California Reveal Math, Algebra 1
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California Reveal Math, Algebra 1
11 chapters, 122 skills
▶
California Reveal Math, Algebra 1
11 chapters, 122 skills
Unit 1: Using Expressions and Equations
- Factoring a Variable from Multiple Terms to Isolate It
- Solving One-Variable Equations with Letter Coefficients
- Special Cases: Identities and No-Solution Equations
- Properties of Triangle Congruence
- Introduction to Accuracy in Modeling
- Common Error: Evaluating Multi-Variable Metric Expressions
- Additive and Multiplicative Inverse Properties
- Substitution Property of Equality
- Absolute Value Equations: Isolating the Absolute Value First
- Introduction to Descriptive Modeling
- Constructing and Comparing Metric Expressions
- Writing Absolute Value Equations from Context
Unit 2: Relations and Functions
- Sketching Graphs Using Key Features
- Choosing Appropriate Axis Scales and Origins for Graphing Relations
- Finding the Line of Symmetry by Checking Equidistant Points
- Identifying Functions from Relations Using Tables and Mapping Diagrams
- Identifying Continuous and Discrete Functions
- Continuous vs. Discrete Domains
- Domain and Range from a Graph
- Evaluating a Function Using Function Notation
- Repeated Outputs vs. Repeated Inputs: What Breaks a Function?
- Neither Continuous nor Discrete: Hybrid and Step Graphs
- Solving Equations by Graphing Related Functions
- Identifying Relative Extrema and Turning Points
- Comparing Key Features of Two Functions
- Identifying Linear vs. Nonlinear Functions from an Algebraic Expression
Unit 3: Linear and Nonlinear Functions
- Plotting Ordered Pairs: Keeping x and y in the Right Order
- Evaluating Piecewise Functions at Specific x-Values
- Rate of Change from Graphs and Tables
- Reflections of Linear Functions Across Axes
- Converting Absolute Value Functions to Piecewise Linear Form
- Parent Function of Linear Functions and Introduction to Transformations
- Arithmetic Sequences as Linear Functions and Discrete Graphs
- Graphing f(x)=a|x-h|+k Using Vertex and Slope
- Domain, Range, and Axis of Symmetry from Vertex
Unit 4: Creating Linear Equations
- Slope-Intercept Form: y = mx + b
- Writing an Equation from Any Two Points
- Slope of an Inverse Linear Function: Reciprocal, Not Negative Reciprocal
- Correlation Coefficient r: Strength, Direction, and Thresholds
- Correlation vs. Causation
- Four-Step Algebraic Method for Finding Inverses of Linear Functions
- Inverse Function Notation: f⁻¹(x) Is Not a Reciprocal
- Point-Slope Form: Definition and Structure
- Interpreting Inverse Functions in Real-World Contexts
Unit 5: Linear Inequalities
Unit 6: Systems of Linear Equations and Inequalities
- Application: Feasible Regions and Integer Solutions
- Application: Solving Word Problems with Substitution
- Special Cases in Elimination with Multiplication
- Elimination by Multiplying Both Equations
- Application: Modeling Real-World Problems as Systems of Equations
- Avoiding Distribution Errors in Substitution
- Special Cases After Elimination: Dependent and Inconsistent Systems
Unit 7: Exponents and Roots
- Sums and Products of Rational and Irrational Radical Expressions
- Simplifying nth Root Radicals
- Power of a Quotient Property
- Recognizing When Common Bases Are Impossible and Logarithms Are Needed
- Summary of Core Exponent Properties
- Distributing Rational Exponents Over Products and Quotients
- Power of a Power Property
- Solving Equations with Fractional Exponents
- Error Analysis: Correctly Equating Exponents Using the Power Property
Unit 8: Exponential Functions
- Domain, Range, Intercepts, and End Behavior of Exponential Functions
- Converting Explicit to Recursive Rules (Arithmetic & Geometric)
- Evaluating Terms Iteratively from a Recursive Rule
- Vertical Dilation and Reflection: f(x) = ab^x
- Horizontal Translations of Exponential Functions
- Identifying Geometric Sequences by Checking Consecutive Ratios
