enVision, Algebra 1
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11th Grade Skills (279)
enVision, Algebra 1
11 chapters, 193 skills
▶
enVision, Algebra 1
11 chapters, 193 skills
Chapter 1: Solving Equations and Inequalities
- Applications: Real-World Compound Inequalities
- Application: Solving Word Problems with One-Step Inequalities
- Real Numbers as Union of Rational and Irrational
- Solving Mixture Problems
- Comparing Real Numbers via Decimals
- Operations Between Rational and Irrational Numbers
- Closure Properties of Rational Numbers
- Equations with no solution
- Formulas and Literal Equations
- Distributing Negative Signs and Handling Parentheses with Negatives
- Plotting Real Numbers on a Number Line
- Mixture problems using equations with variables on both sides
- Solving temperature conversion formulas
- Distributing Before Collecting Variables
- Graphing Step 1: Using Open vs. Closed Circles for the Boundary Point
- No Solution Case for Absolute Value Equations
- Solving the distance formula for rate and time
- Solving Rectangle Perimeter Formula for Different Variables
Chapter 2: Linear Equations
- Special Cases: Vertical and Horizontal Lines
- Writing an Equation from a Graph
- Graphing Using Intercepts
- Graphing Lines from Point-Slope Form
- Real-World Applications of Point-Slope Form
- Standard Form of Linear Equations
- Calculating Slope from Two Points
- Converting Point-Slope to Slope-Intercept Form
- Converting Slope-Intercept to Standard Form
- Classifying Lines Using Slopes
Chapter 3: Linear Functions
- Vertical Translation: Adding Constants to Linear Functions
- Recursive Formula for Arithmetic Sequences
- Association vs. Correlation
- Calculator Data Entry and Correlation Errors
- Converting Between Recursive and Explicit Formulas
- Defining the Line of Best Fit
- Scaling Linear Functions: Multiplying Inputs and Outputs
- Horizontal Translation: Modifying Function Inputs
- Writing Equations for Lines of Best Fit
- Choosing Real-World Inputs (Domain Constraints)
- Creating and Reading Scatter Plots
- Interpreting Scatter Plots: Association
- Continuous vs Discrete Domains
- Drawing the Line of Fit
- Graphing Linear Functions
- Defining Function Transformations
- Creating Comparison Tables for Function Transformations
- Linear Regression
- Residuals and Model Evaluation
- Correlation vs Causation
- Converting Between Function and Equation Notation
- Using a Line of Fit to Make Predictions
Chapter 4: Systems of Linear Equations and Inequalities
- Proper Use of Parentheses in Substitution
- When to Use Elimination Method
- Special Cases and Graphical Verification
- Step-by-Step Elimination Procedure
- Back-Substitution in Systems
- Choosing Which Variable to Eliminate
- Multiplication Property of Equality
- Application: Solving Real-World Systems by Graphing
- Overlapping Regions
- The Three Possible Outcomes
- Defining a System of Linear Equations
- Writing Systems from Graphs
- Shading Rules for Slope-Intercept Form
Chapter 5: Piecewise Functions
- Vertical Translations of Piecewise-Defined Functions
- Step Functions as Piecewise Constant Functions
- Horizontal Translations of Piecewise Functions
- Writing Transformed Piecewise Functions from Graphs
- Absolute Value Function Properties
- Combined Transformations of Piecewise Functions
- Vertical Stretches, Compressions, and Reflections of Piecewise Functions
- Vertex and Axis of Symmetry for Absolute Value Functions
- Piecewise Function Definition and Cases Notation
- Evaluating Piecewise Functions
- Boundary Points in Piecewise Functions
- Ceiling Function Definition and Notation
- Floor Function Definition and Notation
- Domain and Range of Step Functions
- Real-World Step Function Applications
- Absolute Value Function Vertex Form and Transformations
- Rounding Numbers
- Vertical Transformations of Absolute Value Functions
Chapter 6: Exponents and Exponential Functions
- Compound Interest Applications
- Discrete vs Continuous Quantities in Exponential Models
- Connection Between Geometric Sequences and Exponential Functions
- Converting Between Recursive and Explicit Formulas for Geometric Sequences
- Converting Between Decay Rate and Decay Factor
