2019 Practice Exam Ap Calc Ab

2019 AP Calculus AB Practice Exam: A Comprehensive Guide to Success

The AP Calculus AB exam is a significant hurdle for high school students aiming for college credit. Success hinges on consistent practice and a deep understanding of the core concepts. This comprehensive guide focuses on the 2019 AP Calculus AB exam, offering a detailed breakdown of the exam format, crucial topics, effective study strategies, and practice problem examples to help you ace the test.

Understanding the 2019 AP Calculus AB Exam Structure

The 2019 AP Calculus AB exam consisted of two sections:

Section I: Multiple Choice

• Number of Questions: 45 questions
• Time Allotted: 1 hour 45 minutes (105 minutes)
• Types of Questions: Multiple choice questions tested your understanding of various Calculus AB topics. These questions ranged in difficulty and included both straightforward calculations and more complex problem-solving scenarios. Many involved interpreting graphs, tables, or functions.

Section II: Free Response

• Number of Questions: 6 questions
• Time Allotted: 1 hour 30 minutes (90 minutes)
• Types of Questions: This section tested your ability to apply calculus concepts to solve complex problems. You'll encounter both calculator-permitted and calculator-prohibited questions. Expect a variety of question types, including:
  • Derivatives: Finding derivatives using various rules (power rule, product rule, quotient rule, chain rule), interpreting derivatives in context (slope, rate of change), and applying derivatives to optimization problems.
  • Integrals: Evaluating definite and indefinite integrals using various techniques (substitution, integration by parts – though less likely on the AB exam), understanding the fundamental theorem of calculus, and applying integrals to find areas and volumes.
  • Applications of Derivatives: Related rates, optimization, curve sketching, motion problems (position, velocity, acceleration).
  • Applications of Integrals: Area between curves, volumes of revolution (disk/washer and shell methods).

Key Topics Covered in the 2019 AP Calculus AB Exam

Mastering these core concepts is paramount for success:

1. Limits and Continuity

• Understanding Limits: Intuitive understanding of limits, evaluating limits graphically, numerically, and algebraically, using limit laws, and dealing with indeterminate forms (L'Hopital's rule is not on the AB exam but understanding indeterminate forms is crucial).
• Continuity: Defining continuity, identifying discontinuities (removable, jump, infinite), and applying the Intermediate Value Theorem.

Example: Find the limit as x approaches 2 of (x² - 4) / (x - 2). (This requires factoring and simplification).

2. Derivatives

• Definition of the Derivative: Understanding the derivative as the instantaneous rate of change, calculating derivatives using the limit definition, and interpreting the derivative geometrically (slope of the tangent line).
• Derivative Rules: Proficiently applying the power rule, product rule, quotient rule, and chain rule.
• Implicit Differentiation: Finding derivatives of implicitly defined functions.
• Related Rates: Solving problems involving related rates by identifying variables, setting up equations, and differentiating with respect to time.
• Extrema and Optimization: Finding critical points, classifying extrema (local max/min), and applying the first and second derivative tests to solve optimization problems.
• Mean Value Theorem: Understanding and applying the Mean Value Theorem.

Example: A spherical balloon is being inflated at a rate of 10 cubic centimeters per second. How fast is the radius increasing when the radius is 5 cm? (Related rates problem).

3. Integrals

• Definite and Indefinite Integrals: Evaluating definite and indefinite integrals using the power rule and understanding the fundamental theorem of calculus.
• Area Under a Curve: Finding the area between a curve and the x-axis using definite integrals.
• Area Between Curves: Calculating the area between two curves.
• Average Value of a Function: Calculating the average value of a function over an interval.
• Fundamental Theorem of Calculus: Understanding both parts of the fundamental theorem and applying them to solve problems.

Example: Find the area bounded by the curves y = x² and y = x. (Area between curves).

4. Applications of Derivatives and Integrals

• Motion Problems: Analyzing motion problems involving position, velocity, and acceleration.
• Curve Sketching: Sketching curves by analyzing derivatives, finding critical points, inflection points, and asymptotes.
• Volumes of Revolution: Calculating volumes of solids of revolution using the disk/washer and shell methods.

Effective Study Strategies for the AP Calculus AB Exam

Success requires a strategic approach to studying:

• Thorough Understanding of Concepts: Don't just memorize formulas; understand the underlying principles. Work through numerous examples to build intuition.
• Consistent Practice: Regular practice is crucial. Solve a variety of problems from textbooks, practice exams, and online resources. Focus on problems that challenge your understanding.
• Review Past Exams: Analyze past AP Calculus AB exams (including the 2019 exam) to identify your strengths and weaknesses. Focus your study efforts on areas where you need improvement.
• Focus on Problem-Solving Skills: AP Calculus AB is less about memorization and more about problem-solving. Practice applying concepts in different contexts.
• Seek Help When Needed: Don't hesitate to ask your teacher, tutor, or classmates for help when you are struggling with a concept.
• Time Management: Practice working under timed conditions to simulate the actual exam environment. Learn to pace yourself effectively.
• Utilize Available Resources: Take advantage of textbooks, online resources, study guides, and practice exams.

Practice Problem Examples (mimicking 2019 exam style)

Multiple Choice (No Calculator):

1. If f(x) = x³ - 6x², find the critical points of f(x).
2. Evaluate the definite integral ∫₀¹ (2x + 1) dx.
3. Find the derivative of g(x) = (x² + 1) / (x - 2).

Multiple Choice (Calculator Permitted):

1. A particle moves along a straight line with velocity v(t) = t² - 4t + 3. Find the total distance traveled by the particle from t = 0 to t = 4.
2. Find the area bounded by the curves y = eˣ, y = 0, x = 0, and x = 1.

Free Response (No Calculator):

1. Let f(x) = x³ - 3x² + 2.
   • Find the intervals where f(x) is increasing and decreasing.
   • Find the local extrema of f(x).
   • Find the intervals where f(x) is concave up and concave down.
   • Find the inflection points of f(x).
   • Sketch the graph of f(x).

Free Response (Calculator Permitted):

1. A water tank has the shape of an inverted cone with a radius of 5 meters and a height of 10 meters. Water is being pumped into the tank at a rate of 2 cubic meters per minute. How fast is the water level rising when the water is 4 meters deep?

Conclusion: Achieving AP Calculus AB Success

The 2019 AP Calculus AB exam, like all AP exams, demanded a strong grasp of fundamental concepts and the ability to apply them effectively. By focusing on a thorough understanding of limits, derivatives, and integrals, practicing consistently with diverse problem sets, and utilizing effective study strategies, you can significantly increase your chances of success. Remember to focus on problem-solving skills, manage your time wisely, and seek help when needed. With diligent preparation, achieving a high score on the AP Calculus AB exam is well within your reach. Remember to consult your teacher and course materials for the most accurate and relevant information specific to your curriculum.