- Identifying Exponential Growth vs. Decay from Context
- Vertical Translations of Exponential Functions
- Graphing Exponential Functions: Table of Values and Smooth Curve
- Exponential Transformations in Non-Financial Contexts
- Reflections of Exponential Functions: X-Axis vs. Y-Axis
- Introduction to Recursive Rules for Sequences
- Horizontal Dilation of Exponential Functions
- Exponential Growth vs. Decay: Identifying Base b
Unit 9: Polynomials
- Multiplying Binomials Using FOIL
- Solving Equations with Monomial Distribution
- Closure Property of Polynomials Under Multiplication
- Distributing a Negative Monomial Over a Polynomial
- General Factoring Strategy for Binomials and Trinomials
- Multiply Polynomials Using the Box Method
- Special Cases: Perfect Square Trinomials and Prime Polynomials
- Additive Inverses in Grouping: Factor Out −1 to Match Binomials
- Factoring Out the GCF Before Factoring a Trinomial
Unit 10: Quadratic Functions
- Vertex as Minimum or Maximum Value
- Vertical and Horizontal Translations of Quadratic Functions
- Number of Solutions in a Linear-Quadratic System
- Combining Multiple Transformations in Vertex Form
- Predicting with Models: Interpolation vs. Extrapolation
- Solving Quadratic Equations by Factoring: ac Method
- Solving Quadratic Equations by Factoring Perfect Square Trinomials
- Reflections of Quadratic Functions Across Axes
- Vertical Stretches and Compressions of Quadratic Functions
- End Behavior of Quadratic Functions
- Intercepts and Symmetry Points of a Quadratic Function
- Solving Quadratic Equations by Factoring out the GCF
- Shifting to Years-Since-Baseline for Modeling
- Applying the Negative Sign in the Axis of Symmetry Formula
- Writing Functions from Tables
- Writing a Quadratic Function from Its Zeros
- Solving Quadratic Equations by Difference of Squares
- Function Multiplication vs. Function Composition
- Subtracting Functions and the Negative Trap
- Solving by Completing the Square (a ≠ 1): Full Solution
- Rewriting a Quadratic Equation in Standard Form
- Real-World Applications: Completing the Square for Maximum Height and Range
- No Real Solutions When Completing the Square
- Applying the Quadratic Formula with Decimal and Non-Integer Coefficients
Unit 11: Statistics
- Conditional Relative Frequencies & The Grand-Total Trap
- Linear Transformations of Data: Effects on Statistics
- Interpreting Associations Between Variables
- Constructing and Interpreting Box Plots
- Interpreting Standard Deviation with the Empirical Guideline
- Constructing and Comparing Double Displays
- Bar Graph vs. Histogram: Choosing the Correct Display
- The Effect of Outliers on Statistics
- Using Technology to Compute and Compare
Saxon Algebra 1
12 chapters, 676 skills
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Saxon Algebra 1
12 chapters, 676 skills
Chapter 1: Real Numbers and Basic Operations
- Adding and Subtracting Real Numbers
- Adding Numbers With the Same Sign
- Rules for Subtracting Real Numbers
- Variable
- Intersection and Union
- Evaluating Algebraic Expressions
- Coefficient
- Unit Analysis
- Order of Operations
- Understanding Variables and Expressions
- Opposites
- Finding Absolute Value and Adding Real Numbers
- Using Unit Analysis to Convert Measures
- Product Property of Exponents
- Classifying Real Numbers
- Symbols of Inclusion
- Using Order of Operations
- Simplifying Expressions Using the Product Property of Exponents
- Evaluating Algebraic Expressions with Exponents
- Fractions Act As Grouping Symbols
- Hierarchy of Real Number Subsets
- Absolute Value
- The Language of Algebra
- Converting Units of Volume
- Counterexamples
- Rules For Adding Integers
- Order of magnitude
- Converting Units of Area
- Simplifying Expressions with Rational Numbers
- Closed
- Adding And Subtracting Signed Numbers
- Application: Phone Charges
- Simplifying and Comparing Expressions with Symbols of Inclusion
- Application:Dive Depth
- Terms of an expression
- What Is An Exponent?
