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  • Algebra 2
    • Unit 1: Equations and Inequalties
      • 1.1 Real Numbers, Operations, and Unit Analysis
      • 1.2 and 1.3 Algebraic Expressions, Equations, and Models
      • Algebra About Me
      • 1.4 Rewriting Equations and Formulas
      • 1.6 Solving Linear Inequalties in One Variable
      • Unit 1 Review
      • Algebra 2 Unit 1 Solutions
    • Unit 2: Linear Equations and Functions
      • 2.1 Functions and their Graphs
      • 2.2 Slope and Rate of Change
      • 2.3, 2.4, 2.6 Equations and Indequalities and their Graphs
      • 2.5 Correlation and Best Fitting Lines
      • 2.7 Piecewise Functions
      • 2.8 Absolute Value Functions
      • Unit 2 Reviews
      • Unit 2 Solutions
    • Unit 3: Systems of Linear Equations/Inequalities
      • 3.1 and 3.2 Solving Linear Systems
      • 3.3 Graphing and Solving Systems of Linear Inequalities
      • 3.4 Linear Programming
      • 3.6 Solving Systems of Linear Equations in 3 Variables
      • Unit 3 Review
      • Unit 3 Solutions
    • Unit 5: Quadratic Functions
      • 5.1 Graphing Quadratic Functions
      • Multiplying Polynomials
      • 5.2 Solving Quadractic Equations by Factoring
      • 5.3 Solving Quadratic Equations by Square Roots
      • 5.4 Complex Numbers
      • 5.5 Completing the Square
      • 5.1-5.5 Review
      • 5.6 Quadratic Formula
      • 5.7 Graphing and Solving Quadratic Inequalities
      • 5.8 Writing Vertex and Intercept Forms of Quadratic Functions
      • Unit 5 Review
      • Unit 5 Solutions
    • Semester 1 Final Review
    • Unit 6: Polynomial Functions
      • 6.1 Properties of Exponents
      • 6.2 Evaluating and Graphing Polynomial Functions
      • 6.3 Adding, Subtracting, and Multiplying Polynomials
      • 6.4 Factoring and Solving Polynomial Equations
      • 6.5 The Remainder and Factor Theorem
      • 6.6 Finding Rational Zeros
      • 6.7 Using the Fundamental Theorem of Algebra
      • 6.8 Analyzing Graphs of Polynomial Functions
      • 6.9 Modeling with Polynomial Functions
      • Unit 6 Review
      • Unit 6 Solutions
    • Unit 7: Powers, Roots, Radicals
      • 7.1 Nth Roots/Rational Exponents
      • 7.2 Properties of Rational Exponents
      • 7.3 Power Functions and Function Operations
      • 7.1-7.3 Review
      • 7.4 Inverse Functions
      • 7.5 Square Root and Cube Root Functions
      • 7.6 Solving Radical Equations
      • Unit 7 Review
      • Unit 7 Solutions
    • Unit 8: Exponential and Logarithmic Functions
      • 8.1 and 8.2 Exponential Growth and Decay
      • 8.3 The Number e
      • 8.4 Logarithmic Functions
      • 8.5 Properties of Logarithms and the Change of Base Formula
      • 8.6 Solving Exponential and Logarithmic Functions
      • 8.7 Modelling with Exponential and Power Functios
      • 8.8 Logistic Growth Functions
      • Unit 8 Review
      • Unit 8 Solutions
    • Unit 9: Rational Equations and Functions
      • 9.2 Graphing Simple Rational Functions
      • 9.4 Simplifying Rational Functions
      • 9.5 Addition, Subtraction, and Complex Fractions
      • 9.6 Solving Rational Equations
      • Unit 9 Solutions
    • Unit 10
    • Unit 11
    • Unit 13: Trig ratios and functions
      • 13.1 Right Triangle Trigonometry
      • 13.2 General Angles and Radian Measure
      • Deriving the Unit Circle
      • 13.3 Trigonometric Functions of Any Angle
      • 13.4 Inverse Trigonometric Functions
      • 13.5 Law of Sines
      • 13.6 Law of Cosines
    • Parent Graphs
  • AP Calculus
    • Unit #1: Limits and Continuity
    • Team Calculus
      • Sweatshirt Designs
    • AP Calculus Old curriculum
      • Unit 1: Limits, Derivatives, Integrals, and Integrals
        • 1.1 The Concept of Intantaneous Rate
        • 1.2 Rate of Change by Equation, Graph, or Table
        • 1.3 One Type of Integral of a Function
        • 1.4 Definite Integrals by Trapezoids, from Equations and Data
        • Unit 1 Solutions
      • Unit 2: Properties of Limits
        • 2.1 and 2.2: Graphical and Algebraic approaches to the
        • 2.3 The Limit Threorems
        • 2.4 Continuity and Discontinuity
        • 2.5 Limits Involving Infinity
        • 2.6 Intermediate Value Theorem
        • Unit 2 Review
        • Unit 2 Solutions
      • Unit 3: Derivatives, Antiderivatives, and Indefinite Integrals
        • 3.1 Graphical Interpretation of Derivative
        • 3.2 Difference Quotient
        • 3.3 Derviative Functions Numerically and Graphically
        • 3.4 Derivative of the Power Function and Another Definition of Derivative
