exprn II
6 Determine Whether Number is Solution of Eqn
7 Translate Word Problem to Equation

1.2 The Commutative, Associative, and Distributive Laws
1 Use Commutative Law of Addition
2 Use Commutative Law of Multiplication
3 Use Associative Law of Addition
4 Use Associative Law of Multiplication
5 *Write Equiv Expressions Using Comm/Assoc Laws
6 *Show Equivalence Using Comm/Assoc Laws
7 Use Distributive Law to Multiply
8 List Terms in Expression
9 Use Distributive Law to Factor

1.3 Fraction Notation
1 List Factors of Number
2 Find Prime Factorization of Number
3 Reduce Fraction
4 Multiply Fractions
5 Divide Fractions
6 Add Fractions
7 Subtract Fractions

1.4 Positive and Negative Real Numbers
1 Solve Apps: Identify Real Number in Situation
2 Graph Rational Number on Number Line
3 Find Decimal Notation for Fraction
4 Write True Sentence Using "<" or ">"
5 Write Equivalent Inequality
6 Classify Inequality as True or False
7 Find Absolute Value
8 Identify Numbers

1.5 Addition of Real Numbers
1 Add Two Integers
2 Add Signed Fractions and Decimals
3 Add More Than Two Real Numbers
4 Solve Apps: Add Real Numbers
5 Combine Like Terms
6 Find Perimeter of Figure

1.6 Subtraction of Real Numbers
1 Find Opposite or Additive Inverse
2 Find -x Given x
3 Find -(-x) Given x
4 Express Subtraction Verbally
5 Subtract Integers
6 Subtract Fractions and Decimals
7 Translate to Mathematical Language
8 Simplify Expression with Addition/Subtraction
9 Identify Terms in Expression
10 Combine Like Terms
11 Solve Applications: Subtraction

1.7 Multiplication and Division of Real Numbers
1 Multiply Integers
2 Multiply Fractions and Decimals
3 Divide Real Numbers
4 Write Negative Fractional Exprn in Equiv Forms
5 Find Reciprocal
6 Add Fractions
7 Subtract Fractions
8 Multiply Fractions
9 Divide Fractions

1.8 Exponential Notation and Order of Operations
1 Write Product Using Exponential Notation
2 Simplify Exponential Expression
3 Use Order of Operations (No Grouping)
4 Use Order of Operations (Grouping)
5 Evaluate Expression Given Value of Variable
6 Write Equivalent Expression w/o Parentheses
7 Remove Parentheses and Combine Like Terms
8 *Know Concepts: Algebraic Expressions I
9 *Know Concepts: Algebraic Expressions II
10 *Know Concepts: Algebraic Expressions III
11 *Know Concepts: Algebraic Expressions IV
12 *Know Concepts: Algebraic Expressions V
13 *Know Concepts: Algebraic Expressions VI
14 *Know Concepts: Algebraic Expressions VII

Ch. 2 Equations, Inequalities, and Problem Solving

2.1 Solving Equations
1 Solve Equation Using Addition Principle
2 Solve Equation Using Multiplication Principle
3 Tech: Solve Equation Using Calculator

2.2 Using the Principles Together
1 Solve Equation (Two Steps)
2 Solve Equation (More Than Two Steps)
3 Solve Equation with Fractions or Decimals
4 Solve Equation with Parentheses

2.3 Formulas
1 Solve Apps: Use Formula
2 Solve Formula for Variable
3 ^Solve Formula for Variable

2.4 Applications with Percent
1 Write Percent as Decimal
2 Write Decimal as Percent
3 Write Fraction as Percent
4 Calculate Percent of Number
5 Find Number Given Percent of Number
6 Find What Percent One Number is of Another
7 Solve Apps: Percent
8 ^Solve Apps: Percent

2.5 Problem Solving
1 Solve Apps: Numbers
2 Solve Apps: Geometry
3 Solve Apps: Miscellaneous

2.6 Solving Inequalities
1 Determine Whether Number is Soln of Inequal
2 Graph Inequality on Number Line
3 Describe Graph Using Set-Builder Notation
4 Solve Inequality Using Add Principle and Graph
5 Solve Inequality Using Mult Princ and Graph
6 Solve Inequal Using Both Principles and Graph
7 Solve Inequality Using Dist Property and Graph

