You’re given 30 minutes to complete the first two—Part A. These both require a calculator. Then you’ll have 1 hour for the remaining four—Part B. These, however, are tech-free. Not to worry, though, in the sections ahead we’ll detail what you can expect in each part and how to maximize your score.

The free-response section contains 6 questions and counts for 50% of the total AP Exam score. Each question is scored using a point-based rubric, and the questions are weighted equally within the free-response section. Focus on earning rubric points through correct work, justification when required, and clear notation.

For AP Calculus, both AB and BC exams have 6 FRQs. The AB and BC exams include 3 common free-response questions that assess content from the AB Calculus course. On the BC exam, the remaining free-response questions may assess BC-only content in addition to AB content, so BC students should be prepared for the full BC course.

The FRQs assess a variety of content and skills across the course rather than a fixed yearly template. Students may encounter numerical, graphical, analytical, tabular, contextual, and justification-based tasks. Exact topics and representations vary from year to year, so students should prepare broadly for all course content.

On the BC exam, three free-response questions assess BC content in addition to the three common AB questions. BC-only topics such as parametric/polar/vector topics or sequences and series may appear, and students should be prepared for BC content in either calculator or non-calculator settings as appropriate to the question.

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📖 Content

The AP course emphasizes 3 big ideas: change, limits, and analysis of functions. While the specific content varies from year-to-year, in aggregate the exam will test your ability to understand and interpret functions represented in a variety of forms: graphically, from a table, in written form, and as an equation.

Each FRQ typically contains several related parts or sub-tasks. The exact number can vary from question to question.

Across the FRQ section as a whole, the exam includes a roughly equal mix of procedural and conceptual tasks.

Process-Oriented: find the derivative; estimate the value of a definite integral; or identify the location or value of a relative maximum
Conceptual: interpret the graph of the first derivative, f'; verify the conditions of the Mean Value Theorem (MVT); explain why the rate of change of a system is positive or negative with justification

Note: these lists are not exhaustive, but the FAQs section below discusses other examples

In addition, at least two questions will feature an authentic scenario. This means they’ll give you more context than an abstract equation or graph.

✋ Justification

So what do you need to do differently in the FRQ section? In the words of every math teacher you’ve ever had: show your work*.*

This emphasis on justification is more than mere suggestion. A large share of the available credit comes from the mathematical work you show and how clearly you communicate your reasoning. Of course, what constitutes good justification depends on the question. See the comparisons below.

While this is accurate, it isn’t clear that this is the derivative nor how we arrived here. A better answer would include evidence of our process.

Here, we clearly show we’re taking the derivative—using the power rule and the chain rule. If we make an arithmetic error, the reader knows what we were attempting. In these situations you may earn yourself some of the available points. However, if you make a calculation error in the first solution, you’ll earn no points at all.

Again, technically the result is accurate. Still, we could do much better to communicate our line of thinking.

Step one indicates that we’ve taken the derivative at x=3. Next we show the location of the point of intersection (3, p(3)). Finally, we label our result.

Before we move on, just a few more quick examples.

A sign chart by itself may not always earn full justification credit; you should connect the sign information to the mathematical conclusion in words or notation. For example: “Because f'(x) changes from positive to negative at x = a, f has a local maximum at x = a.” Always follow the wording of the prompt and provide enough reasoning to support the conclusion.

Common FRQ Task Verbs

Common AP Calculus FRQ task verbs include calculate/write an expression, determine, evaluate, estimate, explain, justify, interpret, and identify/indicate. Read these carefully: “calculate” usually requires showing the expression and obtaining a value; “determine” often means using a definition, theorem, or test; “interpret” means connect the mathematics to the context, often with units; and “justify” or “explain” requires a clear mathematical reason, not just an answer.

💯 Scoring

As mentioned earlier, each FRQ counts equally. Each free-response question is scored with a rubric, and the entire free-response section makes up 50% of your exam score. The multiple-choice section also makes up 50%. College Board does not publish a simple official "raw score" formula for students to use on test day, so the best strategy is to maximize points on every part of every question.

AP score cutoffs vary from year to year, so there is no fixed raw score needed for a 4 or 5. Treat any unofficial score-conversion estimates with caution.

Earning Points

AP readers—those people you’re trying to please with your answers—award points based on accuracy and on completeness. To earn maximum marks you’ll need both.

Above, we discussed some particulars of how to justify your answers. It’s important because they contribute significantly to your total score.

That said, you will earn points for other things. You’ll earn points for setting up derivatives and integrals properly; using complete and proper notation; logically moving step-by-step through your mathematical process; and providing the correct answer with the corresponding units, where appropriate. So, what does this look like?

♾️ Derivatives

♾️ Integrals

♾️ New Representation

♾️ Appropriate Units

Rates: At t = 3, the rate at which people are leaving is 142 every hour.
Average: On [3, 7] the average rate of change of v is 6 meters/sec.
Accumulation: The liquid has cooled 8 degrees Fahrenheit over the interval from t = 0 to t = 15 mins.

Part A - Calculator Section

2 Questions; 30 minutes; Graphing Calculator Required. Show enough mathematical work to support your answers, and justify or explain when the prompt asks for it.