- Writing the Explicit Formula for a Geometric Sequence
- Recursive Formula for Geometric Sequences (Property Form)
- Solving Exponential Equations with Rational Exponents
- Y-Intercept Changes in Translated Exponential Functions
- Identifying Initial Amount vs Constant Ratio
- Writing Exponential Functions from Data
- Converting Between Growth Rate and Growth Factor
- Horizontal Translation Direction and Parameter Sign
- Range Changes in Vertical Translations
- Identifying Translations from Tables
Chapter 7: Polynomials and Factoring
- Exponent Rules in Polynomial Multiplication
- Vertical Alignment Method for Polynomial Operations
- Complete Factoring with GCF and Special Patterns
- Overview: Factoring ax² + bx + c
- Factoring Trinomials with Substitution
- GCF as First Step in Factoring Strategy
- Area Applications of Special Products
- Finding Dimensions from Trinomial Area Expressions
- Identifying Like Terms in Polynomials
- Polynomial Factoring in Geometric Area Problems
- Extracting Binomial Common Factors
Chapter 8: Quadratic Functions
- Average Rate of Change for Quadratic Functions
- Finding Reflection Points Across Axis of Symmetry
- Verifying Constant X-Value Differences
- Graphing Quadratic Functions Using Key Properties
- Interpreting R² Values for Model Quality
- Key Features of Parabolas
- Problem-Solving Strategy for Quadratic Modeling
- Linear Data Has Constant First Differences
- Vertex Form Definition and Structure
- Quadratic Function f(x) = ax²
- Complete Vertical Motion Model
- Axis of Symmetry for Parent Function
- Increasing and Decreasing Intervals
- Identifying the Y-Intercept from Standard Form
- Residual Plot Analysis for Quadratic Models
- Second Differences Identify Quadratic Functions
- Exponential Functions Have Constant Ratios
- Growth Rate Comparison of Function Types
- Evaluating Quadratic Model Appropriateness
- Real-World Applications of Vertex Form
Chapter 9: Solving Quadratic Equations
- Solve Linear-Quadratic Systems by Elimination
- Solve Linear-Quadratic Systems by Substitution
- Linear-Quadratic System Definition
- Number of Solutions for Quadratic Equations
- Multiplying Radical Expressions with Multiple Terms
- Using the Discriminant to Predict Graph Behavior
- Solving Quadratic Equations in Real-World Contexts
- Solve Linear-Quadratic Systems by Graphing
- Converting to Vertex Form by Completing the Square
- Real-World Problem Solving with Quadratics
- Perfect vs Non-Perfect Square Solutions
- Complete Step-by-Step Solution Process for ax² + b = c
- Simplifying Square Roots with Variable Powers
- The Discriminant
- Defining a Quadratic Equation
- Defining Zeros of a Function
- Estimating Solutions Using Sign Changes in Tables
- Using Factored Form to Identify Solutions
- Using the Discriminant to Determine Number of Solutions
Chapter 10: Working With Functions
- Vertical Translations: f(x) = √x + k
- Defining Absolute Maximum and Minimum Values
- Summary of Common Function Properties
- Monotonic Behavior of Cube Root Functions
- Graphing Cube Root Functions with Translations
- Average Rate of Change for Square Root Functions
- Square Root Function
- Reference Point Tracking for Function Translations
- Compressions and Stretches in Vertex Form
- Defining End Behavior
- Combined Translations: Quadratic Functions
- Horizontal Translations: f(x) = √(x - h)
- Real-World Application: Cylinder Surface Area Functions
- Domain and Range of Combined Functions
- Square Root Function Properties
- Defining Line of Symmetry
- Combined Transformations of Square Root Functions
- Steepness of Cube Root Function
- General Translation Formulas for All Functions
- Translations of Radical and Absolute Value Functions
- Reflections Across the X-Axis
- General Function Transformations
- Graphing Inverse Functions by Reflection
- Identifying Vertical vs Horizontal Transformations
- Average Rate of Change for Cube Root Functions
- Real-World Application: Modeling with Combined Functions
Chapter 11: Statistics
- Clustering and Outliers in Data Displays
- Defining Joint Frequency
- Interpreting Dot Plot Shapes
- Comparing Data Sets
- Relative Frequency Formulas in Two-Way Tables
- How Shape Affects the Mean and Median
