AP CALCULUS AB
AP Calculus AB – Student Guide
AP Calculus AB - Exam Overview
The AP Calculus AB Exam will test your understanding of the mathematical concepts covered in the course units, as well as your ability to determine the proper formulas and procedures to use to solve problems and communicate your work with the correct notations. A graphing calculator is permitted for parts of the exam.
Note: You may not take both AP Calculus AB and Calculus BC Exams within the same year.
Exam Duration
3 hours 15 mins
Exam Components
Section I: Multiple Choice - 45 questions | 1hr 45mins | 50% of Score
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Part A: Graphing calculator not permitted (33.3% of score)
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Part B: Graphing calculator required for some questions (16.7% of score)
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Questions include algebraic, exponential, logarithmic, trigonometric, and general types of functions.
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Questions include analytical, graphical, tabular, and verbal types of representations.
Section II: Free Response - 6 questions | 1hr 30mins | 50% of Score
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Part A: 2 problems | Graphing calculator required (16.7% of score)
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Part B: 4 problems | Graphing calculator not permitted (33.3% of score)
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Questions include various types of functions and function representations and a roughly equal mix of procedural and conceptual tasks.
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Questions include at least 2 questions that incorporate a real-world context or scenario into the question.
In Section I Part A and Section II Part B, calculators are not allowed on the exam. For AP Calculator Policy, click here.
AP Calculus AB Exam – Scoring
For the first section (multiple-choice), for every question you answer correctly, you will get one point each. There is no negative marking. It means that even if your answer is wrong or left blank, no points are deducted.
Next is the free response section. Its scoring system is a bit complicated. Rather than being graded by AI, it is reviewed by AP graders and scored following guidelines for the AP Calculus AB Exam.
For more information about AP Calculus AB Exam and scoring, you can visit the College Board’s website.
AP Calculus AB Exam – Credit
Keep in mind, credit and advanced standing based on AP scores vary widely from school to school. Though a score of 3 is typically considered passing, it is not always enough to receive credit. Regulations regarding which APs qualify for course credits or advanced placement depend on the policy that your desired college or university has for AP exams.
AP Calculus AB Exam - Study Resources
• College Board Classroom Resources
• Desmos
• GeoGebra
• Khan Academy: AP Calculus AB
• Albert.io: AP Calculus AB-BC
• Symbolab
• WeBWork
AP Calculus AB Exam Tips
The following strategies for answering the free-response questions will help you on exam day.
Keep an eye on your time.
Monitor your time carefully. Make sure not to spend too much time on any question so you’ll have enough time to answer all of them. You may want to look over all the questions as you begin each part of the free-response section before starting work.
During the second timed portion of the free-response section (Part B), you are permitted to continue work on problems in Part A, but you are not permitted to use a calculator during this time.
If you do work that you think is incorrect, simply put an “X” through it instead of spending time erasing it completely: crossed-out work won’t be graded.
Show your work, even when you’re using a calculator.
Show all the steps you took to reach your solution on questions involving calculations, even if a question may not explicitly remind you to do so. The exam reader wants to see if you know how to solve the problem. Answers without supporting work will usually not receive credit.
Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied.
If you use your calculator to solve an equation, compute a numerical derivative, or find a definite integral, then be sure to write the equation, derivative, or integral first: an answer without this information might not get full credit, even if the answer is correct. Remember to write your work in standard notation (e.g., ∫𝑥2𝑑𝑥51) rather than calculator syntax (e.g., fnInt (X2, X,1,5)), as calculator syntax is not acceptable.
Other important notes:
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Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If you use decimal approximations in calculations, your work will be scored on accuracy. Unless otherwise specified, your final answers should be accurate to 3 places after the decimal point.
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Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
Try to solve each part of the question.
Many free-response questions are divided into parts such as (a), (b), (c), and (d), with each part calling for a different response. Credit for each part is awarded independently, so you should attempt to solve each part. For example, you may receive no credit for your answer to part (a), but still receive full credit for part (b), (c), or (d). If the answer to a later part of a question depends on the answer to an earlier part, you may still be able to receive full credit for the later part, even if that earlier answer is wrong.
Be sure to fully answer the question being asked.
For example, if a question asks for the maximum value of a function, do not stop after finding the x-value at which the maximum value occurs. Be sure to express your answer in correct units if units are given and always provide a justification when it is asked for.
When asked to justify or to explain an answer, think about how that can be done.
For example, if you are asked to justify a point of inflection, you need to show that the sign of the second derivative changes. Simply saying that the second derivative equals zero or is undefined is not a justification.
Do not round partial answers.
Store partial answers in your calculator so that you can use them unrounded in further calculations.
Practice!
Answering free-response questions from previous AP Exams is a great way to practice: it allows you to compare your own responses with those that have already been evaluated and scored. Free-response questions and scoring guidelines are available on the Exam Preparation section of the Exam page for AP Calculus AB.
Task Verbs
Pay close attention to the task verbs used in the free-response questions. Each one directs you to complete a specific type of response. Here are the task verbs you’ll see on the exam:
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Approximate: Use rounded decimal values or other estimates in calculations, which require writing an expression to show work.
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Calculate/Write an expression: Write an appropriate expression or equation to answer a question. 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. “Calculate” tasks might also be formulated as “How many?” or “What is the value?”
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Determine: Apply an appropriate definition, theorem, or test to identify values, intervals, or solutions whose existence or uniqueness can be established. “Determine” tasks may also be phrased as “Find.”
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Estimate: Use models or representations to find approximate values for functions.
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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.
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Explain: Use appropriate definitions or theorems to provide reasons or rationales for solutions and conclusions. “Explain” tasks may also be phrased as “Give a reason for...”
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Identify/Indicate: Indicate or provide information about a specified topic, without elaboration or explanation.
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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.
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Interpret (when given a representation): Identify mathematical information represented graphically, symbolically, verbally, and/or numerically, with and without technology.
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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.
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Represent: Use appropriate graphs, symbols, words, and/or tables of numerical values to describe mathematical concepts, characteristics, and/ or relationships.
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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.
You can also view Past Exam Questions and Scoring Information for you to have a glance at what questions to expect during the exam day.
Conclusion
The AP Calculus AB Exam is a tough one to master because it focuses on differential and integral calculus while relying heavily on a strong foundation in algebra, geometry, trigonometry, and elementary functions. To be successful on the exam you will need to learn the concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. You should have knowledge about how to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and you should be able to use technology to help solve problems, experiment, interpret results, and support conclusions. Keep in mind that credit and advanced standing based on AP scores vary widely from school to school. If you are ready to accept this challenge, then go for it! Make that determination of yours become the key to your success! Good luck!