Part A is the calculator-required portion of Section II. You are expected to use an approved graphing calculator on these two questions; these questions are designed around numerical, graphical, or tabular work where technology is part of the intended solution process.

Exactly what do they mean when they say calculator required?

In Part A, the calculator is required because some questions involve numerical, graphical, or tabular work that is most efficiently done with technology. You may need to evaluate expressions, estimate values, analyze graphs, or use calculator features such as finding intersections, zeros, or extrema when appropriate.

Part A questions may require calculator use to evaluate expressions numerically, work with tables or graphs, estimate values, or analyze information efficiently with technology. Read each prompt carefully to determine exactly what the calculator is being used for.

If a prompt asks for the location of an extremum, it often wants the input value (such as x or t) where the extremum occurs. Read carefully: some questions instead ask for the maximum or minimum value, or for the full point on the graph.

f(x) achieves a local minimum at x=6.374 because f'(x)=0 here and f'(x) changes sign from negative to positive.

And if they ask for the absolute maximum? Then they may want the maximum function value.

g(6) = 123 is the absolute maximum value, as it’s greater than the value of g at both endpoints: g(0)=100 and g(8) = 74.

OK. But how am I supposed to justify? I’m glad you asked. Let’s look at an example.

📖 Worked Example

A local citrus vendor stocks her stand with 100 pounds of clementines at 9 a.m, at which time the market opens. She leaves her partner in control of the stand and returns to the farm to pick up more fruit. Customers buy her fruit at a rate of

where p(t) is in pounds and t is the number of hours since 9 a.m. Three hours later, the vendor returns with a resupply and moves them from the truck to the stand at a rate modeled by

And there you have it! In Part A, you’ll lean heavily on your calculator. And as long as you provide good, clear mathematics notation, appropriate reasoning, and correct units, you’ll be prepared to collect maximum points!

📱 A Note on Calculators

You must bring a College Board–approved graphing calculator for the calculator-required portions of the exam. Calculator policies can change, so check the current AP Exam Calculator Policy on the official College Board website before test day. You may bring a backup approved calculator as well.

You are permitted to bring a backup calculator, though if you’re using fresh batteries and pack a few extras (just in case) you should have plenty of insurance.

Part B - Non-Calculator Section

4 Questions; 60 minutes; Graphing Calculator Prohibited

Part B is the calculator-not-permitted portion of Section II. You may not use a calculator on these four questions, so solutions must rely on algebraic reasoning, calculus concepts, and careful interpretation of the given representations.

Alas, you’ll need to put away your trusty TI—or other approved model—in the final section of the exam. Looking for consolation? Well, on a number of the problems your calculator wouldn’t offer much help or time-savings anyway. How could that be?

In Part B, you solve problems without a calculator, so success depends on strong analytical work, careful interpretation of given representations, and clear justification. Graphs, tables, equations, and slope fields may appear anywhere in the FRQ section.

What can you discern about g''(t) at t=a if you’re given a picture of g(t)?

Use a table of f(t) values to guarantee the existence of a particular f'(t) value.

Could you produce a specific solution to a differential equation from a slope field?

These examples should give you some idea, but for clarity let’s work an example.

📖 Worked Example

The function g is differentiable on the closed interval [-6, 3] and satisfies g(-2) = 15. The graph of g' consists of a semicircle, a line segment, and a quarter-circle, as shown above, where g'(2) = 1.

Congratulations! Once you complete Part B, you’ve completed your exam. On test day remember to use good, clear mathematics notation, and justify your answer when the prompt asks for explanation or when your mathematical work needs to support the result.

FAQs About FRQs

We’re not done quite yet. Here’s a final reference for things we may not have covered above.

Q: I made a mistake, should I erase it?

A: If it’s minor, sure. With more significant mistakes, however, it’s quicker and clearer to cross out your work. You can always point the reader forward with an arrow.

Q: What if I found two solutions and I’m not sure which is correct?

A: If you give two different answers to the same question and do not clearly indicate which one you want graded, you risk losing credit because one answer may contradict the other. If you revise your work, cross out the incorrect solution clearly and box or label your final answer.

Q: Do I have to round my answers to 3 decimal places?

A: Unless the prompt specifies a rounding requirement, a reasonable decimal approximation is generally acceptable. Keep enough decimal places to avoid causing later rounding error, and follow any explicit rounding directions in the question.

Q: Can use the nDeriv notation my calculator uses?

A: No. Use standard mathematical notation, such as f'(x) or $\frac{d}{dx}$ , rather than calculator syntax like nDeriv.

Q: If a question doesn’t ask me to justify or show my work, do I need to?

A: You should always show enough mathematical work to support your answer. When a prompt says "justify," "explain," or "show that," you must provide reasoning. Even when those words are not used, clear setup and correct notation are important because rubric points are often awarded for mathematical work, not just the final answer.

Q: What happens if I make an error in part (b) and need to use my answer in part (c)?

A: AP scoring often allows follow-through credit when a later part is done correctly using an earlier incorrect result, provided the later work is mathematically consistent and the error does not invalidate the method being assessed. However, follow-through is not unlimited, so students should correct errors when they notice them and clearly show their reasoning.