- Expressions with Absolute-Value Symbols
- Foundations of Algebra
- Evaluating and Comparing Algebraic Expressions
- Simplifying Expressions with Exponents
- Application: Half Price Sale
- Comparing Algebraic Expressions
- Ordering Rational Numbers
- Adding Numbers With Different Signs
Chapter 2: Algebraic Expressions and Equations
- Coordinate plane
- Theoretical Probability
- Identity Property
- Multiplying Signed Numbers
- Dividing Signed Numbers
- Independent and dependent variables
- The Distributive Property
- Square root
- Simplifying and Evaluating Variable Expressions
- Associative Property
- Using the Properties of Real Numbers to Simplify Expressions
- Application in Real-World Problems
- "Less than" phrases
- Dividing Positive and Negative Fractions
- Solving Fraction Equations
- Algebraic Expressions
- Exponents And Order Of Operations
- Simplifying Before Evaluating
- Subtraction Property of Equality
- Complement Of An Event
- Perfect square
- Estimating Square Roots to the Nearest Integer
- Sample Space
- Inverse Operations
- Raising a Number to a Power
- Combining Like Terms With Exponents
- Welcome to Algebra: The Power of Inverse Operations
- Multiplying and Dividing Real Numbers
- Algebra 1: The Language of Relationships
- Addition Property of Equality
- Application: Savings
- Translating Words into Algebraic Expressions
- Commutative Property
- Solutions to an equation with two variables
- Like terms
- The Language of Algebra
- Translating Algebraic Expressions into Words
- Using the Distributive Property to Simplify Expressions
- Comparing Expressions With Square Roots
- Distributing Negative Numbers
- Using Formulas In Real Life
- Solving One-Step Equations by Adding or Subtracting
- Combining Like Terms Without Exponents
- The Power of Algebra: From Numbers to Symbols
- Distributing with Variables and Exponents
- Graphing relationships
- Application: Consumer Math
- Evaluating Variable Expressions
- Application: Measurement
Chapter 3: Functions and Graphing
- Like terms
- Literal equation
- Combining like terms first
- Vertical-Line Test
- Distributing a sneaky negative
- Identifying the Domain and Range
- Domain and Range
- Application: Zoology
- Solving Equations with Fractions
- Identifying Misleading Representations of Data
- Solving Two-Step Equations
- Identity
- Misleading Line Graphs
- Solving Literal Equations
- Inverse Operations
- Solving for a Variable
- Multiplication Property of Equality
- Solving Decimal Equations
- Reciprocal
- Interpreting Double-Bar Graphs
- Stem-and-leaf plot
- Clearing Decimals With Powers Of 10
- Solving Decimal Equations Directly
- Variables on both sides
- Solving Equations with Variables on Both Sides
- Vertical line test
- Inverse operations
- Example Card：Determining If a Set of Ordered Pairs Is a Function
- Misleading Circle Graphs
- Solving for Variables on Both Sides
- Verify
- Welcome to Algebra: The Power of Functions
- Finding a Part of a Number
- No solution equations
- Differentiating Between Relations and Functions
- Circle graph
- Solving One-Step Equations by Multiplying or Dividing
- Solving a Formula for a Variable
- Using Tables to Graph Functions
- Solving Equations with Grouping Symbols
- Linear equation
- Division Property of Equality
- Bar graphs
- Analyzing and Comparing Statistical Graphs
- Function
- Misleading Bar Graphs
- Function Notation
- Solving Multi-Step Equations
- Solving word problems
- Solving with Negative Coefficients
Chapter 4: Linear Equations and Proportions
- Arithmetic Sequence Formula
- Solving Proportions Using Cross Products
- Finding the n-th Term of an Arithmetic Sequence
- Arithmetic sequence
- Independent and Dependent Events
- Simplifying Expressions Using the GCF
- Power of a Power Property
- Multiplying with Scientific Notation
- Ratios of the Perimeter, Area, and Volume of Similar Figures