        • 3.5 Displacement, Velocity, and Acceleration
        • 3.6 Intro to Sine, Cosine, and Composite Functions
        • 3.7 Derivatives of Composite Functions: The Chain Rule
        • 3.8 Sinusoidal Equations
        • 3.9 Exponential and Logarithmic Functions
        • Unit 3 Solutions
        • Unit 3 Review
      • Unit 4: Products and Quotients
        • 4.2 Derivative of a Product (Product Rule)
        • 4.3 Quotient Rule
        • 4.4 Derivative of Other Trig Functions
        • 4.5 Derivatives of Inverse Trig Functions
        • 4.6 Differentiability and Continuity
        • 4.8: Implicit Differentiation
        • 4.9 Related Rates
      • Unit 5: Definite and Indefinite Integrals
        • 5.2 Linear approximations and Differentials
      • AP Calculus Solutions (2025-2026)
      • Calculus 1st Semester Final Review
        • AP Calc 1st Semester Final Review Solutions
    • College Board
  • Geometry
    • Unit 1: Basics of Geometry
      • 1.1 Points, Lines, and Planes
      • 1.2 Measuring Segments and Unit Analysis
      • 1.3 Midpoint and Distance Formula
      • 1.1-1.3 Review
      • 1.4 Area and Perimeter in the Coordinate Plane
      • 1.5 Measuring Angles
      • 1.6 Pairs of Angles
      • Unit 1 Solutions
      • Unit 1 Review
    • Unit 2: Reasoning and Proofs
      • 2.4 and 2.6 Algebraic Reasoning
    • Unit 3: Parallel and Perpendicular Lines
      • Review of Linear Equations
      • Review of Linear Systems of Equations
      • 3.1 Pairs of Lines and Angles
      • 3.2 Parallel Lines and Transversals
      • 3.3 Using Special Angle Pairs to Determine if Pairs of Lines are Parallel
      • 3.1-3.3, 2.4, and Linear Equations/Systems Review for Quiz
      • 3.4 and 3.5 Parallel and Perpendicular Lines
      • Chapter 3 Solutions
    • Unit 4: Transformations
      • Introduction to Transformations
      • 4.1 Translations
      • 4.2 Reflections
      • 4.3 Rotations
      • Tessellations
      • 4.5 Dilations
      • Unit 4 Solutions Geometry
      • Unit 4 Review
    • Statistical Survey Project
    • Geometry 1st Semester Review
      • 1st Semester Review Solutions
    • Unit 5: Congruent Triangles
      • 5.1 Angles of Triangles
      • 5.2 Congruent Polygons
      • 5.3, 5.4, 5.5, 5.6 Triangle Congruence Theorems and Equilateral/Isosceles
      • Geometry Unit 5 Solutions
    • Unit 6: Relationships within Triangles
      • 6.1 Perpendicular and Angle Bisectors
      • 6.3 Medians and Altitudes of Triangles
      • 6.5 Inequalities in One Triangle
      • Geometry Unit 6 Solutions
      • Unit 6 Review
    • Unit 7: Quadrilaterals and Other Polygons
      • 7.1 Angles of Polygons
      • 7.2 and 7.3 Properties of Parallelograms and Proving a Quadrilateral is a P
      • 7.4 Properties of Parallelograms
      • 7.5 Properties of Trapezoids and Kites
      • Unit 7 Review
      • Unit 7 Solutions
    • Data Detectives
    • Unit 8: Similarity
      • 8.1 Similar Polygons
      • 8.2 and 8.3 Proving Triangles Similar
      • Serpinsky Triangle
      • Mulitplying Polynomials
      • Factoring Friends
      • Solving Quadratic Functions
      • Solving Proportions and Similar Triangles Involving Quadratics
      • Unit 8 Review
      • Unit 8 Solutions to Selected Problems
    • Unit 9: Right Triangles and Trigonometry
      • 9.1 Pythagorean Theorem and Simplifying Radicals
      • 9.2 Special Right Triangles
      • Unit Circle
      • 9.3 Similar Right Triangles
      • 9.4 The Tangent Ratio
      • Finding Heights of Tall Things
      • 9.5 Sine and Cosine Ratios
      • 9.6 Solving Right Triangles
      • Unit 9 Solutions
    • Unit 10: Circles
      • 10.1: Lines and Segments that Intersect Circles
      • 10.7: Circles in the Coordinate Plane
      • Unit 10 Solutions
    • Statistics and Probability
    • Unit 11: Circumference, Area, and Volume
    • Geometry Resources
    • Geometry Copies of Completed Notes
    • Geometry 2nd Semester Final Review
      • Solutions 2nd Semester Final Review
  • PreCalculus
    • Unit 1: Functions and Mathematical Models
      • 1.1 Functions: Graphically, Algebraically, Numerically, and Verbally
      • 1.2 Types of Functions
      • 1.3 and 1.6 Transformations on Functions
      • 1.4 Compostition of Functions
      • 1.5 Inverse Functions
      • Unit 1 Solutions
      • Unit 1 Review
    • Unit 2: Properties of Elementary Functions
      • 2.2 Identifying Functions from Graphical Patterns
      • 2.3 Indentifying Functions from Numerical Patterns
