✍️ Free Response Questions (FRQ)
Calculus Free Response Questions
👑 Unit 1: Limits & Continuity
1.5Determining Limits Using Algebraic Properties of Limits
1.6Determining Limits Using Algebraic Manipulation
1.10Exploring Types of Discontinuities
1.11Defining Continuity at a Point
1.12Confirming Continuity over an Interval
🤓 Unit 2: Differentiation: Definition & Fundamental Properties
2.4Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
🤙🏽 Unit 3: Differentiation: Composite, Implicit & Inverse Functions
3.0Unit 3 Overview: Differentiation: Composite, Implicit, and Inverse Functions
3.1The Chain Rule
3.3Differentiating Inverse Functions
3.4Differentiating Inverse Trigonometric Functions
👀 Unit 4: Contextual Applications of the Differentiation
4.2Straight-Line Motion: Connecting Position, Velocity, and Acceleration
4.4Intro to Related Rates
4.6Approximating Values of a Function Using Local Linearity and Linearization
✨ Unit 5: Analytical Applications of Differentiation
5.0Unit 5 Overview: Analytical Applications of Differentiation
5.2Extreme Value Theorem, Global vs Local Extrema, and Critical Points
5.3Determining Intervals on Which a Function is Increasing or Decreasing
5.4Using the First Derivative Test to Determine Relative (Local) Extrema
5.7Using the Second Derivative Test to Determine Extrema
🔥 Unit 6: Integration and Accumulation of Change
6.11Integrating Using Integration by Parts
💎 Unit 7: Differential Equations
7.0Unit 7 Overview: Differential Equations
7.7Finding Particular Solutions Using Initial Conditions and Separation of Variables
🐶 Unit 8: Applications of Integration
8.1Finding the Average Value of a Function on an Interval
8.2Connecting Position, Velocity, and Acceleration of Functions Using Integrals
8.3Using Accumulation Functions and Definite Integrals in Applied Contexts
8.4Finding the Area Between Curves Expressed as Functions of x
8.5Finding the Area Between Curves Expressed as Functions of y
8.6Finding the Area Between Curves That Intersect at More Than Two Points
8.7Volumes with Cross Sections: Squares and Rectangles
8.8Volumes with Cross Sections: Triangles and Semicircles
8.9Volume with Disc Method: Revolving Around the x- or y-Axis
8.10Volume with Disc Method: Revolving Around Other Axes
8.11Volume with Washer Method: Revolving Around the x- or y-Axis
🦖 Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)
9.0Unit 9 Overview: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
9.1Defining and Differentiating Parametric Equations
♾ Unit 10: Infinite Sequences and Series (BC Only)
10.0Unit 10 Overview: Infinite Series and Sequences
10.1Defining Convergent and Divergent Infinite Series
10.6Comparison Tests for Convergence
10.7Alternating Series Test for Convergence
10.1110.11 Finding Taylor Polynomial Approximations of Functions
10.14Finding Taylor or Maclaurin Series for a Function
🧐 Multiple Choice Questions (MCQ)
⏱️ 3 min read
October 28, 2020
Not my favorite color-by-letter. Image Courtesy of Alberto G.
For many students in AP Calculus, the multiple-choice section is easier than the free-response section. You'll be asked more straightforward skills-based questions, problems typically don't build off of each other, and you have the power to guess. Still, doing well on the multiple-choice requires good test-taking strategies and lots of practice. Here are our tips and tricks to help you do your best in May!
➕Check out this in-depth multiple choice study guide for more info.
Understanding the format of the exam is key to dividing your studying and pacing yourself when doing practice questions.
The multiple-choice section makes up 50% of your score, and you have an hour and 45 minutes to answer 45 questions. This section has 2 parts:
Part A: 60 minutes for 30 non-calculator questions.
Part B: 45 minutes for 15 calculator-required questions.
And here's how often each unit shows up on the test:
|Unit||Exam Weighting (AB)||Exam Weighting (BC)|
|Unit 1: Limits and Continuity||10-12%||4-7%|
|Unit 2: Differentiation: Definition and Fundamental Properties||10-12%||4-7%|
|Unit 3: Differentiation: Composite, Implicit, and Inverse Functions||9-13%||4-7%|
|Unit 4: Contextual Applications of Differentiation||10-15%||6-9%|
|Unit 5: Analytical Applications of Differentiation||15-18%||8-11%|
|Unit 6: Integration and Accumulation of Change||17-20%||17-20%|
|Unit 7: Differential Equations||6-12%||6-9%|
|Unit 8: Applications of Integration||10-15%||6-9%|
|Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC only)||11-12%|
|Unit 10: Infinite Sequences and Series (BC only)||17-18%|
If it's a skill you're confident in, do the problem first. Often, the College Board includes "good" wrong answers that can lead you in the wrong direction. Don't get distracted by your answer options unless you need to see them to know what you have to do. Remember to trust your gut!
Star problems you struggle with to come back to later. You only have 2-3 minutes per question, so you should get through the test first before you double-check your answers. Make sure to mark a temporary answer on your bubble sheet (e.g. putting a slash through a bubble) so you don't accidentally fill in your answers one space off from where they should be.
If you have time, double-check. Sometimes, there will be a tiny difference between the correct answer and one of the wrong answers. Did you add instead of subtracting? Did you forget a negative? Sometimes, simple algebra mistakes can cost you a question.
Take note of your weaknesses. As you practice multiple choice questions, write down the types of questions you get wrong. Use this information to guide your studying before you take another practice test.
When all else fails, guess. Use your typical guessing strategies (like sticking with the same letter answer any time you guess), and eliminate wrong answers whenever possible. Try not to leave any questions blank, since you won't be penalized for wrong answers. After all, you have at least a 25% chance of guessing right!
For free AP multiple choice practice, try:
These sample questions from the College Board
For free skill practice, try:
If you want more AP-style multiple choice practice, consider buying a prep book. They usually sell for under $20 and have upwards of 3 full-length practice tests. Check out this list of the best prep books [coming soon] for Fiveable's top picks!
If you know the format, use these strategies, and practice until you're confident, you'll rock the multiple choice section of the exam. Good luck! 🎉
2550 north lake drive
milwaukee, wi 53211
92% of Fiveable students earned a 3 or higher on their 2020 AP Exams.
*ap® and advanced placement® are registered trademarks of the college board, which was not involved in the production of, and does not endorse, this product.
© fiveable 2020 | all rights reserved.