2.7 Solving Applications with Inequalities
1 Translate Sentence to Algebraic Inequality
2 Solve Apps: Geometry
3 Solve Apps: Formulas
4 Solve Apps: Miscellaneous
5 *Know Concepts: Eqns, Inequal, Prob Solv I
6 *Know Concepts: Eqns, Inequal, Prob Solv II
7 *Know Concepts: Eqns, Inequal, Prob Solv III

Ch. 3 Introduction to Graphing

3.1 Reading Graphs, Plotting Points, and Estimating Values
1 Solve Apps: Analyze Bar, Circle, Line Graphs
2 Plot Points on Coordinate Axes
3 Find Coordinates of Point
4 Determine in Which Quadrant Point is Located
5 Identify Quadrant by Signs of Coordinates
6 Solve Apps: Display Data in Line Graph
7 Solve Apps: Estimate/Predict Using Line Graph

3.2 Graphing Linear Equations
1 Determine Whether Ordered Pair is Soln of Eqn
2 *Verify/Find Solutions of Equation
3 Graph Linear Equation
4 Solve Apps: Solve by Graphing

3.3 Graphing and Intercepts
1 Find x- and y-Intercepts from Graph
2 Find x- and y-Intercepts from Equation
3 Find Intercepts and Graph Equation
4 Graph Horizontal or Vertical Line Given Eqn
5 Write Eqn of Horiz or Vert Line Given Graph

3.4 Rates
1 Solve Apps: Find Rate of Change
2 Solve Apps: Draw Linear Graph
3 Solve Apps: Use Graph to Calc Rate of Change

3.5 Slope
1 Solve Apps: Find Rate of Change from Graph
2 Find Slope from Graph
3 Find Slope of Line from Pair of Points
4 Find Slope of Horizontal or Vertical Line
5 Solve Apps: Slope and Grade

3.6 Slope-Intercept Form
1 Draw Line Given Slope and y-Intercept
2 Find Slope and y-Intercept of Line
3 Find Slope-Intercept Eqn Given Slope/Intercept
4 Graph Linear Equation
5 Solve Apps: Find/Interpret Equation of Line
6 Determine Whether Lines are Parallel

3.7 Point-Slope Form
1 Write Point-Slope Eqn Given Point and Slope
2 Write Slope-Intercept Eqn Given Slope, Point
3 Graph Line Given Point and Slope
4 Graph Line Expressed in Point-Slope Form
5 Know Concepts: Introduction to Graphing I
6 Know Concepts: Introduction to Graphing II
7 Know Concepts: Introduction to Graphing III

Ch. 4 Polynomials

4.1 Exponents and Their Properties
1 Multiply Expressions with Exponents
2 Divide Expressions with Exponents
3 Simplify Expression with Zero Exponent
4 Raise Term to Power
5 Raise Fraction to Power

4.2 Polynomials
1 Identify Terms of Polynomial
2 Determine Coefficient and Degree of Each Term
3 Determine Coefficient/Degree of Leading Term
4 Classify as Monomial, Binomial, Trinomial, or None
5 Combine Like Terms
6 Evaluate Polynomial
7 Solve Apps: Estimate Polynomial Value from Graph
8 Solve Apps: Polynomials

4.3 Addition and Subtraction of Polynomials
1 Add Polynomials
2 Write Opposite of Polynomial
3 Subtract Polynomials
4 Solve Apps: Perimeter and Area

4.4 Multiplication of Polynomials
1 Multiply Monomials
2 Multiply Polynomial by Monomial
3 Multiply Binomials
4 *Draw Rectangle to Represent Product
5 Multiply Polynomials

4.5 Special Products
1 Multiply Binomials
2 Multiply Conjugate Binomials
3 Square Binomial
4 Multiply Polynomials
5 Solve Apps: Find Total Shaded Area

4.6 Polynomials in Several Variables
1 Evaluate Polynomial in Several Variables
2 Solve Apps: Polynomials in Several Variables
3 Identify Coefficient and Degree of Term
4 Identify Degree of Polynomial
5 Combine Like Terms
6 Add/Subtract Polynomials
7 Multiply Polynomials
8 Solve Apps: Find Polynomial Giving Shaded Area