- Power of a Quotient Property
- Finding x- and y-intercepts
- Simplifying and Evaluating Expressions Using the Power Property of Exponents
- Graphing Using Intercepts
- Simplifying with Negative Exponents
- Factoring a Polynomial
- Prime Factorization of Numbers
- Arithmetic Sequences
- Distributing Over Addition
- Product Property of Exponents
- Similar
- Writing and Solving Proportions
- Finding Unit Rates
- Exploring Zero and Negative Exponents
- Scale drawing
- Using Rates, Ratios, and Proportions
- Greatest common factor (GCF)
- Dependent events
- Independent events
- Quotient Property of Exponents
- Definition of Odds
- Algebraic Expressions and Their Properties
- Scientific Notation
- Solving Multi-Step Proportions
- Interpreting Intercepts in Real-World Context
- The Power of Algebraic Representation
- Converting Rates
- Scale factor
- Power of a Product Property
- Simplifying Algebraic Fractions
- Locating and Using Intercepts
- Standard Form of a Linear Equation
- Rational expression
- Using the Distributive Property to Simplify Rational Expressions
- Dividing with Scientific Notation
Chapter 5: Inequalities and Linear Systems
- Slope-Intercept Form of an Equation
- Simplifying Rational Expressions
- Simplifying Rational Expressions
- Rate of change
- Welcome to Algebra 1: The Language of Relationships
- What Is a Percent?
- Range of A Set of Data
- Translating Inequalities into Words
- Special Slopes
- Application: Calculating Wages and Finances
- Graphing Inequalities
- Slope of a line
- Analyzing Measures of Central Tendency
- Modeling Real-World Problems
- Finding the Percent of Increase or Decrease
- Welcome to Algebra 1: The Language of Problem-Solving
- Identifying Solutions to Inequalities
- Horizontal and vertical lines
- Writing an Equation From a Graph
- Simplifying Expressions with Square Roots and Higher-Order Roots
- Using a Proportion
- Principal Square Root and Notation
- When Rational Expressions are Undefined
- Writing an Inequality from a Graph
- Slope
- Welcome to Algebra: The Language of Patterns
- Fractional Exponents
- Measure Of Central Tendency
- Graphing Inequalities
- Higher-Order Roots
- Writing Equations in Slope-Intercept Form
- Rate of Change
- Using an Equation to Find a Percentage
- Application: Finding Markups and Discounts
- Finding Slope Using the Slope Formula
- Caution
- Graphing with Slope-Intercept
- Inequality
- Even roots of negative numbers
- Translating Sentences into Inequalities
- Outlier
- Solving Real-World Problems
- Introduction to Algebra: The Language of Symbols
Chapter 6: Polynomials and Factoring
- Direct Variation
- Example Card: Multiplying Binomials Using the FOIL Method
- Application: Play Tickets
- Solving Systems by Graphing
- Example Card: Product of a Sum and Difference
- Example Card: Finding the LCM of Polynomials
- Box-and-whisker plot
- Example Card: Application Problem
- Example Card: Multiplying Binomials Using the Distributive Property
- Example Card: Finding the LCM of Two Numbers
- Example Card: Solving a Word Problem with Direct Variation
- Multiplying A Binomial And A Trinomial
- Multiplying Monomials And Polynomials
- Example Card: Squaring a Binomial
- Displaying Data in a Box-and-Whisker Plot
- Mental Math
- Simplifying Expressions with Integer Exponents
- Solving Systems of Linear Equations by Graphing
- Identifying Excluded Values
- Using the Distributive Property
- Application: Rate Plans
- LCM of Algebraic Expressions
- Solving systems by graphing
- Solving Systems of Linear Equations by Substitution
- Simplifying Rational Expressions with Like Denominators
- The FOIL Method
- Solving Systems of Linear Equations by Graphing
- Solution of a system of linear equations
- Outlier
- Square of a Binomial
- Adding and Subtracting Polynomials
- Like terms
- Example Card: Verifying a Solution
- Solution of a system of linear equations
