# AP CALCULUS AB ACADEMIC LIBRARY

*First Semester*

*All honor level courses from Edgenuity are not written from a biblical worldview and you may find some material that is different from that view we hold—from our web page on a biblical worldview “we look to the Bible for our beliefs and how we should operate. We believe students at this level can use wisdom in such courses, but if you are uncomfortable, please select from our Ignitia course offerings.*

## Getting Started In Edgenuity

##### THE STUDENT EXPERIENCE

##### MATH COURSE

## Taking the AP Exam – College Board

Students considering taking the AP Exam should be enrolled by the first of September. Taking the AP Exam is not required for high school credit, but could result in both high school credit and college credit if the student meets the scoring criteria passing the exam. Students will need to arrange to take the AP Exam in their local area which would be in May for this cycle. Visit the College Board for details on taking the exam as a homeschool student.

## AP Calculus AB Online – First Semester

##### Unit 1: Precalculus Review

- Introduction to AP Calculus
- Warm-Up
- Introduction to AP Calculus AB
- Instruction
- Introduction to AP Calculus AB

- Writing Two-Variable Linear Equations Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – What information is needed to write the equation of a line?
- Summary – Review and connect what you learned.

- Reading Lesson 1.1
- Instruction – Reading Lesson
- Practice Problems 1.1 – Read section 1.1 in the textbook and complete associated exercises.

- Composition of Functions Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – How can you write a new function that uses the output of one function as the input of another?
- Summary – Review and connect what you learned.

- Symmetry Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – How can you tell if a relation has symmetry?
- Summary – Review and connect what you learned.

- Piecewise Defined Functions Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – How do you define and analyze a function when it cannot be described by a single rule?
- Summary – Review and connect what you learned.

- Reading Lesson 1.2
- Instruction – Reading Lesson
- Practice Problems 1.2 – Read section 1.2 in the textbook and complete associated exercises.

- Graphing Exponential Functions Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – What are the key features of the graph of an exponential function?
- Summary – Review and connect what you learned.

- Base e Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – What other common bases are used for exponential and logarithmic functions?
- Summary – Review and connect what you learned.

- Modeling with Exponential and Logarithmic Equations Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – What kinds of real-world problems can you solve using exponential and logarithmic functions?
- Instruction – What kinds of real-world problems can you solve using exponential and logarithmic functions?
- Summary – Review and connect what you learned.

- Reading Lesson 1.3
- Instruction – Reading Lesson
- Practice Problems 1.3 Read section 1.3 in the textbook and complete associated exercises.

- Parametric Equations
- Instruction – Learn about parametric equations.
- Example Problem: Defining a Line Parametrically – How do you define a curve parametrically?
- Example Problem: Converting Parametric Equations to Cartesian Form – How do you convert parametric equations to Cartesian form?
- Example Problem: Graphing Parametric Equations – How do you determine graphs of parametric equations?

- Reading Lesson 1.4
- Instruction – Reading Lesson
- Practice Problems 1.4 – Read section 1.4 in the textbook and complete associated exercises.

- Function Inverses Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – What does it look like when one relation “undoes” another?
- Summary – Review and connect what you learned.

- Graphing Logarithmic Functions Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – What methods can you use to graph the inverses of exponential functions?
- Summary – Review and connect what you learned.

- Properties of Logarithms Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – How can you use properties of logarithms to rewrite or evaluate logarithmic expressions?
- Summary – Review and connect what you learned.

- Reading Lesson 1.5
- Instruction – Reading Lesson
- Practice Problems 1.5 – Read section 1.5 in the textbook and complete associated exercises.

- Radian Measure Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – What is radian measure and how is it related to degree measure?
- Summary – Review and connect what you learned.

- Evaluating the Six Trigonometric Functions Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – How can you use the relationships among trigonometric functions to evaluate them?
- Summary – Review and connect what you learned.

- Solving Trigonometric Equations Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – How can you use the concept of inverse functions to solve an equation that includes a trigonometric
- Summary – Review and connect what you learned.

- Modeling with Periodic Functions Guided Notes
- Warm-Up – Get ready for the lesson.
- Instruction – How can sine and cosine help you solve real-world problems involving cycles?
- Summary – Review and connect what you learned.

- Reading Lesson 1.6
- Instruction – Reading Lesson
- Practice Problems 1.6 – Read section 1.6 in the textbook and complete associated exercises.

