The 2026 AP Calculus BC exam scores: 5: 46%; 4: 22%; 3: 14%; 2: 14%; 1: 4% The 2026 AP Calculus BC exam was taken by ~171,000 students — roughly 1% of the U.S. high school population. AP Calculus BC Multiple-Choice Questions (MCQ) • AP Calculus BC students scored especially well on questions related to Unit 1: Limits and Continuity (35% earned all points) and Units 4 and 5: Applications of Differentiation, such that students earning AP 3+ scores answered most of these questions correctly. • The most challenging MCQ content area was Unit 10: Infinite Sequences and Series, a unit requiring students to master convergence tests, power series, and error bounds for series approximations, for example. Earning 100% of these points was rare, given how difficult and advanced this unit is; 3% of students achieved a perfect score on this unit. AP Calculus BC Free-Response Questions (FRQ) Each AP exam has multiple versions for different time zones. I'll focus the commentary below on the version taken by most students: apcentral.collegeboard.org/m… Collectively spanning the AP Calculus BC curriculum, the six FRQs included rate modeling with tabular data, polar curve analysis, differential equations, graphical reasoning, area-volume applications, and Maclaurin series. Throughout the FRQs, students must communicate reasoning. For example, they needed to construct arguments, interpret a definite integral in context, evaluate the validity of a slope field, and determine the convergence of a series. Since AP scores are reported on a 5-point scale, the free-response questions deliberately include some very difficult points designed to differentiate AP 5s from AP 4s, points of varying difficulty to differentiate AP 4s, 3s, and 2s, and more foundational points to separate AP 2s from AP 1s. The following commentary will focus on the questions unique to Calculus BC: FRQ #2 — Polar Curve: Area and Tangent Lines Q2, the Polar Curve question, tested students' ability to work with polar functions — finding the area of a polar region using a definite integral, working with the slope of a line tangent to a polar curve, and analyzing curve behavior. The second point in Part C (answer using a derivative test) and both points for Part D were the most difficult points of this FRQ. These served to differentiate students achieving AP 5s, who could typically earn these points, from other students. FRQ #5 — Area, Volume, and Perimeter Q5, the Area-Volume question, asked students to evaluate a definite integral without the use of a calculator, write an integral expression for the volume of a solid of revolution, write an integral for the perimeter of a region (arc length), and evaluate an improper integral. Students receiving AP 1s were not usually able to earn points on this question. Rather, it served especially well to differentiate among AP 3s, 4s, and 5s. For example: • Students earning AP 3s consistently earned points across Parts A and B, as well as the antiderivative point in Part D, whereas students receiving AP 2s did not. • Students earning AP 5s were consistently able to succeed on Part C, the most difficult part of this FRQ, whereas students receiving AP 3s and 4s were more likely to struggle and only earn partial points here. FRQ #6 — Maclaurin Series In this demanding question, which tended to differentiate between AP scores of 4 and 5, students were given a Maclaurin series for a function g and asked to find the sum of g(3) (an alternating geometric series), find a series for the derivative g', justify an error bound, and write a Maclaurin series for a related function. • In Part B, students earning AP 3s could typically write two terms of the series for g', while students earning AP 4s were more likely to proceed and write the remaining two terms. • In Part D (ii), students earning AP 4s were typically able to write two terms of the series for the related function, and students earning AP 5s were typically able to write all three terms. • Part C was the most challenging segment of this FRQ, with these points generally earned only by students achieving AP 5s. All subjects' AP score distributions for 2026 will be posted here when available: apstudents.org/score-distrib…