- Sum and Difference
- Identifying Direct Variation from Ordered Pairs
- Example Card: Solving by Graphing
- Degree of a monomial
- Finding Special Products of Binomials
- Example Card: Solving a System by Graphing
- Simplifying Rational Expressions
- Example Card: Rearranging Before Substitution
- The Classic Binomial Blunder
- Finding the Least Common Multiple
- LCM of Polynomials
- Real-World LCM: Scheduling
- Point-Slope Form
- Example Card: Identifying and Displaying Outliers
- Graphing a Direct Variation
- Application: Rate Plans
- Rearrange Before Substitution
- Example Card: Displaying Data in a Box-and-Whisker Plot
- Steps for Solving by Substitution
- Writing an Equation Given a Point
- Least Common Multiple
- Lines for Real-World Problems
- Example Card: Identifying Direct Variation in an Equation
- Standard form of a polynomial
- Multiplying Polynomials
- Determining the Equation of a Line Given Two Points
- Identifying, Writing, and Graphing Direct Variation
- Writing an Equation from Two Points
- Graphing with a Point and Slope
- Example Card: Verifying a Solution
Chapter 7: Rational Expressions and Radicals
- Inclusive events
- Example Card: Combining Like Radicals
- Example Card: Finding the Probability of Mutually Exclusive Events
- Writing Equations of Parallel and Perpendicular Lines
- Example Card: Solving a Dependent System
- Key
- Displaying Data in Stem-and-Leaf Plots and Histograms
- Like Radicals
- Constant of variation
- Example Card: Multiplying by a Negative Number
- Example Card: Using the Addition Property of Inequality
- Writing Equations of a Perpendicular Line
- Example Card: Elimination Using Multiplication
- Applied Probability in Surveys
- Slopes of Perpendicular Lines
- Example Card: Writing Equations of Parallel Lines
- Simplifying With Variables
- Example Card: Dividing by a Negative Number
- Example Card: Making a Stem-and-Leaf Plot
- Inverse variation
- Consistent and Independent
- Addition Property of Inequality
- Simplifying Radical Expressions
- Product Property of Radicals
- Division Property of Inequality for c < 0
- Simplifying With Perfect Squares
- Example Card: Simplifying Before Combining
- Slopes of Parallel Lines
- Mutually exclusive events
- Elimination by Addition
- Example Card: Elimination by Adding Equations
- Writing Equations of Parallel Lines
- Application: Coin Collecting
- Example Card: Finding the Probability of Inclusive Events
- Example Card: Writing Equations of Perpendicular Lines
- Solving Inequalities by Multiplying or Dividing
- Relative frequency
- Subtraction Property of Inequality
- Multiplication Property of Inequality for c > 0
- Checking Inequality Solutions
- Solving Systems of Linear Equations by Elimination
- Histogram
- Example Card: Simplifying With Perfect Squares
- Division Property of Inequality for c > 0
- Example Card: Simplifying With Variables
- Simplifying Before Combining
- Example Card: Using the Product Rule
- Graphing Inequality Solutions
- Simplifying With Prime Factors
- Multiplying to Create Opposites
- Mutually Exclusive and Inclusive Events
- Combining Like Radicals
- Dependent Systems
- Product Rule for Inverse Variation
- Stem-and-leaf plot
- Inconsistent Equations
- Solving and Classifying Special Systems of Linear Equations
- Example Card: Analyzing a Stem-and-Leaf Plot
- Example Card: Solving an Inconsistent System
- Elimination by Subtraction
- Example Card: Using the Subtraction Property of Inequality
- Solving Inequalities by Adding or Subtracting
- Adding and Subtracting Radical Expressions
- Example Card: Identifying an Inverse Variation
- Multiplication Property of Inequality for c < 0
- Identifying, Writing, and Graphing Inverse Variation
Chapter 8: Advanced Factoring and Functions
- Example Card: Solving Multi-Step Inequalities with Simplification
- Asymptote
- Factoring Out The GCF