4.7 Division of Polynomials
1 Divide by Monomial
2 Divide by Binomial I
3 Divide by Binomial II

4.8 Negative Exponents and Scientific Notation
1 Change Negative Exponent to Positive Exponent
2 Change Positive Exponent to Negative Exponent
3 Multiply Using Rules for Exponents
4 Divide Using Rules for Exponents
5 Raise to Power
6 Raise to Power (Rational Expression)
7 Convert to Decimal Notation
8 Convert to Scientific Notation
9 Multiply or Divide in Scientific Notation
10 Solve Apps: Scientific Notation
11 *Know Concepts: Exponents and Their Properties
12 *Know Concepts: Polynomials
13 *Know Concepts: Scientific Notation

Ch. 5 Polynomials and Factoring

5.1 Introduction to Factoring
1 Factor Monomial
2 Factor Out Greatest Common Factor
3 Factor Out Common Binomial Factor
4 Factor by Grouping

5.2 Factoring Trinomials of the Type x^2 + bx + c
1 Factor Trinomial of the Type x^2 + bx + c
2 Factor Trinomial with Monomial Factor
3 Factor Trinomial with Fractions/Decimals
4 Factor Trinomial with Two Variables

5.3 Factoring Trinomials of the Type ax^2 + bx + c
1 Factor Trinomial (Lead Coefficient not 1)
2 Factor Trinomial with Common Monomial Factor
3 Factor by Grouping
4 Factor Trinomial with Two Variables

5.4 Factoring Perfect-Square Trinomials and Differences of Squares
1 Determine Whether Trinomial is Perfect Square
2 Factor Trinomial Square
3 Factor Trinomial Square with Monomial Factor
4 Determine if Binomial is Difference of Squares
5 Factor Difference of Squares
6 Factor Difference of Squares with Monomial Factor
7 Factor Fourth-Degree Difference of Squares

5.5 Factoring: A General Strategy
1 ^Factor Binomial
2 ^Factor Trinomial
3 ^Factor Polynomial

5.6 Solving Quadratic Equations by Factoring
1 Solve Factored Eqn Using Principle of Zero Products
2 Solve Quad Eqn Using Principle of Zero Products I
3 Solve Quad Eqn Using Principle of Zero Products II
4 Use Graph to Solve Equation
5 Find x-Intercepts Given Graph of Equation

5.7 Solving Applications
1 Solve Apps: Number Problems
2 Solve Apps: Geometry
3 Solve Apps: Pythagorean Theorem
4 Solve Apps: Games, Handshakes
5 Solve Apps: Rocket Height
6 *Know Concepts: Factoring I
7 *Know Concepts: Factoring II
8 *Know Concepts: Factoring III

Ch. 6 Rational Expressions and Equations

6.1 Rational Expressions
1 List Numbers Where Expression is Undefined
2 Reduce Rational Expression

6.2 Multiplication and Division
1 Multiply (Leave Product in Factored Form)
2 Multiply Rational Expressions I
3 Multiply Rational Expressions II
4 Find Reciprocal
5 Divide Rational Expressions

6.3 Addition, Subtraction, and Least Common Denominators
1 Add/Subtract Fractions (Common Denominator)
2 Find Least Common Multiple of Numbers
3 Find Least Common Multiple of Expressions
4 Rewrite Expressions with Common Denominator

6.4 Addition and Subtraction with Unlike Denominators
1 Add/Subtract Rational Exprns (Monomial Denom)
2 Add/Subtract Rational Expressions
3 Add/Subtract Rational Exprns (Opposite Denoms)
4 Add/Subtract More Than Two Rational Exprns

6.5 Complex Rational Expressions
1 Simplify Complex Rational Expression I
2 Simplify Complex Rational Expression II

6.6 Solving Rational Equations
1 Solve Rational Eqn (Monomial Denominators)
2 Solve Rational Equation
3 Solve Equation with Three Terms

6.7 Applications Using Rational Equations and Proportions
1 Solve Apps: Find Number
2 Solve Apps: Work
3 Solve Apps: Distance
4 Solve Apps: Geometry
5 Solve Apps: Proportions
6 *Know Concepts: Rational Exprns and Eqns I
7 *Know Concepts: Rational Exprns and Eqns II
8 *Know Concepts: Rational Exprns and Eqns III

