# PRE-ALGEBRA ACADEMIC LIBRARY (2ND SEMESTER)

## Getting Started In Edgenuity

##### THE STUDENT EXPERIENCE

##### MATH COURSE

##### Unit 6: DEFINITE INTEGRALS

- Introduction to Unit 6
- Instruction – Unit 6 Introduction

- Estimating with Finite Sums
- Instruction – Learn about estimating with finite sums. Place value 2
- Example Problem: Using Approximation Methods. How are the approximation methods used to estimate area under a curve?
- Example Problem: Relating Distance to a Velocity vs. Time Graph. How does the area under the curve apply to velocity?
- Example Problem: Approximating the Amount Accumulated. How do you estimate the amount accumulated?
- Example Problem: Connecting the Area under the Curve to the Volume of a Sphere. How can you extend the area under a curve to estimate the volume of a sphere?
- Example Problem: Estimating Population Density. How do you apply approximations to determine population density?

- Reading Lesson 6.1: Estimating with Finite Sums
- Instruction – Reading Lesson
- Practice Problems 6.1 – Read section 6.1 in the textbook and complete associated exercises.

- Definite Integrals
- Instruction – Learn about definite integrals.
- Example Problem: Expressing Riemann Sums as Definite Integrals. How do you use integral notation to express a limit of Riemann sums?
- Example Problem: Using Area to Evaluate Definite Integrals. How do you evaluate definite integrals using area formulas?
- Example Problem: Writing Accumulator Functions. How can you use definite integrals to solve problems using accumulation? Example Problem: Evaluating Definite Integrals of Non-Continuous Functions. How do you evaluate definite integrals with discontinuities?

- Reading Lesson 6.2: Definite Integrals
- Instruction – Reading Lesson
- Practice Problems 6.2 – Read section 6.2 in the textbook and complete associated exercises.

- Definite Integrals and Antiderivatives
- Instruction – Learn about definite integrals and antiderivatives.
- Example Problem: Using the Properties of Definite Integrals. What are the properties of definite integrals?
- Example Problem: Using the Properties of Definite Integrals. How can you calculate definite integrals using their properties?
- Example Problem: Using the Properties of Definite Integrals to Evaluate the Upper and Lower Bounds for an Integral. How can you evaluate the upper and lower bounds of a definite integral?
- Example Problem: Using the Mean Value Theorem. How can you use the mean value theorem for definite integrals to find the point where the average value occurs?
- Example Problem: Calculating the Integral with Antiderivatives. How is the area under the curve related to antiderivatives?

- Reading Lesson 6.3: Definite Integrals and Antiderivatives
- Instruction – Reading Lesson
- Practice Problems 6.3 – Read section 6.3 in the textbook and complete associated exercises.

- Fundamental Theorem of Calculus, Parts 1 and 2
- Instruction – Learn about the fundamental theorem of calculus.
- Example Problem: Applying the First Part of the Fundamental Theorem. How do you determine derivatives of functions defined with integrals?
- Example Problem: Analyzing Graphs with the Fundamental Theorem of Calculus. How do you analyze graphs with the fundamental theorem of calculus?
- Example Problem: Constructing a Function with the Fundamental Theorem. How can you use the fundamental theorem of calculus to build a function?
- Example Problem: Applying the Second Part of the Fundamental Theorem. How do you evaluate definite integrals with the fundamental theorem of calculus?
- Example Problem: Analyzing Rates of Change in the Real World. How do you analyze rates of change with the fundamental theorem of calculus?

- Reading Lesson 6.4: Fundamental Theorem of Calculus
- Instruction – Reading Lesson
- Practice Problems 6.4 – Read section 6.4 in the textbook and complete associated exercises.

- Trapezoidal Rule
- Instruction – Learn about the trapezoidal rule.
- Example Problem: Approximating the Area under a Curve by Using the Trapezoidal Rule. How do we use the trapezoidal rule to approximate the area under a curve?
- Example Problem: Comparing the Trapezoidal Rule to Other Area Approximations. How does the trapezoidal rule compare with the LRAM, RRAM, and MRAM?