- Unit Test
- Unit Test Answers

##### Unit 2: Limits and Continuity

- Introduction to Unit 2
- Instruction
- Unit 2 Introduction

- Rates of Change, Limits, and the Squeeze Theorem
- Instruction – Learn about the limits of functions and their properties.
- Example Problem: Evaluating Limits – How do you use the definition of a limit and its properties to evaluate the limit of a function?
- Example Problem: Identifying Conditions When Limits Do Not Exist – How do you determine if a limit does not exist?
- Example Problem: Determining One-Sided and Two-Sided Limits – How do you determine one-sided and two-sided limits?
- Example Problem: Using the Squeeze Theorem – How do you use the squeeze theorem to indirectly find limits?

- Reading Lesson 2.1
- Instruction – Reading Lesson
- Practice Problems 2.1 – Read section 2.1 in the textbook and complete associated exercises.

- Limits Involving Infinity and Vertical and Horizontal Asymptotes
- Instruction – Learn about limits involving infinity and vertical and horizontal asymptotes.
- Example Problem: Calculating Limits Toward Infinity – How do you calculate limits as x approaches positive or negative infinity?
- Example Problem: Using Limits to Find Horizontal Asymptotes – How do you use limits to find horizontal asymptotes of rational functions?
- Example Problem: Using Limits to Find Vertical Asymptotes – How do you use limits to find vertical asymptotes of rational functions?
- Example Problem: Determining End-Behavior Models – How do you use limits to find end-behavior models for complex functions?

- Reading Lesson 2.2
- Instruction
- Reading Lesson
- Practice Problems 2.2 – Read section 2.2 in the textbook and complete associated exercises.

- Continuous Functions and Intermediate Value Theorem
- Instruction – Learn about continuous functions and the intermediate value theorem.
- Example Problem: Identifying Discontinuities – How can you identify points of discontinuity?
- Example Problem: Removing a Discontinuity -How can a function be extended or modified to remove discontinuities?
- Example Problem: Determining the Continuity of a Composition of Functions – How can you use composition of functions to determine continuity?
- Example Problem: Verifying Continuity Using the Intermediate Value Theorem – How is the intermediate value theorem used?

- Reading Lesson 2.3
- Instruction – Reading Lesson
- Practice Problems 2.3 – Read section 2.3 in the textbook and complete associated exercises.

- Slope, Tangent Line, and Normal Line
- Instruction – Learn about slope, tangent lines, and normal lines.
- Example Problem: Calculating the Average Rate of Change – How do you calculate the average rate of change of a function?
- Example Problem: Determining the Slope of a Tangent Line at a Point – How do you determine the slope of a tangent line at a point using limits?
- Example Problem: Calculating Instantaneous Rate of Change – How do you determine the instantaneous rate of change of a function?
- Example Problem: Determining the Equation of a Tangent to a Curve – How do you determine the equation of a tangent to a curve?
- Example Problem: Determining the Equation of a Normal Line to a Curve – How do you determine the equation of a normal to a curve?

- Reading Lesson 2.4
- Instruction – Reading Lesson
- Practice Problems 2.4 – Read section 2.4 in the textbook and complete associated exercises.

- Unit Test
- Unit Test Answers

##### Unit 3: Derivatives

- Introduction to Unit 3
- Instruction
- Unit 3 Introduction

- Derivatives of Functions
- Instruction – Learn about derivatives of functions. Example Problem: Using the Definition of a Derivative –
- How do we compute the derivative of a function using the definition of a derivative?
- Example Problem: Calculating the Derivative at a Point – How do we compute the derivative of a function at a point?
- Example Problem: Approximating the Graph of a Derivative When Given the Graph of the Function How do we approximate the graph of the derivative f ‘ when we are given the graph of the function f?
- Example Problem: Determining If a Function Is Differentiable on a Closed Interval How do we determine if a function is differentiable on a closed interval?
- Example Problem: Calculating the Derivative When Given a Data Set How do we approximate a derivative when given a data set?

- Reading Lesson 3.1
- Instruction – Reading Lesson
- Practice Problems 3.1 – Read section 3.1 in the textbook and complete associated exercises.

- Derivatives and Continuity
- Instruction – How do you approximate the numerical derivative of a function?
- Example Problem: Approximating the Numerical Derivative of a Function. How do you approximate the numerical derivative of a function?
- Example Problem: Finding Cases Where a Function is Not Differentiable. What are the cases when a function is not differentiable?
- Example Problem: Exploring Points of Non-Differentiability. Why are functions not differentiable at cusps, vertical tangents, and discontinuities?
- Example Problem: Determining If Continuity Implies Differentiability. Does continuity imply differentiability?

- Reading Lesson 3.2
- Instruction – Reading Lesson
- Practice Problems 3.2 – Read section 3.2 in the textbook and complete associated exercises.