The 2026 AP Calculus AB Exam scores: 5: 20%; 4: 28%; 3: 17%; 2: 24%; 1: 11% The 2026 AP Calculus AB Exam was taken by ~292,000 students, roughly 2% of the U.S. high school population. AP Calculus AB Multiple-Choice Questions (MCQ): Students earning scores of 3 or higher scored very well on questions related to Unit 1: Limits and Continuity. Students achieving an AP 5 typically answered 100% of these questions right, whereas to earn a 4, students typically missed no more than 1 point, and to earn a 3, students typically missed no more than 2 points. The two most difficult MCQs measured aspects of Unit 6: Integration and Accumulation of Change, and were typically only earned by students achieving AP 5s. Students receiving AP 2s were generally unable to earn many points on questions related to this unit, so this unit is very much a differentiator between students earning scores of 3+, who were able to succeed on a variety of these questions, and students earning scores of 1 and 2, who could not. AP Calculus AB Free-Response Questions (FRQ): Each AP exam has multiple versions, for different time zones. I'll focus the commentary below on the version taken by most students: apcentral.collegeboard.org/m… Since AP scores are reported on a 5-point scale, the free-response questions deliberately include some very difficult points to differentiate AP 5s from AP 4s, points of varying difficulty to differentiate AP 4s, 3s, and 2s, and more foundational points to separate AP 2s from AP 1s. FRQ #1, the Modeling Rates of Change question, required students to estimate a rate of change, construct a midpoint Riemann sum, interpret the meaning of a definite integral in context, set up and evaluate a definite integral for accumulation, and apply the Intermediate Value Theorem. The question spans nine points, creating a broad range of difficulty: • The two points in Part C, which required students to provide a definite integral for accumulation and evaluate it using the calculator, were earned by 80% and 72% of students respectively, meaning that most students who understood the fundamentals of integration could set up and execute these computations. Accordingly, these points differentiated between students receiving AP scores of 2, who were generally able to earn these points, and students receiving AP scores of 1, who were not. • Comprised of points that were aspirational for most students, Part D was exceptionally difficult, and so provided opportunities for the most advanced students to demonstrate exceptionally strong knowledge and skills. FRQ #2, the Area and Volume question, presented two functions f and g bounding regions and asked students to calculate areas of regions using definite integrals, set up an integral for the volume of a solid with rectangular cross sections, and set up an integral for the volume of a solid generated by revolving a region about the y-axis. Other than the first point within Part C (presenting an integrand of a certain form in a definite integral for the area of a region), which some students receiving an AP 2 were able to earn, this FRQ, like most AP Calculus FRQs, focuses on differentiating performance among AP 3s, 4s, and 5s, who were each typically able to earn a variety of points across this FRQ, with AP 5s typically earning all points possible. FRQ #3, the Modeling with Differential Equations question, was the most difficult FRQ on this year's exam, laser focused on differentiating between scores of 4 and 5, with students achieving AP 5s able to earn significantly more points on this question than other students. The question asked students to explain why a given slope field could not represent the given differential equation, find the slope of a tangent line, determine whether a tangent line approximation is an overestimate or an underestimate, and solve the differential equation using separation of variables. FRQ #4, the Graphical Analysis question, presented students with the graph of f′ (the derivative) for a twice-differentiable function f and asked them to use the graph to evaluate a related derivative, identify points of inflection of the graph of f, determine where the function f is increasing and concave down, and determine the locations of absolute extrema of the function f. While students receiving AP 1s were unable to engage with the difficulty of this FRQ, the question provided multiple opportunities for students receiving AP scores of 2, 3, 4, and 5 to distinguish themselves — a question that differentiates performance very well across this spectrum. For example: • Students achieving an AP 3 were typically able to set up and answer Part A correctly, answer Part C, and earn other points throughout this FRQ, while students receiving an AP 2 were not. • Students achieving an AP 4 or an AP 5 were generally able to earn some of the points available in the more difficult Part D, whereas students earning an AP 3 typically did not. FRQ #5, the Particle Motion question, provided students with analytical and graphical representations of the velocity of a toy car moving along a straight path. Students overall scored higher on this FRQ than any other on this exam. Part A (finding acceleration as the derivative of the given velocity function) included a basic entry point that differentiated between students receiving AP 2s, who could typically earn this point, and students receiving AP 1s, who could not. Students achieving AP 3s, 4s, and 5s generally earned the majority of points possible across this FRQ. Part D served as the key differentiator between students earning AP 4s and 5s, who were usually able to earn points in this part, and students earning AP 3s, who were often less able to succeed on Part D. FRQ #6, the Analysis of Functions question, presented students with a table of values for a twice-differentiable function f and its derivative. Without a graphing calculator, students had to evaluate a limit, apply the chain rule to find a related derivative, solve an initial value problem, find the derivative of a function defined by an integral, and apply the product rule to find a derivative. From a psychometric perspective, this question may be the best on the exam, as the available points very neatly differentiate performance levels across the spectrum of students receiving AP 2s, 3s, 4s, and 5s. (Students receiving AP 1s typically earned no points on this question, which was beyond their ability level.) • The points available in Part B and one of the points available in Part D were all points that students earning an AP 3 could consistently earn, whereas students receiving an AP 2 had more mixed performance here. • Students receiving AP 5s generally earned all points in Part C, something students earning other scores could not usually achieve. All subjects' AP score distributions for 2026 will be posted here when available: apstudents.org/score-distrib…

