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PRE-ALGEBRA ​ACADEMIC LIBRARY (2ND SEMESTER)

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  • PRE-ALGEBRA ​ACADEMIC LIBRARY (2ND SEMESTER)

AP Calculus Ab Academic Library (2nd Semester)

This is your second semester course outline for AP Calculus. This continues the course from first semester.

You are making progress as you begin this second semester. If you are planning to take the AP Exam in May for this course it is strongly recommended that significant time is spent at the conclusion of the course in preparing for the actual exam. Students will typically see better performance if they have taken several practice exams prior to the actual exam.

Go To 2nd Semester Math 500
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Getting Started In Edgenuity

THE STUDENT EXPERIENCE
MATH COURSE
Unit 6: DEFINITE INTEGRALS
  1. Introduction to Unit 6
    1. ​Instruction – Unit 6 Introduction
  2. Estimating with Finite Sums
    1. ​Instruction – Learn about estimating with finite sums. Place value 2
    2. Example Problem: Using Approximation Methods. How are the approximation methods used to estimate area under a curve?
    3. Example Problem: Relating Distance to a Velocity vs. Time Graph. How does the area under the curve apply to velocity?
    4. Example Problem: Approximating the Amount Accumulated. How do you estimate the amount accumulated?
    5. 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?
    6. Example Problem: Estimating Population Density. How do you apply approximations to determine population density?
  3. Reading Lesson 6.1: Estimating with Finite Sums
    1. ​Instruction – Reading Lesson
    2. Practice Problems 6.1 – Read section 6.1 in the textbook and complete associated exercises.
  4. Definite Integrals
    1. ​Instruction – Learn about definite integrals.
    2. Example Problem: Expressing Riemann Sums as Definite Integrals. How do you use integral notation to express a limit of Riemann sums?
    3. Example Problem: Using Area to Evaluate Definite Integrals. How do you evaluate definite integrals using area formulas?
    4. 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?
  5. Reading Lesson 6.2: Definite Integrals
    1. Instruction – Reading Lesson
    2. Practice Problems 6.2 – Read section 6.2 in the textbook and complete associated exercises.
  6. Definite Integrals and Antiderivatives
    1. Instruction – Learn about definite integrals and antiderivatives.
    2. Example Problem: Using the Properties of Definite Integrals. What are the properties of definite integrals?
    3. Example Problem: Using the Properties of Definite Integrals. How can you calculate definite integrals using their properties?
    4. 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?
    5. 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?
    6. Example Problem: Calculating the Integral with Antiderivatives. How is the area under the curve related to antiderivatives?
  7. Reading Lesson 6.3: Definite Integrals and Antiderivatives
    1. Instruction – Reading Lesson
    2. Practice Problems 6.3 – Read section 6.3 in the textbook and complete associated exercises.
  8. Fundamental Theorem of Calculus, Parts 1 and 2
    1. Instruction – Learn about the fundamental theorem of calculus.
    2. Example Problem: Applying the First Part of the Fundamental Theorem. How do you determine derivatives of functions defined with integrals?
    3. Example Problem: Analyzing Graphs with the Fundamental Theorem of Calculus. How do you analyze graphs with the fundamental theorem of calculus?
    4. Example Problem: Constructing a Function with the Fundamental Theorem. How can you use the fundamental theorem of calculus to build a function?
    5. Example Problem: Applying the Second Part of the Fundamental Theorem. How do you evaluate definite integrals with the fundamental theorem of calculus?
    6. Example Problem: Analyzing Rates of Change in the Real World. How do you analyze rates of change with the fundamental theorem of calculus?
  9. Reading Lesson 6.4: Fundamental Theorem of Calculus
    1. Instruction – Reading Lesson
    2. Practice Problems 6.4 – Read section 6.4 in the textbook and complete associated exercises.
  10. Trapezoidal Rule
    1. ​Instruction – Learn about the trapezoidal rule.
    2. 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?
