2025 AP Calculus AB Free-Response Questions: Complete Solutions

The 2025 AP Calculus AB FRQs covered: (1) Applications of derivatives including related rates and optimization; (2) Riemann sums and definite integral approximations; (3) Differential equations with slope fields and particular solutions; (4) Fundamental Theorem of Calculus applications; (5) Area between curves and volume calculations; (6) Analysis of function behavior using derivatives and integrals. All questions align with the AB curriculum framework.

There are 6 FRQs worth 54 total points. Questions 1-2 are worth 9 points each (15 minutes each, calculator-active), and Questions 3-6 are worth 9 points each (15 minutes each, no calculator). Graders award partial credit for showing correct work and reasoning, even if the final answer is incorrect. The FRQ section counts for 50% of your total composite score.

No, only on Part A (Questions 1-2). These calculator-active questions typically involve numerical integration, finding derivatives at specific points, or solving equations requiring graphing technology. Questions 3-6 (Part B) are calculator-inactive and test analytical skills, algebraic manipulation, and symbolic integration.

Official questions are released by College Board on AP Central after exam administration. Visit the AP Calculus AB Course Homepage on AP Central for free downloads of FRQs and scoring guidelines from 1998-present. The 2025 questions were released in May 2025.

AB FRQs focus on fundamental calculus: limits, derivatives, integrals, FTC, basic differential equations, and applications. BC adds advanced topics like parametric/polar equations, vector functions, series (Taylor, Maclaurin, convergence tests), advanced integration techniques (partial fractions, improper integrals), and logistic differential equations. BC students take 6 BC-level FRQs, while AB students focus on core concepts.

Practice under timed conditions, focusing on one topic per session. Complete FRQs from 2015-present as they reflect current format. Create an error log to track mistakes. Review official scoring guidelines to understand what graders expect. Target 10-15 practice FRQs per major topic (derivatives, integrals, differential equations, applications) before the exam.

Top mistakes: (1) Not showing enough work for full credit; (2) Forgetting units in word problems; (3) Misapplying Fundamental Theorem of Calculus; (4) Sign errors in derivatives/integrals; (5) Incomplete justifications - forgetting to cite theorems like MVT or IVT; (6) Not including dx in integral notation; (7) Rounding too early in multi-step problems; (8) Missing domain restrictions.

Each 9-point FRQ typically has 3-4 parts. Part (a) is usually 2-3 points, parts (b) and (c) are 2-3 points each, and part (d) if present is 1-2 points. Questions requiring justification or interpretation often carry more points. Check the official scoring rubric for exact distributions.

Generally no, unless the question specifically asks for simplification. For calculator-active questions, give decimal answers to 3 decimal places. For no-calculator questions, exact forms like "(e³ - 1)/2" are acceptable. However, clearly show your setup and work - that's where most points come from.

Yes! Each part is scored independently. If your answer to (a) is incorrect but you use it correctly in subsequent parts, you can still earn full credit for those parts. This is called "error carried forward" - you won't lose points twice for the same mistake.

Students typically score 50-60% on the FRQ section. Scoring 27/54 points (50%) combined with similar MCQ performance usually earns a 3. For a 5, aim for 38-42+ FRQ points (70-78%). For a 4, target 32-37 points (60-69%). Remember, the curve adjusts yearly based on overall difficulty.

Part A (Q1-Q2, calculator): 30 minutes total (15 min each). Part B (Q3-Q6, no calculator): 60 minutes total (15 min each). However, adjust based on difficulty - don't spend 20+ minutes on one question. If stuck, move on and return later. Save 5 minutes at the end to review and add units/justifications.

Difficulty varies annually, but College Board maintains consistency through curve adjustments. The 2025 AB exam featured standard topics with moderate difficulty. The differential equations question was more challenging, while derivative applications and Riemann sums were straightforward. Overall, it aligned with 2019-2024 difficulty levels.

Essential resources: (1) Official College Board scoring guidelines; (2) AP Classroom practice questions; (3) Review books (Barron's, Princeton Review, 5 Steps to a 5); (4) Khan Academy AP Calculus AB; (5) Paul's Online Math Notes; (6) Past released exams (1998-2024) on AP Central; (7) College Board's Course and Exam Description (CED).

The formula sheet provides basic derivative/integral rules, but you MUST memorize: chain rule, product rule, quotient rule, trig derivatives, u-substitution patterns, volume formulas (disk, washer, shell), average value formula, and when to apply FTC Part 1 vs. Part 2. Also know key theorems: MVT, IVT, EVT.

Use Riemann sums when: (1) asked to estimate or approximate; (2) given discrete data points; (3) the question says "left Riemann sum," "right Riemann sum," or "midpoint." Use definite integrals when you have a continuous function and need an exact answer. On calculator-active questions, your calculator's ∫ function gives exact numerical values.

Use proper notation: integral signs with limits and differentials (∫[a,b] f(x)dx - never forget dx!), derivative notation (dy/dx, f'(x), d/dx), limit notation (lim x→c), and equals signs between steps. Graders deduct points for missing dx in integrals or ambiguous notation.

Yes! On Part A, use your calculator's capabilities: nDeriv for numerical derivatives, fnInt for definite integrals, solve function for finding intersections, and table/graph features for analysis. However, you still must show setup. For example, write "∫[0,2] x²dx = " before giving the calculator result.

Prioritize breadth over depth - attempt every question rather than perfecting a few. Even incomplete work earns partial credit. If time is short, write key setup steps: the integral you'd evaluate, the theorem you'd apply, or the derivative formula. Aim for 2-3 points per question rather than leaving any blank.

The complete PDF is embedded above with full-screen viewing capability. You can also download it from the College Board's AP Central website along with official scoring guidelines. Our solutions include detailed step-by-step work and explanations for all 6 questions.