- Differentiation Rules
- Instruction – Learn about differentiation rules.
- Example Problem: Applying the Power Rule to Calculate Derivatives. How do we apply the power rule to calculate derivatives?
- Example Problem: Applying the Product Rule to Calculate Derivatives. How do we apply the product rule to calculate derivatives?
- Example Problem: Applying the Quotient Rule to Calculate Derivatives. How do we apply the quotient rule to calculate derivatives?
- Example Problem: Calculating Higher-Order Derivatives Using Rules of Differentiation. How do we calculate higher-order derivatives using rules of differentiation?
- Example Problem: Calculating Instantaneous Rate of Change Using the Derivative. How do we calculate the instantaneous rate of change using the derivative?

- Reading Lesson 3.3
- Instruction – Reading Lesson
- Practice Problems 3.3 – Read section 3.3 in the textbook and complete associated exercises.

- Applications of Derivatives
- Instruction – Learn about applications of derivatives.
- Example Problem: Describing Motion Using the Position Function. How do you describe the motion of an object along a line given only the position function?
- Example Problem: Analyzing the Motion of an Object Traveling Vertically. How do you describe the motion of an object that travels vertically?
- Example Problem: Applying Rates of Change to Area. How do you calculate the rate of change of the area of a growing figure?
- Example Problem: Applying Rates of Change to Economics. How is rate of change applied to economics?

- Reading Lesson 3.4
- Instruction – Reading Lesson
- Practice Problems 3.4 – Read section 3.4 in the textbook and complete associated exercises.

- Differentiating Trigonometric Functions
- Instruction – Learn how to differentiate trigonometric functions.
- Example Problem: Using Trigonometric Functions and the Product Rule. How do you use the product rule with trigonometric functions?
- Example Problem: Using Trigonometric Functions and the Quotient Rule. How do you use the quotient rule with trigonometric functions?
- Example Problem: Using Derivatives of Trigonometric Functions in the Real World. How do you use derivatives of trigonometric functions in the real world?

- Reading Lesson 3.5
- Instruction – Reading Lesson
- Practice Problems 3.5 -Read section 3.5 in the textbook and complete associated exercises.
- Project: Designing a Roller Coaster
- Explain the mathematics of roller coaster construction.

- AP Multiple Choice/Free Response
- Instruction – The Multiple-Choice and Free-Response Sections
- FRQ Preparation – Prepare for your response.
- Unit 3 Free-Response Questions – Complete free-response questions for Unit 3.

- Unit Test
- Unit Test Answers

##### Unit 4: More Derivatives

- Introduction to Unit 4
- Instruction
- Unit 4 Introduction

- Differentiating Functions Using the Chain Rule
- Instruction – Learn how to differentiate functions using the chain rule.
- Example Problem: Finding Derivatives Using the Chain Rule. How do you apply the chain rule to find the derivative of a composite function?
- Example Problem: Determining the Slope of Parametric Curves. How do you use the chain rule to determine the slopes of a curve defined parametrically?

- Reading Lesson 4.1
- Instruction – Reading Lesson
- Practice Problems 4.1 – Read section 4.1 in the textbook and complete associated exercises.

- Differentiating Functions Using Implicit Differentiation
- Instruction – Learn how to differentiate functions using implicit differentiation.
- Example Problem: Calculating the Slope of the Tangent to a Circle. How do you find the slope of a line tangent to a point on a circle?
- Example Problem: Finding the Normal Line. How do you apply implicit differentiation to find the line normal to conic section?
- Example Problem: Determining If Curves are Orthogonal. How do you use implicit differentiation to show that two curves are orthogonal?

- Reading Lesson 4.2
- Instruction – Reading Lesson
- Practice Problems 4.2 -Read section 4.2 in the textbook and complete associated exercises.

- Differentiating Functions Containing Inverse Trigonometric Functions
- Instruction – Learn how to differentiate functions containing inverse trigonometric functions.
- Example Problem: Calculating Derivatives of Inverse Functions. How do you calculate the derivative of the inverse of a function?
- Example Problem: Calculating Derivatives of Inverse Trigonometric Functions. How do you calculate the derivative of an inverse trigonometric function?

- Reading Lesson 4.3
- Instruction – Reading Lesson
- Practice Problems 4.3 – Read section 4.3 in the textbook and complete associated exercises.

- Differentiating Exponential and Logarithmic Functions
- Instruction – Learn how to differentiate exponential and logarithmic functions.
- Example Problem: Calculating the Derivative of an Exponential Function with a Base of e. How do you determine the derivative of an exponential function with a base of e?
- Example Problem: Calculating the Derivative of an Exponential Function with a Base Other Than e. How do you determine the derivative of an exponential function with a base other than e?
- Example Problem: Calculating the Derivative of a Natural Logarithmic Function. How do you calculate the derivative of a natural logarithmic function?
- Example Problem: Calculating the Derivative of a Logarithmic Function with a Base Other Than e. How do you calculate the derivative of a logarithmic function with a base other than e?