- Flipping The Inequality Sign
- Frequency distribution
- Solving Two-Step and Multi-Step Inequalities
- Line of best fit
- Solving a Conjunction
- Trend line
- Compound Inequality
- Example Card: Calculating a Line of Best Fit
- Calculating Frequency Distributions
- Absolute-value equation
- Example Card: Multiplying Binomials with Radicals
- Calculating Probability
- Factoring with Two Variables
- Example Card: Solving a Disjunction
- Example Card: Graphing a Scatter Plot and Trend Line
- Example Card: Factoring when b and c are Positive
- Graphing Using Asymptotes
- Rearranging Before Factoring
- Factoring Trinomials: $ax^2 + bx + c$
- Negative Leading Coefficient
- Scatter plot
- Example Card: Factoring When c is Positive
- Factoring Trinomials: Positive C
- Factoring With Positive Terms
- Applying the Distributive Property
- Example Card: Determining Excluded Values
- Example Card: Identifying Asymptotes
- Solving Two-Step Inequalities
- Example Card: Factoring when c is Negative
- Example Card: Solving Inequalities by Reversing the Sign
- Solving Compound Inequalities
- Example Card: Isolating the Absolute-Value Expression
- Example Card: Factoring with a Negative Leading Coefficient
- Factoring With Multiple Variables
- Rational function
- Graphing Rational Functions
- Example Card: Graphing Frequency and Experimental Probability
- Correlation
- Standard Form First
- Example Card: Factoring When c is Negative
- Factoring Trinomials by Using the GCF
- Compound event
- Simplifying Before Solving
- Isolate Before You Calculate
- The Two-Path Solution
- Factoring Trinomials: $x^2 + bx + c$
- Multiplying Binomials with Radicals
- Example Card: Factoring with a GCF
- Special Cases: Zero and Negatives
- Factoring With a Negative C
- Factoring With Two Variables
- Making and Analyzing Scatter Plots
- Factoring Trinomials: Negative C
- Disjunction
- Example Card: Solving a Basic Absolute-Value Equation
- Example Card: Simplifying Products of Radicals
- Rearranging Terms before Factoring
- Product Property of Radicals
- Determining Excluded Values
- Example Card: Finding Outcomes of a Compound Event
- Multiplying Radical Expressions
- Solving Absolute-Value Equations
- Example Card: Solving a Conjunction (Phone Bill)
- Clearing Fractions With The Lcm
Chapter 9: Quadratic Functions and Equations
- Factoring Special Products
- Example Card: Multiplying a Rational Expression by a Polynomial
- Example Card: Subtracting Expressions with Unlike Denominators
- Identifying Quadratic Functions
- Example Card: Subtracting Expressions with Common Denominators
- Quadratic function
- Example Card: Identifying a Quadratic Function
- Contradiction
- Example Card: Factoring with a Sign Change
- Pythagorean Theorem
- Axis of Symmetry Formula
- Example Card: Factoring the Difference of Two Squares
- Vertex of a parabola
- Pythagorean Triple
- Identity
- Example Card: Simplifying and Solving 'AND' Inequalities
- Multiplying Rational Expressions
- Multiplying and Dividing Rational Expressions
- Identifying Characteristics of Quadratic Functions
- Standard form of a quadratic function
- Adding and Subtracting Rational Expressions
- Factoring Trinomials by Grouping
- Caution
- Example Card: Finding the Midpoint of a Segment
- The Midpoint Formula
- Direction of a parabola
- Application: Transportation
- Difference of Two Squares
- Solving Inequalities with Variables on Both Sides
- Solving Inequalities with Variables on Both Sides
- Pythagorean Theorem on a Grid
- Changing Signs When Factoring
- Example Card: Factoring a Trinomial by Grouping
- Finding a Common Denominator
- Adding With Common Denominators
- Simplifying Each Side Before Solving
- Factor First to Simplify
- Solving Problems Using the Pythagorean Theorem
- Example Card: Finding the Distance Between Two Points
- Converse of the Pythagorean Theorem