      • 2.4 and 2.5 Logarithms: Properties, Bases, and Equations
      • 2.6 Logarithmic Functions
      • 2.7 Logistic Functions
      • Unit 2 Solutions
      • 2.1-2.5 Review for Quiz
      • Desmos Math Art - Halloween
      • Unit 2 Review
    • Unit 13: Matrices
      • 13.2 Matrix Operations and Solutions of LInear Systems Without Grapher
      • Unit 13 Solutions
    • Unit 4: Polynomial and Rational Functions
      • 4.2 Quadratic Functions, Factoring, and Complex Numbers
      • 4.3 Graphs and Zeros of HIgher Degree Polynomials
      • 4.4 Fitting Polynomial Functions to Data
      • 4.5 Rational Functions: Asymptotes and Discontinuities
      • 4.6 Operations with Rational Expressions
      • 4.7 Fractional Equations and Extraneous Solutions
      • Unit 4 Solutions
    • 1st Semester Review
    • Unit 5: Periodic Functions and Right Triangle Problems
      • 5.2: Measurement of Rotation
      • 5.3 Sine and Cosine Functions
      • 5.4: The Six Trigonometric Functions
      • 5.5: Inverse Trigonometric Functions
      • Unit 5 Solutions
      • 5.1-5.4 Review for Quiz
    • Unit 6: Applications of Trigonometric and Circular Functions
      • 6.2 General Sinusoid Graphs
      • 6.3 Graphs of Tangent, Cotangen, Secant, and Cosecant
      • 6.4 Radian Measure of Angles
      • Unit 6 Solutions Precalc
      • 6.5 Circular Functions
      • 6.6 Inverse Circular Relations
      • 6.7 Sinusoidal Functions as Mathematical Models
      • 6.8 Rotary Motion
    • Unit 7: Trigonometric Function Properties and Identities
      • 7.2: Pythagorean, Reciprocal, and Quotient Properties
      • Unit 7 Solutions (precalc)
      • 7.3: Identities and Algebraic Transformations of Expressions
      • 7.4 arcsine, arctangent, arccosine
      • 7.6 Graphs and Prinicipal Branches
    • Unit 16: Calculus Concepts
      • 16.2: Limits
      • Unit 16 Solutions
    • 2nd Semester Final Review
      • 2nd Semester Final Review Solutions
  • Cornell Notes
    • Examples of Cornell Notes
    • Cornell University
  • About
    • About Mrs. Frisk
    • Why Math?
    • Your Brain on Math
    • Ferndale HIgh School
    • Pi
    • The Flipped Classroom
    • Frisky Frog and Mother Function
    • Numbers
  • Resources
    • College Resources
    • National Symbols and Leaders
  • Data Science
    • Basketball Data Analytics
    • Data Talks
    • Correlation
  • Testing
    • CAASPP Data
  • Chromebook Acceptable Use Policy
  • Tutorials
  • Report Website Error
  • Website and Course Survey
  • Site map
Friskymath
  • Home
  • Algebra 2
    • Unit 1: Equations and Inequalties
      • 1.1 Real Numbers, Operations, and Unit Analysis
      • 1.2 and 1.3 Algebraic Expressions, Equations, and Models
      • Algebra About Me
      • 1.4 Rewriting Equations and Formulas
      • 1.6 Solving Linear Inequalties in One Variable
      • Unit 1 Review
      • Algebra 2 Unit 1 Solutions
    • Unit 2: Linear Equations and Functions
      • 2.1 Functions and their Graphs
      • 2.2 Slope and Rate of Change
      • 2.3, 2.4, 2.6 Equations and Indequalities and their Graphs
      • 2.5 Correlation and Best Fitting Lines
      • 2.7 Piecewise Functions
      • 2.8 Absolute Value Functions
      • Unit 2 Reviews
      • Unit 2 Solutions
    • Unit 3: Systems of Linear Equations/Inequalities
      • 3.1 and 3.2 Solving Linear Systems
      • 3.3 Graphing and Solving Systems of Linear Inequalities
      • 3.4 Linear Programming
      • 3.6 Solving Systems of Linear Equations in 3 Variables
      • Unit 3 Review
      • Unit 3 Solutions
    • Unit 5: Quadratic Functions
      • 5.1 Graphing Quadratic Functions
      • Multiplying Polynomials
      • 5.2 Solving Quadractic Equations by Factoring
      • 5.3 Solving Quadratic Equations by Square Roots
      • 5.4 Complex Numbers
      • 5.5 Completing the Square
      • 5.1-5.5 Review
      • 5.6 Quadratic Formula
      • 5.7 Graphing and Solving Quadratic Inequalities
      • 5.8 Writing Vertex and Intercept Forms of Quadratic Functions
      • Unit 5 Review
      • Unit 5 Solutions
    • Semester 1 Final Review
    • Unit 6: Polynomial Functions
      • 6.1 Properties of Exponents
      • 6.2 Evaluating and Graphing Polynomial Functions
      • 6.3 Adding, Subtracting, and Multiplying Polynomials
      • 6.4 Factoring and Solving Polynomial Equations
      • 6.5 The Remainder and Factor Theorem
      • 6.6 Finding Rational Zeros
      • 6.7 Using the Fundamental Theorem of Algebra
      • 6.8 Analyzing Graphs of Polynomial Functions
      • 6.9 Modeling with Polynomial Functions
