# 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**