AP CALCULUS AB ACADEMIC LIBRARY
1ST SEMESTER
GETTING STARTED IN EDGENUITY
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 U 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.
- 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.
- Unitest
- 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 Derivative
- Introduction to Unit
- Instructio
- Unit 5 Introductio
- Relative and Absolute Extrem
- 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.
- Instruction – Reading Lesso
- Practice Problems 5.1 – Read section 5.1 in the textbook and complete associated exercises
- The Mean Value Theore
- 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 increasin
- Reading Lesson 5.
- Instruction – Reading Lesso
- Practice Problems 5.2 – Read section 5.2 in the textbook and complete associated exercises
- First and Second Derivative Tes
- 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.
- Instruction – Reading Lesso
- Practice Problems 5.3 – Read section 5.3 in the textbook and complete associated exercises
- Application Problem Solvin
- 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.
- Instruction – Reading Lesso
- Practice Problems 5.4 – Read section 5.4 in the textbook and complete associated exercises
- Newton’s Method, Linearization, and Differential
- 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.
- Instruction – Reading Lesso
- Practice Problems 5.5 – Read section 5.5 in the textbook and complete associated exercises
- Application of Implicit Differentiatio
- 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.
- Instruction – Reading Lesso
- Practice Problems 5.6 – Read section 5.6 in the textbook and complete associated exercises
- Project: Optimizing a Soda Ca
- Use differentiation to optimize the size of a soda can
- Unit 5 AP Practice Question
- Unit 5 Free-Response Question
- Complete free-response questions for Unit 5
- Unit Tes
- Unit Test Answer
Cumulative Exam
- Cumulative Exam
- Cumulative Exam Answers