      • Unit 6 Review
      • Unit 6 Solutions
    • Unit 7: Powers, Roots, Radicals
      • 7.1 Nth Roots/Rational Exponents
      • 7.2 Properties of Rational Exponents
      • 7.3 Power Functions and Function Operations
      • 7.1-7.3 Review
      • 7.4 Inverse Functions
      • 7.5 Square Root and Cube Root Functions
      • 7.6 Solving Radical Equations
      • Unit 7 Review
      • Unit 7 Solutions
    • Unit 8: Exponential and Logarithmic Functions
      • 8.1 and 8.2 Exponential Growth and Decay
      • 8.3 The Number e
      • 8.4 Logarithmic Functions
      • 8.5 Properties of Logarithms and the Change of Base Formula
      • 8.6 Solving Exponential and Logarithmic Functions
      • 8.7 Modelling with Exponential and Power Functios
      • 8.8 Logistic Growth Functions
      • Unit 8 Review
      • Unit 8 Solutions
    • Unit 9: Rational Equations and Functions
      • 9.2 Graphing Simple Rational Functions
      • 9.4 Simplifying Rational Functions
      • 9.5 Addition, Subtraction, and Complex Fractions
      • 9.6 Solving Rational Equations
      • Unit 9 Solutions
    • Unit 10
    • Unit 11
    • Unit 13: Trig ratios and functions
      • 13.1 Right Triangle Trigonometry
      • 13.2 General Angles and Radian Measure
      • Deriving the Unit Circle
      • 13.3 Trigonometric Functions of Any Angle
      • 13.4 Inverse Trigonometric Functions
      • 13.5 Law of Sines
      • 13.6 Law of Cosines
    • Parent Graphs
  • AP Calculus
    • Unit #1: Limits and Continuity
    • Team Calculus
      • Sweatshirt Designs
    • AP Calculus Old curriculum
      • Unit 1: Limits, Derivatives, Integrals, and Integrals
        • 1.1 The Concept of Intantaneous Rate
        • 1.2 Rate of Change by Equation, Graph, or Table
        • 1.3 One Type of Integral of a Function
        • 1.4 Definite Integrals by Trapezoids, from Equations and Data
        • Unit 1 Solutions
      • Unit 2: Properties of Limits
        • 2.1 and 2.2: Graphical and Algebraic approaches to the
        • 2.3 The Limit Threorems
        • 2.4 Continuity and Discontinuity
        • 2.5 Limits Involving Infinity
        • 2.6 Intermediate Value Theorem
        • Unit 2 Review
        • Unit 2 Solutions
      • Unit 3: Derivatives, Antiderivatives, and Indefinite Integrals
        • 3.1 Graphical Interpretation of Derivative
        • 3.2 Difference Quotient
        • 3.3 Derviative Functions Numerically and Graphically
        • 3.4 Derivative of the Power Function and Another Definition of Derivative
        • 3.5 Displacement, Velocity, and Acceleration
        • 3.6 Intro to Sine, Cosine, and Composite Functions
        • 3.7 Derivatives of Composite Functions: The Chain Rule
        • 3.8 Sinusoidal Equations
        • 3.9 Exponential and Logarithmic Functions
        • Unit 3 Solutions
        • Unit 3 Review
      • Unit 4: Products and Quotients
        • 4.2 Derivative of a Product (Product Rule)
        • 4.3 Quotient Rule
        • 4.4 Derivative of Other Trig Functions
        • 4.5 Derivatives of Inverse Trig Functions
        • 4.6 Differentiability and Continuity
        • 4.8: Implicit Differentiation
        • 4.9 Related Rates
      • Unit 5: Definite and Indefinite Integrals
        • 5.2 Linear approximations and Differentials
      • AP Calculus Solutions (2025-2026)
      • Calculus 1st Semester Final Review
        • AP Calc 1st Semester Final Review Solutions
    • College Board
  • Geometry
    • Unit 1: Basics of Geometry
      • 1.1 Points, Lines, and Planes
      • 1.2 Measuring Segments and Unit Analysis
      • 1.3 Midpoint and Distance Formula
      • 1.1-1.3 Review
      • 1.4 Area and Perimeter in the Coordinate Plane
      • 1.5 Measuring Angles
      • 1.6 Pairs of Angles
      • Unit 1 Solutions
      • Unit 1 Review
    • Unit 2: Reasoning and Proofs
      • 2.4 and 2.6 Algebraic Reasoning
    • Unit 3: Parallel and Perpendicular Lines
      • Review of Linear Equations
      • Review of Linear Systems of Equations
      • 3.1 Pairs of Lines and Angles
      • 3.2 Parallel Lines and Transversals
      • 3.3 Using Special Angle Pairs to Determine if Pairs of Lines are Parallel
      • 3.1-3.3, 2.4, and Linear Equations/Systems Review for Quiz
      • 3.4 and 3.5 Parallel and Perpendicular Lines
      • Chapter 3 Solutions
    • Unit 4: Transformations
      • Introduction to Transformations
      • 4.1 Translations
      • 4.2 Reflections
      • 4.3 Rotations
      • Tessellations
      • 4.5 Dilations
      • Unit 4 Solutions Geometry
      • Unit 4 Review