- Reading Lesson 6.5: Trapezoidal Rule
- Instruction – Reading Lesson
- Practice Problems 6.5 – Read section 6.5 in the textbook and complete associated exercises.
- Project: Analyzing Driving Data
- Show that the area under a curve equates to the distance traveled.

- Reading Lesson 6.4: Fundamental Theorem of Calculus
- Unit 6 Free-Response Questions
- Complete free-response questions for Unit 6.

- Unit Test
- Unit Test Answers

##### Unit 7: MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS

- Introduction to Unit 7
- Instruction – Unit 7 Introduction

- Slope Fields
- Instruction – Learn about slope fields.
- Example Problem: Finding a General Solution. How do you determine the general solution to a differential equation?
- Example Problem: Finding a Particular Solution. Given additional information, how do you find the one particular solution to a differential equation?
- Example Problem: Constructing a Slope Field. How might the graph of a differential equation appear?
- Example Problem: Graphing the Particular Solution on a Slope Field.How do you sketch the particular solution to a differential equation?

- Reading Lesson 7.1: Slope Fields and Euler’s Method
- Instruction – Reading Lesson
- Practice Problems 7.1 – Read section 7.1 in the textbook and complete associated exercises.

- Antidifferentiation by Substitution
- Instruction – Learn about antidifferentiation by substitution.
- Example Problem: Evaluating Indefinite Integrals. How do you evaluate indefinite integrals without changing variables?
- Example Problem: Applying Indefinite Integrals to Velocity and Position. How do you apply indefinite integrals to functions of velocity and position?
- Example Problem: Using Substitution to Evaluate Indefinite Integrals. How do you use u-substitution to evaluate indefinite integrals?
- Example Problem: Evaluating Definite Integrals Using Substitution. How do you use u-substitution to evaluate definite integrals?

- Reading Lesson 7.2: Antidifferentiation by Substitution
- Instruction – Reading Lesson
- Practice Problems 7.2 – Read section 7.2 in the textbook and complete associated exercises.

- Exponential Growth and Decay
- Instruction – Learn about exponential growth and decay.
- Example Problem: Solving Differential Equations. How does solving a differential equation by separating the variables compare to solving previous differential equations?
- Example Problem: Solving Exponential Growth Problems. How do you solve a problem involving exponential growth?
- Example Problem: Solving Exponential Decay Problems. How do you solve a problem involving exponential decay?
- Example Problem: Solving Cooling Problems. How can we model the change in temperature of an object as it cools?

- Reading Lesson 7.4: Exponential Growth and Decay
- Instruction – Reading Lesson
- Practice Problems 7.4 – Read section 7.4 in the textbook and complete associated exercises.

- Unit 7 AP Practice Questions
- Unit 7 Free-Response Questions
- Complete free-response questions for Unit 7.

- Unit Test
- Unit Test

##### Unit 8: APPLICATIONS OF DEFINITE INTEGRALS

- Introduction to Unit 8
- Instruction – Unit 8 Introduction

- Integral as Net Change
- Instruction – Learn about integral as net change.
- Example Problem: Calculating Displacement and Position. How do you calculate displacement and position given a particular velocity function?
- Example Problem: Finding Total Distance Traveled. How do you calculate the total distance traveled given a particular velocity function?
- Example Problem: Finding Net Change from Rate of Change Functions. How do you find the net change of a quantity from a rate of change function?
- Example Problem: Finding Net Change from Graphs and Tables. How do you find the net change of a quantity from a rate of change given in graphical or tabular form?

- Reading Lesson 8.1: Accumulation and Net Change
- Instruction – Reading Lesson
- Practice Problems 8.1 – Read section 8.1 in the textbook and complete associated exercises.

- Areas in the Plane
- Instruction – Learn about areas in the plane.
- Example Problem: Calculating Area with dx Integration. How do you determine area by integrating with respect to x?
- Example Problem: Calculating Area with dy Integration. How do you determine area by integrating with respect to y?
- Example Problem: Calculating Area Using Subregions. How do you determine area by integrating using subregions?

- Reading Lesson 8.2: Areas in the Plane
- Instruction – Reading Lesson
- Practice Problems 8.2 – Read section 8.2 in the textbook and complete associated exercises.