    3. Example Problem: Comparing the Trapezoidal Rule to Other Area Approximations. How does the trapezoidal rule compare with the LRAM, RRAM, and MRAM?
  11. Reading Lesson 6.5: Trapezoidal Rule
    1. ​Instruction – Reading Lesson
    2. Practice Problems 6.5 – Read section 6.5 in the textbook and complete associated exercises.
    3. Project: Analyzing Driving Data
      1. Show that the area under a curve equates to the distance traveled.
  12. Reading Lesson 6.4: Fundamental Theorem of Calculus
    1. ​Unit 6 Free-Response Questions
    2. Complete free-response questions for Unit 6.
  13. Unit Test
    1. Unit Test Answers
Unit 7: MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS
  1. Introduction to Unit 7
    1. Instruction – Unit 7 Introduction
  2. Slope Fields
    1. ​Instruction – Learn about slope fields.
    2. Example Problem: Finding a General Solution. How do you determine the general solution to a differential equation?
    3. Example Problem: Finding a Particular Solution. Given additional information, how do you find the one particular solution to a differential equation?
    4. Example Problem: Constructing a Slope Field. How might the graph of a differential equation appear?
    5. Example Problem: Graphing the Particular Solution on a Slope Field.How do you sketch the particular solution to a differential equation?
  3. Reading Lesson 7.1: Slope Fields and Euler’s Method
    1. ​Instruction – Reading Lesson
    2. Practice Problems 7.1 – Read section 7.1 in the textbook and complete associated exercises.
  4. Antidifferentiation by Substitution
    1. ​Instruction – Learn about antidifferentiation by substitution.
    2. Example Problem: Evaluating Indefinite Integrals. How do you evaluate indefinite integrals without changing variables?
    3. Example Problem: Applying Indefinite Integrals to Velocity and Position. How do you apply indefinite integrals to functions of velocity and position?
    4. Example Problem: Using Substitution to Evaluate Indefinite Integrals. How do you use u-substitution to evaluate indefinite integrals?
    5. Example Problem: Evaluating Definite Integrals Using Substitution. How do you use u-substitution to evaluate definite integrals?
  5. Reading Lesson 7.2: Antidifferentiation by Substitution
    1. ​Instruction – Reading Lesson
    2. Practice Problems 7.2 – Read section 7.2 in the textbook and complete associated exercises.
  6. Exponential Growth and Decay
    1. ​Instruction – Learn about exponential growth and decay.
    2. Example Problem: Solving Differential Equations. How does solving a differential equation by separating the variables compare to solving previous differential equations?
    3. Example Problem: Solving Exponential Growth Problems. How do you solve a problem involving exponential growth?
    4. Example Problem: Solving Exponential Decay Problems. How do you solve a problem involving exponential decay?
    5. Example Problem: Solving Cooling Problems. How can we model the change in temperature of an object as it cools?
  7. Reading Lesson 7.4: Exponential Growth and Decay
    1. ​Instruction – Reading Lesson
    2. Practice Problems 7.4 – Read section 7.4 in the textbook and complete associated exercises.
  8. Unit 7 AP Practice Questions
    1. ​Unit 7 Free-Response Questions
    2. Complete free-response questions for Unit 7.
  9. Unit Test
    1. Unit Test
Unit 8: ​APPLICATIONS OF DEFINITE INTEGRALS
  1. Introduction to Unit 8
    1. ​Instruction – Unit 8 Introduction
  2. Integral as Net Change
    1. ​Instruction – Learn about integral as net change.
    2. Example Problem: Calculating Displacement and Position. How do you calculate displacement and position given a particular velocity function?
    3. Example Problem: Finding Total Distance Traveled. How do you calculate the total distance traveled given a particular velocity function?
    4. 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?
    5. 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?
  3. Reading Lesson 8.1: Accumulation and Net Change
    1. Instruction – Reading Lesson
    2. Practice Problems 8.1 – Read section 8.1 in the textbook and complete associated exercises.
  4. Areas in the Plane
    1. ​Instruction – Learn about areas in the plane.
    2. Example Problem: Calculating Area with dx Integration. How do you determine area by integrating with respect to x?
    3. Example Problem: Calculating Area with dy Integration. How do you determine area by integrating with respect to y?
