✍️ 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)
⏱️ 4 min read
June 11, 2020
Exam Format and Logistical Details
Types of Problems
How to Approach MC Questions
Directly from College Board and AP: The AP Calculus AB/BC Exams consist of 45 multiple choice questions including:
30 No Calculator multiple choice.
Time: 60 minutes (2 minutes per question)
15 Calculator multiple choice
Time: 45 minutes (3 minutes per question)
In their course exam description, AP outlines the units and percentages included in the multiple choice sections.
Unit 1: Limits and Continuity
Unit 2: Differentiation: Definition and Fundamental Properties
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Unit 4: Contextual Applications of Differentiation
Unit 5: Analytical Applications of Differentiation
Unit 6: Integration and Accumulation of Change
Unit 7: Differential Equations
Unit 8: Applications of Integration
Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC ONLY)
Unit 10: Infinite Sequences and Series (BC ONLY)
The multiple choice sections of the exam combine to count as 50% of the exams score. (The other 50% comes from the free response questions). For each question there will be 4 choices.
AP Scores your multiple choice questions by taking the number of questions you got write and multiplying by 1.2. This makes your total out of 54%. This is because of the six 9-point questions in the free response section that also adds to 54%.
In the multiple-choice section, there is only so much that can be asked that is able to be done in 2 or 3 minutes. These are the sections where they ask a bit more straight-forward skills questions.
Types of functions:
Types of representations:
It is important that when preparing for the AP exam, you practice problems with every type of function and every representation. For example, an integral through a function, a table, and a graph, will all challenge your knowledge of integrals in a different way. It is helpful to focus on what the question is asking you to find, then bring the representation into it to figure out how you can use it to help you get to your answer.
To solve this problem, it is important to make sure you understand integrals, and the connection between having the graph of f, but knowing that we are looking for a value of g.
As I stated earlier, first thought: What are you looking for? We need to find g(5).
Since we need g(5), we look to what g is. It is an integral of the function f, which we have the graph of.
How do we represent and integral on a graph? We take the area! With a few geometric calculations, we should get B as an answer.
Many teachers, college and high school level, put a lot of work into making these multiple choice questions. Not only making the problem and correct answer, but also the wrong answers.
Multiple choice questions can quickly trick us, because if we see our first answer there, we assume it must be right, right?
AP makes what I like to call good wrong answers. These are answers that can be found by making one simple miscalculation or using a method that does not apply to the problem. It is important to make sure we are not trusting the choices, but trusting ourselves!
It can be tempting to look down to the choices of a question before even trying it, to see which answers we can eliminate. While this is helpful for speed, it can often make us quickly discount what might be the right answer.
My advice? Do the problem before even looking at the choices.
Yes, I understand you are being timed and this takes a while, but from my experience you are less likely to get distracted by good wrong answers if you have done out the problem yourself.
Once you have done it once though… trust your first instinct and move on. Go back if you have time!
On the other hand, if you do not understand a problem or are blanking on how to solve it, looking at the answers can be helpful! It may give you the insight you need to remember how to solve the problem.
When in total doubt, make sure to make an educated guess! You do not lose points for incorrect answers, so at least you have a 25% chance of being correct if you pick an answer!
Now, we can tell we are supposed to use u-substitution to get an equivalent form. This question has good wrong answers because if you forgot to change the bounds, then b is the right answer! Whenever using u-substitution, make sure to change the bounds to be in terms of u, making c the actual correct answer.
One type of MC question you will not see in the Free Response section, is converting to summation notation for integrals.
This is a problem you should be ready to see, be sure to check out the unit 6 study guide for more information on these two forms.
Good luck when approaching the multiple choice section!
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