- Reading Lesson 4.4
- Instruction – Reading Lesson
- Practice Problems 4.4 – Read section 4.4 in the textbook and complete associated exercises.

- Unit 4 AP Practice Questions
- Unit 4 Free-Response Questions
- Complete free-response questions for Unit 4.

- Unit Test
- Unit Test Answers

##### Unit 5: Applications of Derivatives

- Introduction to Unit 5
- Instruction
- Unit 5 Introduction

- Relative and Absolute Extrema
- Instruction – Learn about relative and absolute extrema.
- Example Problem: Finding Relative Extreme Values. How do you identify relative extreme values of a function given the functional notation?
- Example Problem: Finding Absolute Extreme Values. How do you identify the absolute extreme values of a function given the functional notation?
- Example Problem: Using the Extreme Value Theorem.
- How do you determine if the extreme value theorem applies to a function on a specific interval?

- Reading Lesson 5.1
- Instruction – Reading Lesson
- Practice Problems 5.1 – Read section 5.1 in the textbook and complete associated exercises.

- The Mean Value Theorem
- Instruction – Learn about the mean value theorem.
- Example Problem: Meeting the Criteria of the Mean Value Theorem. How do you determine if a function meets the criteria of the mean value theorem?
- Example Problem: Finding the Value of c That Satisfies the Mean Value Theorem. How do you find the value of c that satisfies the mean value theorem?
- Example Problem: Determining Increasing and Decreasing Intervals. How do you determine intervals where a function is increasing or decreasing?
- Example Problem: Using the Derivative to Determine the Increasing and Decreasing Intervals. How do you use the derivative to determine the intervals where a function is increasing

- Reading Lesson 5.2
- Instruction – Reading Lesson
- Practice Problems 5.2 – Read section 5.2 in the textbook and complete associated exercises.

- First and Second Derivative Test
- Instruction – Learn about the first and second derivative tests.
- Example Problem: Applying the First Derivative Test. How do you determine relative extrema using the first derivative test?
- Example Problem: Applying the Second Derivative Test. How do you determine concavity and points of inflection using the second derivative test?
- Example Problem: Sketching a Curve Using Derivatives. How do you use derivatives to sketch the graph of a function?

- Reading Lesson 5.3
- Instruction – Reading Lesson
- Practice Problems 5.3 – Read section 5.3 in the textbook and complete associated exercises.

- Application Problem Solving
- Instruction – Learn about application problem solving.
- Example Problem: Optimizing Physical Quantities. How do you optimize physical quantities to solve a problem?
- Example Problem: Maximizing Profits. How does a company ensure maximum profit?
- Example Problem: Maximizing the Volume. How can you use first and second derivatives to maximize volume?
- Example Problem: Maximizing Area. How do you determine the dimensions of a rectangle so as to maximize area?

- Reading Lesson 5.4
- Instruction – Reading Lesson
- Practice Problems 5.4 – Read section 5.4 in the textbook and complete associated exercises.

- Newton’s Method, Linearization, and Differentials
- Instruction – Learn about Newton’s method, linearization, and differentials.
- Example Problem: Approximating Values with Linearization. How do you use linearization to approximate values?
- Example Problem: Applying Newton’s Method to Find Zeros. How do you apply Newton’s method to find the zeros of a function?
- Example Problem: Approximating Change Using Differentials. How do you approximate the change in f using differentials?

- Reading Lesson 5.5
- Instruction – Reading Lesson
- Practice Problems 5.5 – Read section 5.5 in the textbook and complete associated exercises.

- Application of Implicit Differentiation
- Instruction – Learn about applications of implicit differentiation.
- Example Problem: Using Substitution to Solve Related Rate Problems. How do you use substitution to solve related rate problems?
- Example Problem: Calculating the Rate Using Similar Figures. How do you calculate the rate of change when the rates an be related using similar figures?
- Example Problem: Using a Scientific Equation to Calculate Related Rates. How do you calculate the rate of change when the rates are related by a given scientific Example Problem: Determining the Rate of a Changing Angle. How do you determine the rate at which an angle is changing over time?

- Reading Lesson 5.6
- Instruction – Reading Lesson
- Practice Problems 5.6 – Read section 5.6 in the textbook and complete associated exercises.
- Project: Optimizing a Soda Can
- Use differentiation to optimize the size of a soda can.

- Unit 5 AP Practice Questions
- Unit 5 Free-Response Questions
- Complete free-response questions for Unit 5.

- Unit Test
- Unit Test Answers

- Cumulative Exam
- Cumulative Exam
- Cumulative Exam Answers