Dr. Cheryl Kerr • #ᴄᴜʟᴛɪᴠᴀᴛɪɴɢQᴜᴀʟɪᴛʏ🌵

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 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…

When asked to rate their AP course on how well it prepared them for college, students worldwide gave all of their AP subjects high marks, but highest rated of all was AP Calculus. AP Calculus students believe — without yet actually having attended college, to be clear — that the course provided them with unparalleled preparation for the type of coursework they expect to encounter on college campuses. Other AP subjects with the very highest student ratings in response to the prompt “This course prepared me for college” were AP English Literature, AP Research, AP Seminar, AP Spanish Literature, and AP Physics C: Electricity & Magnetism.

The 2026 AP Statistics Exam scores: 5: 17%; 4: 23%; 3: 22%; 2: 17%; 1: 21% The 2026 AP Statistics exam was taken by 281,000 students, ~2% of the U.S. high school population. AP Statistics Multiple-Choice Questions (MCQ): 1. Students performed strongest on questions related to Units 1 and 2 (Exploring One-Variable and Two-Variable Data). The high performance here indicated that many AP Statistics students have solid foundational skills in summarizing and interpreting distributions. To receive an AP 5, students were expected to answer all 10 of these questions right, while to receive an AP 4, students were expected to miss no more than one; students receiving AP 3s were expected to answer 7/10 correctly. 2. The most challenging MCQ content area was Units 4 and 5: Probability and Sampling Distributions, a conceptually demanding area that requires students to reason about randomness, probability rules, and the behavior of sample statistics — the theoretical backbone of all of statistical inference. Accordingly, the difficulty level of these questions is such that they serve well to identify students who qualify for an AP 5. AP Statistics Free-Response Questions (FRQ): apcentral.collegeboard.org/m… Across this 90-minute section, students were asked to calculate five-number summaries and compare distributions, design a randomized experiment and interpret statistical significance, apply normal and binomial probability models, conduct a two-sample t-test from summary statistics, analyze a two-way table with conditional probabilities and a chi-square readiness check, and work through a multi-part linear regression analysis complete with confidence and prediction intervals. In other words, the faculty committee who designed these questions did a wonderful job of replicating the scope of a first college-level course in Statistics — no corners cut. (As I think about what AP teachers do so admirably, this is one of those moments where I feel such awe and gratitude for the ways teachers use the scope of the exam to ensure the students in their class have the benefit of no topics falling by the wayside. There are so many pressures on teachers to let stuff slide – from snow days to spring fever to parents demanding that their children receive high grades – but AP teachers tell me all the time that they’re able to invoke the AP Exam’s demands as a reason for maintaining high standards and motivating students to spend the extra time on task that learning at the advanced level in high school demands. The TIMSS study found that AP students were studying two more hours per week than students taking a similar curriculum without a culminating AP Exam. No wonder the AP students in the study outperformed students from all other countries – that two additional hours of study each week makes a huge, cumulative difference in student learning. But this is also an important reminder that with such a significant amount of additional work, students should not be pressured to take more than 1-2 AP courses per year in high school – the load that the AP Program’s own research shows is sufficient to optimize college completion rates.) 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. Q1, Exploring Distributions: asked students to determine a five-number summary from raw data, use it alongside a boxplot to compare center and variability in context, and then explain via a stem-and-leaf plot the shape characteristics a boxplot inherently conceals. This last task, asking students to articulate why a summary representation loses information about gaps or clusters in a distribution, is a sophisticated statistical reasoning skill, which distinguished scores of AP 4 and AP 5 from the other scores. Otherwise, this was the easiest FRQ, generating data essential to differentiating between AP 1s, which were only expected to earn at least 1 of these points, from AP 2s, which were expected to earn at least 2 of the 4 points possible here. Q2, Experimental Design and Statistical Significance: was the most challenging short free-response question, providing opportunities to identify students who should receive a 5 versus those who should receive a 4. Students had to identify treatments, experimental units, and the response variable; describe a randomization procedure; and interpret the meaning of statistical significance in context. Q3, Probability Models: required students to apply three distinct probability models in a single question — normal, binomial, and geometric — in the context of a sports team's game-opening musical performances. Students calculated a normal probability, used the binomial distribution to find P(X ≥ 3) across ten games, and then switched to the geometric distribution to calculate the mean and standard deviation of the number of games until a long performance occurs — and interpret that standard deviation in context. This question was almost as demanding as Q2, with each part building on independent probabilistic reasoning skills, such that it served to distinguish between AP 3s, 4s, and 5s, who are expected to earn some or all of these points, while students unable to engage with any parts of this question are receive 1s and 2s. Q4, Two-Sample t-Test: presented students with a randomized experiment comparing two fertilizer brands across 116 trees. Given summary statistics for both groups, students had to conduct a full two-sample t-test: stating hypotheses, checking conditions, computing the test statistic, finding a p-value, and drawing a conclusion in context at the α = 0.05 level. The ability to execute all steps of a significance test accurately — and communicate conclusions appropriately — is a cornerstone of college-level Statistics and this question does an excellent job, across its four points, of differentiating the knowledge and skills of a wide range of performance levels: students are expected to score perfectly here to receive an AP 5, earn at least three of the points to earn an AP 4, and at least two of the points to earn an AP 3. Q5, Two-Way Tables, Conditional Probability, and Chi-Square Readiness: gave students a two-way table of 4,193 professional basketball, football, and baseball players categorized by age group. Students were asked to calculate and interpret conditional probabilities, read a mosaic plot, reason about mutual exclusivity and independence (showing work numerically), and assess the conditions for a chi-square test of independence. This question contains several especially difficult points that evaluate students’ qualifications for an AP 5, which students receiving the other AP scores are unable to earn. Q6, Linear Regression: Inference, Confidence Intervals, and Prediction Intervals: was the capstone 4-point investigative task, and it asked students to engage deeply with linear regression analysis using data from 30 professional baseball teams. Students described a scatterplot relationship, used a least-squares regression equation to make a prediction, compared a circled outlier team to others of its salary class, evaluated the relative strength of linear association across high- and low-salary subgroups, calculated both a 95% confidence interval for a mean response and a 95% prediction interval for a single team, and — in the most sophisticated part — explained why prediction intervals are wider than confidence intervals by connecting the conceptual logic of individual-vs.-mean variability to the mathematical structure of the standard error formulas. This question provides a variety of opportunities for students aiming for AP 4s and AP 5s to distinguish themselves, as several of these are quite advanced points. All subjects' AP score distributions for 2026 will be posted here when available: apstudents.org/score-distrib…