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Multiple Choice Questions (MCQ)

Calculus Multiple Choice Questions

4 min readβ€’june 11, 2020

Meghan Dwyer


Table of Contents πŸ“Š

Exam Format and Logistical Details
Types of Problems
How to Approach MC Questions

🧠 Exam Format and Logistical Details

Directly from College Board and AP: The AP Calculus AB/BC Exams consist of 45 multiple choice questions including:
  • 30 No Calculator multiple choice.Β 
    • 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.Β 
Topic
AB
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%
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.Β 
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%.

❓ Types of Problems

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.Β 
Types of functions:
  • Algebraic
  • Exponential
  • Logarithmic
  • Trigonometric
  • General types
Types of representations:
  • Analytical
  • Graphical
  • Tabular
  • Verbal
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.Β 
Example:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(348).png?alt=media&token=792832b5-550e-454b-81f4-a629e2b78b58
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(844).png?alt=media&token=79fc640c-915c-4d8f-b27f-fa51edc7f914
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.Β 
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.Β 
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.Β 

⭕️ How to Approach MC Questions

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?
Not always…!
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!
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(350).png?alt=media&token=8cef897b-786a-4146-b6fe-0c0255d758f2
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.Β 
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.Β 
Once you have done it once though… trust your first instinct and move on. Go back if you have time!Β 
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!
Example:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(845).png?alt=media&token=7746b14b-660e-42ef-a489-24600583ba65
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.Β 
One type of MC question you will not see in the Free Response section, is converting to summation notation for integrals.Β 
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreenshot%20(846).png?alt=media&token=a2da82bd-184d-4404-abd7-6092fec7d7f6
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!Β 

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