2019 AP Calc BC FRQ: A Comprehensive Guide to Success

Understanding the Exam

The 2019 AP Calculus BC Free Response Questions (FRQs) are designed to assess students’ abilities in the following areas:

• Limits and Continuity
• Derivatives
• Integrals
• Applications of Integrals
• Differential Equations

Exam Format

The FRQs consist of six questions, each worth 10 points. Students have two hours to complete the exam.

Question Breakdown

Scoring Rubric

The scoring rubric for the FRQs is based on the following criteria:

• Accuracy: Completeness of solution and correctness of answer
• Method: Clear and logical approach to the problem
• Communication: Clarity and precision of written response

Strategies for Success

To prepare for the 2019 AP Calc BC FRQs, students should focus on the following strategies:

• Master the concepts: Thoroughly understand the fundamental concepts of calculus, including limits, derivatives, integrals, and applications.
• Practice regularly: Solve numerous practice problems to improve problem-solving skills and build confidence.
• Time management: Manage time effectively during the exam by allocating an appropriate amount of time to each question.
• Show your work: Clearly show all steps of your solution to earn partial credit.
• Review previous FRQs: Analyze past FRQs to identify common question types and develop effective strategies.

Question-Specific Tips

Below are some specific tips for each question type:

Limits and Continuity

• Use the epsilon-delta definition of limits to prove continuity at a specific point.
• Apply L’Hopital’s Rule to evaluate indeterminate forms.

Derivatives

• Use the definition of a derivative to find the derivative of a function.
• Employ the Chain Rule, Product Rule, and Quotient Rule to differentiate complex functions.
• Calculate derivatives of logarithmic and exponential functions using the logarithmic and exponential differentiation formulas.

Integrals

• Use the Fundamental Theorem of Calculus to evaluate definite integrals.
• Apply integration techniques such as substitution, integration by parts, and trigonometric substitution to solve indefinite integrals.
• Find area and volume using integrals.

Applications of Integrals

• Use integrals to find the volume of solids of revolution.
• Apply integrals to calculate the work done by a force over a distance.
• Solve optimization problems using integrals.

Differential Equations

• Solve separable differential equations.
• Find particular solutions to first-order linear differential equations.
• Use slope fields to analyze the behavior of solutions to differential equations.

Comprehensive Synthesis

• Combine multiple calculus concepts to solve complex problems.
• Apply calculus to real-world situations.

FAQs

1. How long should I spend on each question?

Approximately 20 minutes per question.

2. What is the most important thing to remember on test day?

Stay calm, manage your time effectively, and show all of your work.

3. What resources are available for practice?

Official AP practice questions, textbooks, online practice platforms, and private tutors.

4. How can I improve my understanding of the concepts?

Attend class regularly, ask questions, review lecture notes, and seek additional help from teachers or tutors.

5. What are some common mistakes to avoid?

Making careless errors, not showing all of your work, and misunderstanding the question.

6. What is the best way to prepare for the synthesis question?

Practice applying calculus to real-world situations and solving problems that require multiple steps.

Tables

Table 1: Question Topics and Points

Table 2: Scoring Rubric

Table 3: Question-Specific Tips

Table 4: FAQs