    • Statistical Survey Project
    • Geometry 1st Semester Review
      • 1st Semester Review Solutions
    • Unit 5: Congruent Triangles
      • 5.1 Angles of Triangles
      • 5.2 Congruent Polygons
      • 5.3, 5.4, 5.5, 5.6 Triangle Congruence Theorems and Equilateral/Isosceles
      • Geometry Unit 5 Solutions
    • Unit 6: Relationships within Triangles
      • 6.1 Perpendicular and Angle Bisectors
      • 6.3 Medians and Altitudes of Triangles
      • 6.5 Inequalities in One Triangle
      • Geometry Unit 6 Solutions
      • Unit 6 Review
    • Unit 7: Quadrilaterals and Other Polygons
      • 7.1 Angles of Polygons
      • 7.2 and 7.3 Properties of Parallelograms and Proving a Quadrilateral is a P
      • 7.4 Properties of Parallelograms
      • 7.5 Properties of Trapezoids and Kites
      • Unit 7 Review
      • Unit 7 Solutions
    • Data Detectives
    • Unit 8: Similarity
      • 8.1 Similar Polygons
      • 8.2 and 8.3 Proving Triangles Similar
      • Serpinsky Triangle
      • Mulitplying Polynomials
      • Factoring Friends
      • Solving Quadratic Functions
      • Solving Proportions and Similar Triangles Involving Quadratics
      • Unit 8 Review
      • Unit 8 Solutions to Selected Problems
    • Unit 9: Right Triangles and Trigonometry
      • 9.1 Pythagorean Theorem and Simplifying Radicals
      • 9.2 Special Right Triangles
      • Unit Circle
      • 9.3 Similar Right Triangles
      • 9.4 The Tangent Ratio
      • Finding Heights of Tall Things
      • 9.5 Sine and Cosine Ratios
      • 9.6 Solving Right Triangles
      • Unit 9 Solutions
    • Unit 10: Circles
      • 10.1: Lines and Segments that Intersect Circles
      • 10.7: Circles in the Coordinate Plane
      • Unit 10 Solutions
    • Statistics and Probability
    • Unit 11: Circumference, Area, and Volume
    • Geometry Resources
    • Geometry Copies of Completed Notes
    • Geometry 2nd Semester Final Review
      • Solutions 2nd Semester Final Review
  • PreCalculus
    • Unit 1: Functions and Mathematical Models
      • 1.1 Functions: Graphically, Algebraically, Numerically, and Verbally
      • 1.2 Types of Functions
      • 1.3 and 1.6 Transformations on Functions
      • 1.4 Compostition of Functions
      • 1.5 Inverse Functions
      • Unit 1 Solutions
      • Unit 1 Review
    • Unit 2: Properties of Elementary Functions
      • 2.2 Identifying Functions from Graphical Patterns
      • 2.3 Indentifying Functions from Numerical Patterns
      • 2.4 and 2.5 Logarithms: Properties, Bases, and Equations
      • 2.6 Logarithmic Functions
      • 2.7 Logistic Functions
      • Unit 2 Solutions
      • 2.1-2.5 Review for Quiz
      • Desmos Math Art - Halloween
      • Unit 2 Review
    • Unit 13: Matrices
      • 13.2 Matrix Operations and Solutions of LInear Systems Without Grapher
      • Unit 13 Solutions
    • Unit 4: Polynomial and Rational Functions
      • 4.2 Quadratic Functions, Factoring, and Complex Numbers
      • 4.3 Graphs and Zeros of HIgher Degree Polynomials
      • 4.4 Fitting Polynomial Functions to Data
      • 4.5 Rational Functions: Asymptotes and Discontinuities
      • 4.6 Operations with Rational Expressions
      • 4.7 Fractional Equations and Extraneous Solutions
      • Unit 4 Solutions
    • 1st Semester Review
    • Unit 5: Periodic Functions and Right Triangle Problems
      • 5.2: Measurement of Rotation
      • 5.3 Sine and Cosine Functions
      • 5.4: The Six Trigonometric Functions
      • 5.5: Inverse Trigonometric Functions
      • Unit 5 Solutions
      • 5.1-5.4 Review for Quiz
    • Unit 6: Applications of Trigonometric and Circular Functions
      • 6.2 General Sinusoid Graphs
      • 6.3 Graphs of Tangent, Cotangen, Secant, and Cosecant
      • 6.4 Radian Measure of Angles
      • Unit 6 Solutions Precalc
      • 6.5 Circular Functions
      • 6.6 Inverse Circular Relations
      • 6.7 Sinusoidal Functions as Mathematical Models
      • 6.8 Rotary Motion
    • Unit 7: Trigonometric Function Properties and Identities
      • 7.2: Pythagorean, Reciprocal, and Quotient Properties
      • Unit 7 Solutions (precalc)
      • 7.3: Identities and Algebraic Transformations of Expressions
      • 7.4 arcsine, arctangent, arccosine
      • 7.6 Graphs and Prinicipal Branches
    • Unit 16: Calculus Concepts
      • 16.2: Limits
      • Unit 16 Solutions
    • 2nd Semester Final Review
      • 2nd Semester Final Review Solutions
  • Cornell Notes
    • Examples of Cornell Notes
    • Cornell University
  • About
    • About Mrs. Frisk
    • Why Math?