- Normal Distribution and Bell Curve
- Variance and Standard Deviation
- Identifying Outliers
- Shapes of Distributions (Symmetric vs. Skewed)
- Sample vs Population Standard Deviation
- Population vs. Sample Variance
- Identifying associations using relative frequencies
- Comparing Histograms with Other Data Displays
- Creating Frequency Tables
- Comparing Histograms with Equal Intervals
- Comparing Box Plots
- Box Plot Shape Analysis
- Empirical Rule (68-95-99.7 Rule)
- Using Standard Deviation to Compare Data Sets
- Drawing Conclusions from Comparing Data Sets
enVision, Algebra 2
7 chapters, 86 skills
▶
enVision, Algebra 2
7 chapters, 86 skills
Chapter 1: Linear Functions and Systems
- Key Features of Linear, Quadratic, and Absolute Value Functions
- Sigma Notation for Arithmetic Series
- Horizontal Stretches and Compressions
- Combining Multiple Transformations
- Applications of three-variable systems using matrices
- Identifying Increasing and Decreasing Intervals
- Finding Solutions by Graphing Intersections
- Domain and Range of Functions
- Positive and Negative Intervals of a Function
- Solve Systems by Elimination
- Reduced Row-Echelon Form
- Absolute Value Function Properties
- Absolute Value as Piecewise Function
- Piecewise Function Definition and Notation
- Reflections Across Axes
- Graphing Piecewise Functions with Boundary Points
- Writing Piecewise Functions from Graphs
- Recursive Definition of Arithmetic Sequences
- Step Functions and Greatest Integer Function
- Verifying Graphical Solutions by Substitution
- Systematic Row Reduction Process
- Solve systems using matrices and reduced row-echelon form
- Converting Between Recursive and Explicit Forms
- Solve Systems by Substitution
Chapter 2: Quadratic Functions and Equations
- Substitution Method for Linear-Quadratic Systems
- Converting to Vertex Form by Completing the Square
- Graph a Quadratic Function Using Key Properties
- Graphing Quadratic Functions in Vertex Form
- Sum and Product of Quadratic Solutions
- Square Roots of Negative Numbers When Completing the Square
- Deriving the Quadratic Formula
- Discriminant Analysis for Linear-Quadratic Systems
- Factoring Quadratic Expressions (Leading Coefficient 1)
Chapter 3: Polynomial Functions
- Irrational Conjugate Root Theorem
- Distinguishing Function Symmetry from Degree
- Constructing Polynomials from Given Roots
- End Behavior Rules for Polynomial Functions
- Synthetic Division to Find Additional Zeros
- Rational Root Theorem
- Solve Polynomial Equations by Factoring
- Classifying Polynomial Functions as Even, Odd, or Neither
- Graph a Polynomial Function by Analyzing Turning Points and Relative Extrema
- Multiplicity of Zeros and Graph Behavior
- Fundamental Theorem of Algebra
- Transformations of Cubic and Quartic Functions
- Real-World Polynomial Models with Domain Restrictions
- Polynomial Operations in Business Functions
Chapter 4: Rational Functions
Chapter 5: Rational Exponents and Radical Functions
Chapter 6: Exponential and Logarithmic Functions
- Loan Payment Calculations Using Geometric Series
- Solving for Unknown Values in Exponential Models
- Solving Exponential and Logarithmic Equations by Graphing
- Compound Interest as Exponential Model
- Sum of a Geometric Series - Annuity Formula
- Solving Logarithmic Equations
- Rewriting Exponential Functions for Different Time Periods
- Key Features of Exponential Functions
- End Behavior of Logarithmic Functions
- Transformations of Logarithmic Functions
- Exponential Regression for Data Sets
- Converting Between Logarithmic and Exponential Forms
- Real-World Applications: Sound Intensity and Earthquake Magnitude
- Converting Between Recursive and Explicit Geometric Sequence Definitions
- Finding Number of Terms Using Logarithms
Chapter 9: Conic Sections
- Identify Parabolas from Equations
- Finding Intersection Points of Lines and Circles
- Vertex Form of Parabolas
- Identifying Hyperbolas from General Form
- Definition of an Ellipse
- Converting Parabola Forms Using Completing the Square
- Derive Parabola Equations from Focus and Directrix
- Identifying Parabola Axis and Orientation
- Completing the Square for Circle Equations