- Example Card: Verifying a Pythagorean Triple
- Example Card: Simplifying Each Side Before Solving an Inequality
- Factoring in the Real World
- Example Card: Solving an Inequality with Variables on Both Sides
- Example Card: Finding Maximum Height Using the Axis of Symmetry
- Solving 'AND' Inequalities
- Example Card: Factoring a Perfect-Square Trinomial
- Factoring Polynomials by Grouping
- Solving Multi-Step Compound Inequalities
- Example Card: Finding a Missing Leg
- Factoring Polynomials by Grouping
- Example Card: Application with Averages
- The Distance Formula
- Zero of a function
- Example Card: Finding the Axis of Symmetry from Zeros
- Finding The Mean With Inequalities
- Example Card: Direction of a Parabola
- Dividing Rational Expressions
- Calculating the Midpoint and Length of a Segment
- Solving 'OR' Inequalities
- Perfect-Square Trinomials
- Example Card: Dividing Rational Expressions
Chapter 10: Systems and Problem Solving
- Dividing a polynomial by a binomial
- Example Card: Solving for y and Reversing the Inequality
- Example Card: Solving a Quadratic Equation by Factoring
- Solving Quadratic Equations by Factoring
- Graphing Quadratic Functions
- Up or Down Parabola
- Tricks for tricky divisions
- Solving Multi-Step Absolute-Value Equations
- Solution of a linear inequality
- Finding the Roots by Factoring Out the GCF
- Investments
- Example Card: Factoring to Simplify Complex Fractions
- Factoring to simplify
- Example Card: Dividing by a Binomial with Opposite Signs
- Solving 'Less Than' Absolute-Value Inequalities
- Combining fractions to simplify
- Example Card: Combining Terms Before Simplifying
- Solving Quadratics by Graphing
- Complex fractions
- Special Case Solutions
- Least Common Denominator
- The Boundary Line
- Graphing Linear Inequalities
- Special Cases: Impossible or Infinite Solutions
- Example Card: Finding Maximum Height
- Example Card: Adding Rational Expressions with Unlike Denominators
- Example Card: Solving an Absolute Value Equation with a Binomial
- Solving Quadratic Equations by Graphing
- Combining Rational Expressions with Unlike Denominators
- Extraneous solution
- Simplifying Complex Fractions
- Zero Product Property
- Example Card: Graphing a Quadratic Function
- Vertical Motion Model
- Solving Quadratic Equations by Factoring
- Application: Physics
- Dividing a polynomial using long division
- Example Card: Long Division with a Remainder
- Simplify by Factoring
- Example Card: Graphing to Find Two Solutions
- Solving work rate problems
- Solving Absolute-Value Inequalities
- One, Two, or No Real Solutions
- Example Card: Using the LCD to Solve Equations
- Example Card: Checking for Extraneous Solutions
- Dividing Polynomials
- Dividing a polynomial by a monomial
- Graphing Linear Inequalities
- Example Card: Factoring Out the GCF to Find Roots
- Rational equation
- Solving Rational Equations
- Solving 'Greater Than' Absolute-Value Inequalities
- Using the LCD to solve equations
- Graphing Quadratic Functions
- Example Card: Graphing a Linear Inequality
- Reverse the inequality
- Example Card: Rearranging and Graphing to Find One Solution
- Example Card: Solving with an Expression Inside
- Example Card: Subtracting and Simplifying Rational Expressions
- Zero of a function
- Solving Absolute-value Equations
- Adding with Unlike Denominators
Chapter 11: Advanced Topics in Algebra
- Geometric sequence
- Solving Absolute-Value Inequalities
- Example Card: Reflections and Stretches
- Recognizing and Extending Geometric Sequences
- Example Card: Solving a Rearranged Quadratic Equation
- Finding the nth Term of a Geometric Sequence
- Example Card: Application for an Object in Motion
- Application: Basketball
- Graphing Exponential Functions
- Example Card: Isolating the Radical First
- Solving $x^2 + bx = c$
- Example Card: Solving $ax^2 + c = 0$
- Graphing Systems of Linear Inequalities