- Volumes
- Instruction – Learn about volumes.
- Example Problem: Calculating Volumes with Disks. How do you determine volumes of solids using disks?
- Example Problem: Calculating Volumes with Disks (dy). How do you determine volumes of solids by integrating with respect to y?
- Example Problem: Calculating Volumes with Washers. How do you determine volumes of solids using washers?
- Example Problem: Calculating Volumes with Known Cross Sections. How do you determine volumes of solids with known cross sections?

- Reading Lesson 8.3: Volumes
- Instruction – Reading Lesson
- Practice Problems 8.3 – Read section 8.3 in the textbook and complete associated exercises.

- Applications from Science and Statistics
- Instruction – Learn about applications of science and statistics.
- Example Problem: Calculating the Work Done in Stretching a Spring. How much work is done in stretching a spring?
- Example Problem: Finding the Work Done When the Force Is Nonlinear. How do you calculate the work done when the force is nonlinear?
- Example Problem: Finding Constant Fluid Force and Fluid Pressure. How do you calculate the fluid force and pressure when the pressure is constant?
- Example Problem: Finding Nonconstant Fluid Force and Fluid Pressure. How do you calculate a nonconstant fluid force and pressure?
- Example Problem: Using the Definite Integral to Find the Probability of an Event.How do you find the probability of an event using the probability density function?

- Reading Lesson 8.5: Applications from Science and Statistics
- Instruction – Reading Lesson
- Practice Problems 8.5 – Read section 8.5 in the textbook and complete associated exercises.

- L’Hospital’s Rule and Other Applications
- Instruction – Learn about L’Hospital’s rule and other applications.
- Example Problem: Applying L’Hospital’s Rule to Evaluate Limits. How do you apply L’Hospital’s rule to evaluate the limit of the indeterminate form 0/0?
- Example Problem: Applying L’Hospital’s Rule to Evaluate Limits. How do you apply L’Hospital’s rule to evaluate the limit of the indeterminate form infinity/infinity?
- Example Problem: Applying L’Hospital’s Rule to Other Indeterminate Forms. How do you apply L’Hospital’s rule to evaluate the limit of other indeterminate forms?
- Example Problem: Comparing Growth Rates

- Reading Lesson 9.2 and 9.3: L’Hospital’s Rule and Other Applications
- Instruction – Reading Lesson
- Practice Problems 9.2 and 9.3 – Read section 9.2 and 9.3 in the textbook and complete associated exercises.
- Project: Calculating the Volume of an Object
- Use calculus to calculate the volume of an object.

- Unit 8 AP Practice Questions
- Unit 8 Free-Response Questions
- Complete free-response questions for Unit 8.

- Unit Test
- Unit Test Answers

##### Unit 9: REVIEW

- Preparing for the Exam
- Warm-Up – Get ready for the lesson
- Instruction – Preparing for the AP Calculus Exam

- Review: Limits and Continuity
- Instruction – Limits and Continuity

- Review: Derivatives
- Instruction – Derivatives

- Review: Applications of Derivatives
- Instruction – Applications of Derivatives

- Review: Integrals
- Instruction – Integrals

- Review: Applications of Integrals
- Instruction – Applications of Integrals

- Review: Differential Equations
- Instruction – Differential Equations

- Practice Exam 1 – Part A
- Instruction – AP Calculus Practice Exam 1 Instructions
- Practice Exam Multiple Choice Section – Part A Answers
- Practice Exam 1 – Part B
- Practice Exam Multiple Choice Section – Part B Answers
- Practice Exam 1 – Free Response Section
- Instruction – The Free-Response Section
- Free-Response Section – Complete Part A of the free-response section
- Free-Response Section – Complete Part B of the free-response section.

- Practice Exam 2 – Part A
- Instruction – AP Calculus Practice Exam 2 Instructions
- Practice Exam Multiple Choice Section – Part A Answers
- Practice Exam 2 – Part B
- Practice Exam Multiple Choice Section – Part B Answers
- Practice Exam 2 – Free Response Section
- Instruction – The Free-Response Section
- Free-Response Section – Complete Part A of the free-response section.
- Free-Response Section – Complete Part B of the free-response section