Analysis FlexBook® for Middle School

Analysis FlexBook® for High School

For Middle School

For High School

Levels are CK-12's student achievement levels.

Basic
Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work.

At Grade (Proficient)
Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter.

Advanced
Students matched to this level are ready for material that requires superior performance and mastery.

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- Analyzing Functions
- Relations and Functions
- Domain and Range
- Intervals and Interval Notation
- Symmetry
- Zeroes and Intercepts
- Average Rate of Change
- Minimums and Maximums
- Discrete and Continuous Functions
- Increasing and Decreasing Functions
- Limits
- Limits and Asymptotes
- Infinite and Non-Existent Limits
- Function Families
- Linear and Absolute Value Function Families
- Square and Cube Function Families
- Square and Cube Root Function Families
- Graphing Cube Root Functions
- Transformations
- Vertical and Horizontal Transformations
- Stretching and Reflecting Transformations
- Combining Transformations
- Notation for Transformations
- Operations on Functions
- Composition of Functions
- Models of Functions
- Linear and Quadratic Models
- Cubic Models

- Polynomial and Rational Functions
- Quadratic Functions
- Methods for Solving Quadratic Functions
- Graphs of Quadratic Functions
- Graphing Polynomials
- Graphs of Polynomials Using Transformations
- Graphs of Polynomials Using Zeros
- Graphing Calculator to Analyze Polynomial Functions
- Rational Functions
- Analysis of Graphs of Rational Functions
- Graphs of Basic Rational Functions
- Graphs of Rational Functions when the Degrees are Equal
- Graphs of Rational Functions when the Degrees are not Equal
- Sign Test for Rational Function Graphs
- Analysis of Rational Functions
- Holes in Rational Functions
- Zeroes of Rational Functions
- Vertical Asymptotes
- Horizontal Asymptotes
- Oblique Asymptotes of Rational Functions
- Solving Rational Equations
- Forms of Inequalities
- Quadratic Inequalities
- Polynomial and Rational Inequalities
- Finding Zeros of Polynomials
- Long Division of Polynomials
- Synthetic Division of Polynomials
- Real Zeros of Polynomials
- Intermediate Value Theorem
- Fundamental Theorem of Algebra

- Exponential and Logarithmic Functions
- Functions and Inverses
- One-to-One Functions and Their Inverses
- Basic Exponential Functions
- Solving Exponential Equations
- Logarithmic Functions
- Graphs of Logarithmic Functions
- Properties of Logarithms
- Product and Quotient Properties of Logarithms
- Power Property of Logarithms
- Inverse Properties of Logarithms
- Common and Natural Logarithms
- Solving Logarithmic Equations
- Change of Base
- Exponential and Logarithmic Models
- Exponential Models
- Logarithmic Models
- Simple and Compound Interest
- The Number e
- Logistic Functions

- Polar Equations and Complex Numbers
- Polar Equations
- Polar Coordinates
- Polar and Cartesian Transformation
- Systems of Polar Equations
- Polar Equations of Conics
- Imaginary Numbers and Complex Numbers
- Imaginary Numbers
- Complex Numbers
- Quadratic Formula and Complex Sums
- Products and Quotients of Complex Numbers
- Polar Form of Complex Numbers
- Product and Quotient Theorems
- Powers and Roots of Complex Numbers

- Vector Analysis
- Two-Dimensional Vectors
- Positions and Midpoints in Two Dimensions
- Three-Dimensional Positions
- Vector Calculations
- Dot Products
- Scalar Projections
- Cross Products
- Vector Projection
- Planes in Space
- Distance Between a Point and a Plane
- Vector Direction
- Vector Equation of a Line
- Vector Analysis Applications

- Conic Sections
- Ellipses
- Ellipses Centered at the Origin
- Equation of an Ellipse
- Ellipses Not Centered at the Origin
- Focal Property of Ellipses
- Parabolas
- Parabolas with Vertex at the Origin
- Parabolas and the Distance Formula
- Parabolas with any Vertex
- Parabolas and Analytic Geometry
- Applications of Parabolas
- Hyperbolas
- Graphs of Hyperbolas Centered at the Origin
- Equations of Hyperbolas Centered at the Origins
- Hyperbolas with any Center
- Hyperbola Equations and the Focal Property
- Hyperbolas and Asymptotes
- Conic Sections and Dandelin Spheres
- General Forms of Conic Sections
- Classifying Conic Sections
- Equations of Circles
- Circles Centered at the Origin
- Circles Not Centered at the Origin
- Degenerate Conics
- Applications of Conics
- Solving Systems of Lines, Quadratics, and Conics

- Sequences, Series, and Mathematical Induction
- Formulas and Notation for Sequences and Series
- Recursive Formulas
- Explicit Formulas
- Sum Notation and Properties of Sigma
- Series Sums
- Partial Sums
- Series Sums and Gauss' Formula
- Problem Solving with Series Sums
- Mathematical Induction
- Inductive Proofs
- Induction and Factors
- Induction and Inequalities
- Sums of Geometric Series
- Sums of Finite Geometric Series
- Sums of Infinite Geometric Series
- Factorials and Combinations
- Binomial Theorem and Expansions
- Sequences
- Arithmetic Sequences
- Finding the nth Term Given the Common Difference and a Term
- Finding the nth Term Given Two Terms for an Arithmetic Sequence
- Geometric Sequences
- Finding the nth Term Given the Common Ratio and the First Term
- Finding the nth Term Given Two Terms for a Geometric Sequence
- Sums of Arithmetic Series
- Sums of Finite Arithmetic Series

- Introduction to Calculus
- Limits in Calculus
- Definition of a Limit
- One-Sided Limits
- Infinite Limits
- Polynomial Function Limits
- Rational Function Limits
- Applications of One-Sided Limits
- Tables to Find Limits
- Tangents to a Curve
- Instantaneous Rates of Change
- Derivatives
- Constant Derivatives and the Power Rule
- Derivatives of Sums and Differences
- Quotient Rule and Higher Derivatives
- Integrals
- Area Under the Curve
- Anti-Derivative
- Fundamental Theorem of Calculus

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