Ch. 7 Systems and More Graphing

7.1 Systems of Equations and Graphing
1 Determine Whether Ordered Pair is Solution
2 Solve Linear System by Graphing

7.2 Systems of Equations and Substitution
1 Solve by Substitution
2 Solve Apps: Numbers
3 Solve Apps: Geometry

7.3 Systems of Equations and Elimination
1 Solve by Elimination
2 Solve Apps: Elimination

7.4 More Applications Using Systems
1 Solve Apps: Total Value
2 Solve Apps: Mixtures
3 ^Solve Apps: Investments

7.5 Linear Inequalities in Two Variables
1 Determine Whether Ordered Pair is a Solution
2 Graph Linear Inequality in Two Variables

7.6 Systems of Linear Inequalities
1 Graph Solution of System (Two Inequalities)
2 Graph Solution (More Than Two Inequalities)

7.7 Direct and Inverse Variation
1 Find Equation of Direct Variation
2 Find Equation of Inverse Variation
3 Solve Apps: Direct Variation
4 Solve Apps: Inverse Variation
5 *Know Concepts: Systems and More Graphing I
6 *Know Concepts: Systems and More Graphing II
7 *Know Concepts: Systems and More Graphing III
8 *Know Concepts: Systems and More Graphing IV
9 *Know Concepts: Systems and More Graphing V
10 *Know Concepts: Systems and More Graphing VI

Ch. 8 Radical Expressions and Equations

8.1 Introduction to Square Roots and Radical Expressions
1 Find Square Root
2 Simplify Square Root of Perfect Square
3 Identify Radicand
4 Classify Square Root as Rational or Irrational
5 Tech: Approximate Square Root
6 Simplify Square Root of Variable Expression
7 Solve Apps: Formulas

8.2 Multiplying and Simplifying Radical Expressions
1 Multiply Radical Expressions I
2 Simplify Radical Expression
3 Multiply Radical Expressions II
4 Solve Apps: Formulas

8.3 Quotients Involving Square Roots
1 Simplify Quotient of Radical Expressions
2 Rationalize Denominator to Simplify Quotient
3 Solve Apps: Formulas

8.4 More Operations with Radicals
1 Add or Subtract Radical Expressions
2 Multiply Radical Expressions
3 Rationalize Denominator and Simplify

8.5 Radical Equations
1 Solve Equation with One Radical
2 Solve Apps: Radical Equations

8.6 Applications Using Right Triangles
1 Find Side of Right Triangle
2 Solve Apps: Right Triangles

8.7 Higher Roots and Rational Exponents
1 Simplify Higher Root
2 Simplify Exprn with Positive Rational Exponent
3 Simplify Exprn with Negative Rational Exponent
4 *Know Concepts: Radical Exprns and Eqns I
5 *Know Concepts: Radical Exprns and Eqns II
6 *Know Concepts: Radical Exprns and Eqns III
7 *Know Concepts: Radical Exprns and Eqns IV

Ch. 9 Quadratic Equations

9.1 Solving Quadratic Equations: The Principle of Square Roots
1 Solve Equation Using Square Root Principle I
2 Solve Equation Using Square Root Principle II

9.2 Solving Quadratic Equations: Completing the Square
1 Complete the Square
2 Solve Quadratic Eqn by Completing the Square

9.3 The Quadratic Formula and Applications
1 Solve Quadratic Equation
2 Tech: Use Quadratic Formula and Calculator
3 Solve Apps: Geometry
4 Solve Apps: Free-Fall and Interest

9.4 Formulas and Equations
1 Solve Formula for Variable (Linear)
2 Solve Formula for Variable (Rational)
3 Solve Formula for Variable (Radical)
4 Solve Formula for Variable (Quadratic)

9.5 Complex Numbers as Solutions of Quadratic Equations
1 Express Complex Number in Terms of i
2 Solve Quadratic Equation

9.6 Graphs of Quadratic Equations
1 Graph Quadratic Equation
2 Find Vertex of Parabola
3 Find Intercepts of Parabola

9.7 Functions
1 Determine Whether Correspondence is a Function
2 Evaluate Function
3 Solve Apps: Functions
4 Graph Function
5 Use Vertical Line Test
6 *Know Concepts: Quadratic Equations I
7 *Know Concepts: Quadratic Equations II
8 *Know Concepts: Quadratic Equations III
9 *Know Concepts: Quadratic Equations IV