- Application: Crafts
- Radicand
- Exponential Function
- Solving Multi-Step Absolute-Value Inequalities
- Using the Quadratic Formula
- Example Card: Translating the Vertex
- Real-world Systems
- Isolating the Square Root
- Quotient Property of Radicals
- Example Card: Identifying an Exponential Function
- Solving $ax^2 + bx = c$
- Example Card: Extending Geometric Sequences
- No Real Solution
- Absolute-value function
- Common ratio
- Translations of absolute-value graphs
- Graphing Absolute-Value Functions
- Solving by Graphing
- Quadratic Equation
- Application: Object in Motion
- Systems with Parallel Lines
- Quadratic Formula
- Example Card: Solving $x^2 = a$
- Example Card: Simplifying Before Rationalizing
- Example Card: Solving by Graphing
- Example Card: Graphing an Exponential Function
- Approximating Solutions
- Dividing Radical Expressions
- Identifying and Graphing Exponential Functions
- Example Card: Identifying Extraneous Solutions
- Solving Quadratic Equations Using Square Roots
- Rationalize the Denominator
- Dividing by a Negative Number
- Solving Radical Equations
- Example Card: Real-World Application
- Solving Quadratic Equations by Completing the Square
- Conjugate
- Solving $x^2 = a$
- Example Card: Finding the nth Term of a Geometric Sequence
- Extraneous Solutions
- Example Card：Solving $x^2 + bx = c$ by Completing the Square
- Vertex of an absolute-value graph
- Comparing Exponential Graphs
- Solving $ax^2 + c = 0$
- Completing the Square
- Identifying an Exponential Function
- Example Card: Using Conjugates to Rationalize
- Example Card：Solving $ax^2 + bx = c$ by Completing the Square
- Radical Equation
- Reflections and stretches
- System of linear inequalities
Chapter 12: Sequences and Special Functions
- Exponential Functions
- Permutation
- Example Card: Finding a Missing Side Using a Trig Ratio
- Example Card: Permutations vs. Combinations
- Finding Sides With Trig Ratios
- Solving by Graphing
- Fundamental Counting Principle
- Graphing Cubic Functions
- Example Card: Applying the Combination Formula
- Example Card: Solving Cubic Equations by Graphing
- Solving Using Substitution
- Solving Cubic Equations by Graphing
- Using the Discriminant
- Combination Formula
- Hint
- Double root
- SOH-CAH-TOA
- Solving Problems Involving Combinations
- Caution
- Domain
- Example Card: Finding the Total with Simple Interest
- Zeros
- Using Trigonometric Ratios
- Linear vs. Exponential Growth
- Finding Angles With Inverse Trig
- Compound interest
- Geometric Probability
- Example Card: Finding Probability Using the Complement
- Example Card: Using the Fundamental Counting Principle
- Factorial
- Example Card: Finding the Number of Permutations
- Number of System Solutions
- Example Card: Solving a System Using Substitution
- Reciprocal Trigonometric Ratios
- Example Card: Solving a System by Graphing
- Interpreting the Discriminant
- The complement of an event
- Solving Simple and Compound Interest Problems
- Graphing and Comparing Linear, Quadratic, and Exponential Functions
- Quadratic Functions
- Function Families
- Cubic Function
- Simple interest
- Solving Problems Involving Permutations
- Example Card: Finding the Number of Solutions
- Combination
- Example Card: Finding All Trig Ratios from Two Sides
- Discriminant
- Linear Functions
- Finding Probability With Combinations
- Example Card: The Power of Compounding
- Example Card: Determining the Domain of a Square-Root Function
- Graphing and Solving Systems of Linear and Quadratic Equations
- Principal
- Graphing Square-Root Functions
- Reflections of the Graph of f(x) = \sqrt{x}
- Square-root function
- Using Geometric Formulas to Find the Probability of an Event
- Example Card: Finding Geometric Probability with Rectangles
- Transformations of the Graph of f(x) = \sqrt{x}
- Example Card: Application: Projectile Motion