    4. Example Problem: Calculating Area Using Subregions. How do you determine area by integrating using subregions?
  5. Reading Lesson 8.2: Areas in the Plane
    1. ​Instruction – Reading Lesson
    2. Practice Problems 8.2 – Read section 8.2 in the textbook and complete associated exercises.
  6. Volumes
    1. ​Instruction – Learn about volumes.
    2. Example Problem: Calculating Volumes with Disks. How do you determine volumes of solids using disks?
    3. Example Problem: Calculating Volumes with Disks (dy). How do you determine volumes of solids by integrating with respect to y?
    4. Example Problem: Calculating Volumes with Washers. How do you determine volumes of solids using washers?
    5. Example Problem: Calculating Volumes with Known Cross Sections. How do you determine volumes of solids with known cross sections?
  7. Reading Lesson 8.3: Volumes
    1. ​Instruction – Reading Lesson
    2. Practice Problems 8.3 – Read section 8.3 in the textbook and complete associated exercises.
  8. Applications from Science and Statistics
    1. ​Instruction – Learn about applications of science and statistics.
    2. Example Problem: Calculating the Work Done in Stretching a Spring. How much work is done in stretching a spring?
    3. Example Problem: Finding the Work Done When the Force Is Nonlinear. How do you calculate the work done when the force is nonlinear?
    4. Example Problem: Finding Constant Fluid Force and Fluid Pressure. How do you calculate the fluid force and pressure when the pressure is constant?
    5. Example Problem: Finding Nonconstant Fluid Force and Fluid Pressure. How do you calculate a nonconstant fluid force and pressure?
    6. 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?
  9. Reading Lesson 8.5: Applications from Science and Statistics
    1. ​Instruction – Reading Lesson
    2. Practice Problems 8.5 – Read section 8.5 in the textbook and complete associated exercises.
  10. L’Hospital’s Rule and Other Applications
    1. Instruction – Learn about L’Hospital’s rule and other applications.
    2. 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?
    3. 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?
    4. 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?
    5. Example Problem: Comparing Growth Rates
  11. Reading Lesson 9.2 and 9.3: L’Hospital’s Rule and Other Applications
    1. ​Instruction – Reading Lesson
    2. Practice Problems 9.2 and 9.3 – Read section 9.2 and 9.3 in the textbook and complete associated exercises.
    3. Project: Calculating the Volume of an Object
      1. ​Use calculus to calculate the volume of an object.
  12. Unit 8 AP Practice Questions
    1. ​Unit 8 Free-Response Questions
    2. Complete free-response questions for Unit 8.
  13. Unit Test
    1. Unit Test Answers
Unit 9: REVIEW
  1. Preparing for the Exam
    1. Warm-Up – Get ready for the lesson
    2. Instruction – Preparing for the AP Calculus Exam
  2. Review: Limits and Continuity
    1. ​Instruction – Limits and Continuity
  3. Review: Derivatives
    1. ​Instruction – Derivatives
  4. Review: Applications of Derivatives
    1. ​Instruction – Applications of Derivatives
  5. Review: Integrals
    1. Instruction – Integrals
  6. Review: Applications of Integrals
    1. ​Instruction – Applications of Integrals
  7. Review: Differential Equations
    1. ​Instruction – Differential Equations
  8. Practice Exam 1 – Part A
    1. ​Instruction – AP Calculus Practice Exam 1 Instructions
    2. Practice Exam Multiple Choice Section – Part A Answers
    3. Practice Exam 1 – Part B
    4. Practice Exam Multiple Choice Section – Part B Answers
    5. Practice Exam 1 – Free Response Section
    6. Instruction – The Free-Response Section
    7. Free-Response Section – Complete Part A of the free-response section
    8. Free-Response Section – Complete Part B of the free-response section.
  9. Practice Exam 2 – Part A
    1. ​Instruction – AP Calculus Practice Exam 2 Instructions
    2. Practice Exam Multiple Choice Section – Part A Answers
    3. Practice Exam 2 – Part B
    4. Practice Exam Multiple Choice Section – Part B Answers
    5. Practice Exam 2 – Free Response Section
    6. Instruction – The Free-Response Section
    7. Free-Response Section – Complete Part A of the free-response section.
    8. Free-Response Section – ​Complete Part B of the free-response section