    • Your Brain on Math
    • Ferndale HIgh School
    • Pi
    • The Flipped Classroom
    • Frisky Frog and Mother Function
    • Numbers
  • Resources
    • College Resources
    • National Symbols and Leaders
  • Data Science
    • Basketball Data Analytics
    • Data Talks
    • Correlation
  • Testing
    • CAASPP Data
  • Chromebook Acceptable Use Policy
  • Tutorials
  • Report Website Error
  • Website and Course Survey
  • Site map
  • More
    • Home
    • Algebra 2
      • Unit 1: Equations and Inequalties
        • 1.1 Real Numbers, Operations, and Unit Analysis
        • 1.2 and 1.3 Algebraic Expressions, Equations, and Models
        • Algebra About Me
        • 1.4 Rewriting Equations and Formulas
        • 1.6 Solving Linear Inequalties in One Variable
        • Unit 1 Review
        • Algebra 2 Unit 1 Solutions
      • Unit 2: Linear Equations and Functions
        • 2.1 Functions and their Graphs
        • 2.2 Slope and Rate of Change
        • 2.3, 2.4, 2.6 Equations and Indequalities and their Graphs
        • 2.5 Correlation and Best Fitting Lines
        • 2.7 Piecewise Functions
        • 2.8 Absolute Value Functions
        • Unit 2 Reviews
        • Unit 2 Solutions
      • Unit 3: Systems of Linear Equations/Inequalities
        • 3.1 and 3.2 Solving Linear Systems
        • 3.3 Graphing and Solving Systems of Linear Inequalities
        • 3.4 Linear Programming
        • 3.6 Solving Systems of Linear Equations in 3 Variables
        • Unit 3 Review
        • Unit 3 Solutions
      • Unit 5: Quadratic Functions
        • 5.1 Graphing Quadratic Functions
        • Multiplying Polynomials
        • 5.2 Solving Quadractic Equations by Factoring
        • 5.3 Solving Quadratic Equations by Square Roots
        • 5.4 Complex Numbers
        • 5.5 Completing the Square
        • 5.1-5.5 Review
        • 5.6 Quadratic Formula
        • 5.7 Graphing and Solving Quadratic Inequalities
        • 5.8 Writing Vertex and Intercept Forms of Quadratic Functions
        • Unit 5 Review
        • Unit 5 Solutions
      • Semester 1 Final Review
      • Unit 6: Polynomial Functions
        • 6.1 Properties of Exponents
        • 6.2 Evaluating and Graphing Polynomial Functions
        • 6.3 Adding, Subtracting, and Multiplying Polynomials
        • 6.4 Factoring and Solving Polynomial Equations
        • 6.5 The Remainder and Factor Theorem
        • 6.6 Finding Rational Zeros
        • 6.7 Using the Fundamental Theorem of Algebra
        • 6.8 Analyzing Graphs of Polynomial Functions
        • 6.9 Modeling with Polynomial Functions
        • Unit 6 Review
        • Unit 6 Solutions
      • Unit 7: Powers, Roots, Radicals
        • 7.1 Nth Roots/Rational Exponents
        • 7.2 Properties of Rational Exponents
        • 7.3 Power Functions and Function Operations
        • 7.1-7.3 Review
        • 7.4 Inverse Functions
        • 7.5 Square Root and Cube Root Functions
        • 7.6 Solving Radical Equations
        • Unit 7 Review
        • Unit 7 Solutions
      • Unit 8: Exponential and Logarithmic Functions
        • 8.1 and 8.2 Exponential Growth and Decay
        • 8.3 The Number e
        • 8.4 Logarithmic Functions
        • 8.5 Properties of Logarithms and the Change of Base Formula
        • 8.6 Solving Exponential and Logarithmic Functions
        • 8.7 Modelling with Exponential and Power Functios
        • 8.8 Logistic Growth Functions
        • Unit 8 Review
        • Unit 8 Solutions
      • Unit 9: Rational Equations and Functions
        • 9.2 Graphing Simple Rational Functions
        • 9.4 Simplifying Rational Functions
        • 9.5 Addition, Subtraction, and Complex Fractions
        • 9.6 Solving Rational Equations
        • Unit 9 Solutions
      • Unit 10
      • Unit 11
      • Unit 13: Trig ratios and functions
        • 13.1 Right Triangle Trigonometry
        • 13.2 General Angles and Radian Measure
        • Deriving the Unit Circle
        • 13.3 Trigonometric Functions of Any Angle
        • 13.4 Inverse Trigonometric Functions
        • 13.5 Law of Sines
