# AP CALCULUS FREE RESPONSE QUESTIONS PDF

May 12 2p Eastern! Unless you have been approved for the make-up date in June, but only your school can request that. There will be a practice simulation posted by College Board within the next few weeks. With so many school closures and the stress of a global pandemic, this review season will be different than usual. If this is your first AP exam, welcome!

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Advanced Placement AP. The other is AP Calculus BC, which covers a slightly bigger and harder array of high-level math concepts. Calculus AB tests your knowledge of various calculus concepts, including derivatives, limits, and differential equations. Both the multiple-choice and free-response sections are divided up into a Part A and a Part B. Note too that you'll have questions on which you may not use a calculator and some on which you are required to use a graphing calculator required on Part B in Section 1, Part A in Section 2.

As explained above, the free-response section is the second section on the AP Calculus AB exam, after the multiple-choice section. According to the College Board , these questions "include various types of functions and function representations and a roughly equal mix of procedural and conceptual tasks.

The points you earn for the six FRQs are combined with your multiple-choice score and converted into a final AP score on a scale of We'll go over how to solve each question to earn full credit. All answers come from the official scoring guidelines. In this problem, parts A-C are each worth 2 points, while part D is worth 3 points.

You will also need to show your work clearly at each step in order to earn full points. Here, you will get a point for approximating using values from the table and another for correctly interpreting with units.

Here, you will get a point for using the definite integral and another for finding the correct answer with supporting work. Wave goodbye to your calculator for this next question! You can earn up to 2 points for parts, A, B, and D, and up to 3 points for part C. You must be able to understand differential functions and derivatives, as well as what intervals are, to get this right. The graph of f is decreasing and concave down on the intervals 1, 1.

Here, you will get a point for providing the correct answer and another point for explaining your reasoning. Here, you'll get a point for using the product rule and another for finding the correct answer With Part A, you get two questions, which together count for A graphing calculator is required for this section — not merely permitted! Below are some examples of how you might be required to use your graphing calculator on the AP Calc exam, according to the College Board :.

Make sure you can do all these major functions and more! Unfortunately, the College Board does not give out any formula sheets for the exam, but your AP Calculus teacher will probably give you a list of some to study for the test. As a general rule, any formula you learn in class will likely be an important one to know for test day. Doing this will help you quickly get used to the difficulty, content, and pacing of both the free-response section and the test as a whole.

Make sure that you time yourself accordingly and tweak any older tests you use for practice so that they reflect the current format of the test. For free-response questions specifically, the College Board offers tons of sample questions in its Exam Description and on its Calculus AB exam page , which has an impressive collection of student sample responses as well.

To earn full points on free-response questions, you'll need to show all your work, from the very first step all the way to the last. Note that showing your work doesn't just mean finding the correct answer, but also indicating the setup and intermediate steps needed to get there. Even if the steps for solving a problem seem really obvious to you, remember that this is the stuff AP graders want to see!

If you find that certain FRQs are taking you longer than 15 minutes, that's a sign that you need to target those question types in your prep and review their content more. AP score. We've got you covered with our collection of Calculus AB practice tests and questions. Let us help you figure out which AP test is the ideal choice for you. And if you decide to opt for Calc BC instead of AB, you'll definitely want to check out our comprehensive guide to the Calculus BC free-response questions coming soon!

We've written a guide for each test about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now:. She is passionate about education, writing, and travel. How to Get a Perfect , by a Perfect Scorer. Score on SAT Math. Score on SAT Reading. Score on SAT Writing. What ACT target score should you be aiming for? How to Get a Perfect 4. How to Write an Amazing College Essay. A Comprehensive Guide. Choose Your Test. Multiple Choice Part A: Free Response Part A: A Model Solution Here, you will get a point for approximating using values from the table and another for correctly interpreting with units.

C Model Solution Here, you will get a point for using the definite integral and another for finding the correct answer with supporting work. Below are model answers to each of the four parts of this question.

A Model Solution The graph of f is decreasing and concave down on the intervals 1, 1. D Model Solution Here, you'll get a point for using the product rule and another for finding the correct answer Below are some examples of how you might be required to use your graphing calculator on the AP Calc exam, according to the College Board : Zooming to reveal local linearity Constructing a table of values to conjecture a limit Developing a visual representation of Riemann sums approaching a definite integral Graphing Taylor polynomials to understand intervals of convergence for Taylor series Drawing a slope field and investigating how the choice of initial condition affects the solution to a differential equation.

Approximate: Use rounded decimal values or other estimates in calculations, which require writing an expression to show work. Unless otherwise directed, calculations also require evaluating an expression or solving an equation, but the expression or equation must also be presented to show work. Evaluate: Apply mathematical processes, including the use of appropriate rounding procedures, to find the value of an expression at a given point or over a given interval. Explain: Use appropriate definitions or theorems to provide reasons or rationales for solutions and conclusions.

Interpret: Describe the connection between a mathematical expression or solution and its meaning within the realistic context of a problem, often including consideration of units. Justify: Identify a logical sequence of mathematical definitions, theorems, or tests to support an argument or conclusion, explain why these apply, and then apply them.

Verify: Confirm that the conditions of a mathematical definition, theorem, or test are met in order to explain why it applies in a given situation. Alternately, confirm that solutions are accurate and appropriate. Hannah Muniz.

About the Author. Ask a Question Below Have any questions about this article or other topics? Ask below and we'll reply! Search the Blog Search. Find Out How. Get the latest articles and test prep tips! Looking for Graduate School Test Prep? Determine expressions and values using mathematical procedures and rules. Translate mathematical information from a single representation or across multiple representations.

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Advanced Placement AP. The other is AP Calculus BC, which covers a slightly bigger and harder array of high-level math concepts. Calculus AB tests your knowledge of various calculus concepts, including derivatives, limits, and differential equations. Both the multiple-choice and free-response sections are divided up into a Part A and a Part B. Note too that you'll have questions on which you may not use a calculator and some on which you are required to use a graphing calculator required on Part B in Section 1, Part A in Section 2. As explained above, the free-response section is the second section on the AP Calculus AB exam, after the multiple-choice section.

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