Ap Calculus Bc Practice Exam 2017

AP Calculus BC Practice Exam 2017: A Comprehensive Guide to Success

The AP Calculus BC exam is a challenging but rewarding experience for high school students. This comprehensive guide focuses on the 2017 AP Calculus BC practice exam, providing a detailed walkthrough, strategy tips, and resources to help you excel. Mastering calculus requires consistent effort and a strong understanding of core concepts. Let's dive into preparing you for success.

Understanding the AP Calculus BC Exam Structure

The AP Calculus BC exam is divided into two sections:

Section I: Multiple Choice (50% of total score)

• Part A: 30 multiple-choice questions; 60 minutes; no calculator allowed. This section tests your conceptual understanding and ability to perform calculations without technology.
• Part B: 15 multiple-choice questions; 45 minutes; calculator permitted. This section allows the use of graphing calculators to solve more complex problems.

Section II: Free Response (50% of total score)

• Part A: 2 free-response questions; 30 minutes; calculator permitted. These questions often involve applications of calculus.
• Part B: 4 free-response questions; 60 minutes; no calculator allowed. These questions focus on conceptual understanding and problem-solving skills without reliance on calculators.

Key Topics Covered in the 2017 AP Calculus BC Exam

The 2017 exam, like subsequent years, thoroughly tested students on the following topics:

1. Limits and Continuity:

• Definition of a limit: Understanding how to evaluate limits using various techniques (direct substitution, factoring, L'Hopital's Rule).
• Continuity: Determining whether a function is continuous at a point and identifying types of discontinuities (removable, jump, infinite).
• One-sided limits: Evaluating limits from the left and right.

2. Derivatives:

• Definition of a derivative: Understanding the derivative as a rate of change, slope of a tangent line, and instantaneous velocity.
• Derivative rules: Mastering the power rule, product rule, quotient rule, chain rule, and implicit differentiation.
• Applications of derivatives: Solving optimization problems, related rates problems, and analyzing graphs of functions (increasing/decreasing, concavity, inflection points).
• Mean Value Theorem and Rolle's Theorem: Understanding and applying these important theorems.

3. Integrals:

• Definition of an integral: Understanding the integral as the area under a curve.
• Fundamental Theorem of Calculus: Mastering both parts of the theorem and their applications.
• Integration techniques: Mastering u-substitution, integration by parts, and trigonometric substitution.
• Applications of integrals: Solving area problems, volume problems (disk/washer method, shell method), and accumulation functions.
• Improper integrals: Evaluating integrals with infinite limits of integration or infinite discontinuities.

4. Differential Equations:

• Solving separable differential equations: Understanding how to solve differential equations by separating variables.
• Slope fields: Interpreting and sketching slope fields.
• Euler's method: Approximating solutions to differential equations using Euler's method.

5. Infinite Series:

• Sequences and series: Understanding convergence and divergence of sequences and series.
• Tests for convergence: Mastering various tests such as the comparison test, limit comparison test, integral test, ratio test, and alternating series test.
• Power series: Finding the radius and interval of convergence.
• Taylor and Maclaurin series: Understanding how to find Taylor and Maclaurin series expansions for functions.

6. Parametric Equations and Polar Coordinates:

• Parametric equations: Finding derivatives, areas, and arc lengths for curves defined parametrically.
• Polar equations: Converting between rectangular and polar coordinates, finding areas and arc lengths in polar coordinates.

Strategies for Success on the 2017 (and Subsequent) AP Calculus BC Exam

1. Master the Fundamentals: A strong foundation in precalculus is crucial. Ensure you have a solid understanding of algebra, trigonometry, and analytic geometry.

2. Practice, Practice, Practice: Work through numerous practice problems. The more you practice, the more comfortable you'll become with the types of questions and the problem-solving techniques required. Use past AP Calculus BC exams and practice tests available online.

3. Understand, Don't Memorize: Focus on understanding the underlying concepts rather than memorizing formulas. Understanding why a formula works will help you apply it effectively in various situations.

4. Develop Strong Problem-Solving Skills: Calculus problems often require a multi-step approach. Practice breaking down complex problems into smaller, manageable parts.

5. Utilize Your Calculator Effectively: For the calculator-permitted sections, learn how to use your graphing calculator to perform calculations, graph functions, and find numerical approximations efficiently. Become familiar with its capabilities beyond basic arithmetic.

6. Time Management: Practice working under timed conditions to improve your speed and efficiency. Allocate your time wisely during the exam.

7. Review Regularly: Consistent review is key to retaining information and strengthening your understanding of the concepts. Regularly review key topics and practice problems.

8. Seek Help When Needed: Don't hesitate to ask your teacher or a tutor for help if you are struggling with a particular concept. Getting clarification early on can prevent misunderstandings from snowballing.

9. Stay Calm and Focused: The exam can be stressful, but try to remain calm and focused. Take deep breaths, and don't get discouraged if you encounter a difficult problem. Move on to other questions and return later if time permits.

Analyzing the 2017 AP Calculus BC Free Response Questions (Illustrative Examples)

While the specific questions from the 2017 exam aren't publicly released in their entirety, we can analyze the general types of free-response questions that typically appear, illustrating the concepts tested.

Example 1: Related Rates

A problem might involve a scenario like a ladder sliding down a wall. You would be given information about the rate at which the ladder is sliding down and asked to find the rate at which the top of the ladder is moving along the wall at a specific moment. This requires applying implicit differentiation and understanding related rates.

Example 2: Optimization

A common problem involves finding the maximum or minimum value of a function subject to certain constraints. For example, finding the dimensions of a rectangular box with a given volume that minimizes surface area. This requires finding critical points and using the second derivative test to determine maxima or minima.

Example 3: Area Between Curves

A problem may require calculating the area between two curves. This involves setting up and evaluating a definite integral, paying careful attention to the limits of integration and the order of the functions.

Example 4: Volume of Solids of Revolution

You might be asked to find the volume of a solid generated by revolving a region around an axis. This could involve the disk/washer method or the shell method. Choosing the appropriate method and setting up the integral correctly is crucial.

Example 5: Differential Equations

A problem may involve solving a separable differential equation or sketching a slope field. This tests your understanding of differential equations and their applications.

Resources for AP Calculus BC Preparation

While specific resources for the 2017 exam are limited, numerous valuable resources exist for preparing for the AP Calculus BC exam in general. These include:

• Textbook: Your AP Calculus BC textbook is an invaluable resource. Review the chapters thoroughly, paying attention to examples and exercises.
• Practice Books: Many reputable publishers offer practice books specifically designed for the AP Calculus BC exam. These books often include practice problems and full-length practice exams.
• Online Resources: Numerous websites and online platforms offer practice problems, videos, and other resources for AP Calculus BC. These can be excellent supplements to your textbook and classroom instruction.
• Study Groups: Forming a study group with classmates can be a beneficial way to learn from each other, share strategies, and quiz each other on key concepts.

By diligently following these strategies, dedicating sufficient study time, and leveraging available resources, you can significantly improve your chances of success on the AP Calculus BC exam. Remember, consistent effort and a deep understanding of the underlying concepts are key to mastering this challenging subject. Good luck!