        • 13.6 Law of Cosines
      • Parent Graphs
    • AP Calculus
      • Unit #1: Limits and Continuity
      • Team Calculus
        • Sweatshirt Designs
      • AP Calculus Old curriculum
        • Unit 1: Limits, Derivatives, Integrals, and Integrals
          • 1.1 The Concept of Intantaneous Rate
          • 1.2 Rate of Change by Equation, Graph, or Table
          • 1.3 One Type of Integral of a Function
          • 1.4 Definite Integrals by Trapezoids, from Equations and Data
          • Unit 1 Solutions
        • Unit 2: Properties of Limits
          • 2.1 and 2.2: Graphical and Algebraic approaches to the
          • 2.3 The Limit Threorems
          • 2.4 Continuity and Discontinuity
          • 2.5 Limits Involving Infinity
          • 2.6 Intermediate Value Theorem
          • Unit 2 Review
          • Unit 2 Solutions
        • Unit 3: Derivatives, Antiderivatives, and Indefinite Integrals
          • 3.1 Graphical Interpretation of Derivative
          • 3.2 Difference Quotient
          • 3.3 Derviative Functions Numerically and Graphically
          • 3.4 Derivative of the Power Function and Another Definition of Derivative
          • 3.5 Displacement, Velocity, and Acceleration
          • 3.6 Intro to Sine, Cosine, and Composite Functions
          • 3.7 Derivatives of Composite Functions: The Chain Rule
          • 3.8 Sinusoidal Equations
          • 3.9 Exponential and Logarithmic Functions
          • Unit 3 Solutions
          • Unit 3 Review
        • Unit 4: Products and Quotients
          • 4.2 Derivative of a Product (Product Rule)
          • 4.3 Quotient Rule
          • 4.4 Derivative of Other Trig Functions
          • 4.5 Derivatives of Inverse Trig Functions
          • 4.6 Differentiability and Continuity
          • 4.8: Implicit Differentiation
          • 4.9 Related Rates
        • Unit 5: Definite and Indefinite Integrals
          • 5.2 Linear approximations and Differentials
        • AP Calculus Solutions (2025-2026)
        • Calculus 1st Semester Final Review
          • AP Calc 1st Semester Final Review Solutions
      • College Board
    • Geometry
      • Unit 1: Basics of Geometry
        • 1.1 Points, Lines, and Planes
        • 1.2 Measuring Segments and Unit Analysis
        • 1.3 Midpoint and Distance Formula
        • 1.1-1.3 Review
        • 1.4 Area and Perimeter in the Coordinate Plane
        • 1.5 Measuring Angles
        • 1.6 Pairs of Angles
        • Unit 1 Solutions
        • Unit 1 Review
      • Unit 2: Reasoning and Proofs
        • 2.4 and 2.6 Algebraic Reasoning
      • Unit 3: Parallel and Perpendicular Lines
        • Review of Linear Equations
        • Review of Linear Systems of Equations
        • 3.1 Pairs of Lines and Angles
        • 3.2 Parallel Lines and Transversals
        • 3.3 Using Special Angle Pairs to Determine if Pairs of Lines are Parallel
        • 3.1-3.3, 2.4, and Linear Equations/Systems Review for Quiz
        • 3.4 and 3.5 Parallel and Perpendicular Lines
        • Chapter 3 Solutions
      • Unit 4: Transformations
        • Introduction to Transformations
        • 4.1 Translations
        • 4.2 Reflections
        • 4.3 Rotations
        • Tessellations
        • 4.5 Dilations
        • Unit 4 Solutions Geometry
        • Unit 4 Review
      • Statistical Survey Project
      • Geometry 1st Semester Review
        • 1st Semester Review Solutions
      • Unit 5: Congruent Triangles
        • 5.1 Angles of Triangles
        • 5.2 Congruent Polygons
        • 5.3, 5.4, 5.5, 5.6 Triangle Congruence Theorems and Equilateral/Isosceles
        • Geometry Unit 5 Solutions
      • Unit 6: Relationships within Triangles
        • 6.1 Perpendicular and Angle Bisectors
        • 6.3 Medians and Altitudes of Triangles
        • 6.5 Inequalities in One Triangle
        • Geometry Unit 6 Solutions
        • Unit 6 Review
      • Unit 7: Quadrilaterals and Other Polygons
        • 7.1 Angles of Polygons
        • 7.2 and 7.3 Properties of Parallelograms and Proving a Quadrilateral is a P