The 2025 AP Calculus AB Exam scores: 5: 20%; 4: 29%; 3: 15%; 2: 23%; 1: 13% Multiple-Choice Questions AP Calculus AB students scored highest on questions related to Unit 2: Differentiation: Definition and Fundamental Properties. 50% of students answered all or all but one of these questions right. The most challenging questions were from Unit 6: Integration and Accumulation of Change. 7% of students answered correctly all or all but one of these questions. Free-Response Questions spr.ly/60104eEKm Students generally scored highest on Q3, in which they modeled reading rates for a student and a teacher. And this was the best question, psychometrically, of the exam, since its points varied significantly in difficulty, enabling good measurement of student abilities across the 1-5 AP scale. The question was worth 9 points total, and students unable to answer at least 2 of those points correctly are generally receiving AP 1s and 2s, while students who could answer 8-9 of the points are typically receiving AP 5s. The most challenging FRQ for AB students was Q1, the modeling of an invasive plant species’ spread within a fruit grove. (Who says farmers don’t need calculus?) Students earning 6-9 points on this question tended to receive AP 5s. Writing justifications for global maxima and minima is a good instructional focus for next year. All subjects’ AP score distributions for 2025 will be posted here when available: spr.ly/60114eEKW

The 2025 AP Calculus BC Exam scores: 5: 44%; 4: 22%; 3: 13%; 2: 15%; 1: 6% Multiple-Choice Questions As is typical, Calculus BC students scored extremely well across the units that are shared with Calculus AB, especially Unit 1, where 55% of students answered every question right, and Units 2-3, where 41% did so. The most challenging Calculus BC questions were from Units 9 and 10, which don’t overlap with Calculus AB. As usual, students found questions about infinite sequences and series most difficult: 4% answered all of these questions right. Free-Response Questions spr.ly/60124eEkg Setting aside the three FRQs shared with Calculus AB, which Calc BC students typically find easier than the BC-specific FRQs, students scored highest on Q5, the differential equation question that requires understanding of the second-degree Taylor polynomial, the Lagrange error bound, and Euler’s method. By far the most difficult question on this year’s BC exam was Q2, polar area, which served to differentiate among BC students, who are qualifying for AP 4s and 5s. Polar area is a good instructional focus for next year. All subjects’ AP score distributions for 2025 will be posted here when available: spr.ly/60134eEk9

The 2024 AP Calculus BC Exam scores: 5: 45%; 4: 22%; 3: 13%; 2: 15%; 1: 5% All subjects’ AP score distributions for 2024 will be posted here when available: apstudents.org/score-distrib…

The 2024 AP Calculus AB Exam scores: 5: 21%; 4: 28%; 3: 15%; 2: 23%; 1: 13% All subjects’ AP score distributions for 2024 will be posted here when available: apstudents.org/score-distrib…