        • 7.4 Properties of Parallelograms
        • 7.5 Properties of Trapezoids and Kites
        • Unit 7 Review
        • Unit 7 Solutions
      • Data Detectives
      • Unit 8: Similarity
        • 8.1 Similar Polygons
        • 8.2 and 8.3 Proving Triangles Similar
        • Serpinsky Triangle
        • Mulitplying Polynomials
        • Factoring Friends
        • Solving Quadratic Functions
        • Solving Proportions and Similar Triangles Involving Quadratics
        • Unit 8 Review
        • Unit 8 Solutions to Selected Problems
      • Unit 9: Right Triangles and Trigonometry
        • 9.1 Pythagorean Theorem and Simplifying Radicals
        • 9.2 Special Right Triangles
        • Unit Circle
        • 9.3 Similar Right Triangles
        • 9.4 The Tangent Ratio
        • Finding Heights of Tall Things
        • 9.5 Sine and Cosine Ratios
        • 9.6 Solving Right Triangles
        • Unit 9 Solutions
      • Unit 10: Circles
        • 10.1: Lines and Segments that Intersect Circles
        • 10.7: Circles in the Coordinate Plane
        • Unit 10 Solutions
      • Statistics and Probability
      • Unit 11: Circumference, Area, and Volume
      • Geometry Resources
      • Geometry Copies of Completed Notes
      • Geometry 2nd Semester Final Review
        • Solutions 2nd Semester Final Review
    • PreCalculus
      • Unit 1: Functions and Mathematical Models
        • 1.1 Functions: Graphically, Algebraically, Numerically, and Verbally
        • 1.2 Types of Functions
        • 1.3 and 1.6 Transformations on Functions
        • 1.4 Compostition of Functions
        • 1.5 Inverse Functions
        • Unit 1 Solutions
        • Unit 1 Review
      • Unit 2: Properties of Elementary Functions
        • 2.2 Identifying Functions from Graphical Patterns
        • 2.3 Indentifying Functions from Numerical Patterns
        • 2.4 and 2.5 Logarithms: Properties, Bases, and Equations
        • 2.6 Logarithmic Functions
        • 2.7 Logistic Functions
        • Unit 2 Solutions
        • 2.1-2.5 Review for Quiz
        • Desmos Math Art - Halloween
        • Unit 2 Review
      • Unit 13: Matrices
        • 13.2 Matrix Operations and Solutions of LInear Systems Without Grapher
        • Unit 13 Solutions
      • Unit 4: Polynomial and Rational Functions
        • 4.2 Quadratic Functions, Factoring, and Complex Numbers
        • 4.3 Graphs and Zeros of HIgher Degree Polynomials
        • 4.4 Fitting Polynomial Functions to Data
        • 4.5 Rational Functions: Asymptotes and Discontinuities
        • 4.6 Operations with Rational Expressions
        • 4.7 Fractional Equations and Extraneous Solutions
        • Unit 4 Solutions
      • 1st Semester Review
      • Unit 5: Periodic Functions and Right Triangle Problems
        • 5.2: Measurement of Rotation
        • 5.3 Sine and Cosine Functions
        • 5.4: The Six Trigonometric Functions
        • 5.5: Inverse Trigonometric Functions
        • Unit 5 Solutions
        • 5.1-5.4 Review for Quiz
      • Unit 6: Applications of Trigonometric and Circular Functions
        • 6.2 General Sinusoid Graphs
        • 6.3 Graphs of Tangent, Cotangen, Secant, and Cosecant
        • 6.4 Radian Measure of Angles
        • Unit 6 Solutions Precalc
        • 6.5 Circular Functions
        • 6.6 Inverse Circular Relations
        • 6.7 Sinusoidal Functions as Mathematical Models
        • 6.8 Rotary Motion
      • Unit 7: Trigonometric Function Properties and Identities
        • 7.2: Pythagorean, Reciprocal, and Quotient Properties
        • Unit 7 Solutions (precalc)
        • 7.3: Identities and Algebraic Transformations of Expressions
        • 7.4 arcsine, arctangent, arccosine
        • 7.6 Graphs and Prinicipal Branches
      • Unit 16: Calculus Concepts
        • 16.2: Limits
        • Unit 16 Solutions
      • 2nd Semester Final Review
        • 2nd Semester Final Review Solutions
    • Cornell Notes
      • Examples of Cornell Notes
      • Cornell University
    • About
      • About Mrs. Frisk
      • Why Math?
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