Introduction
This guide is designed to empower educators and students in AP Calculus AB by leveraging the capabilities of Generative AI. Based on a thorough analysis of the official College Board curriculum for 2024-2025, these 101 prompts are crafted to be clear, actionable, and curriculum-aligned.
For best results, use these prompts as a starting point. Feel free to add more context, specify the desired tone, or request different formats. The key is to treat the AI as a knowledgeable assistant that can help you plan, learn, and create more effectively.
Section 1: Educator Prompts (50)
These prompts are designed to assist with every stage of teaching, from initial planning to final review.
Stage 1: Planning & Preparation (15 Prompts)
Syllabus Outline: “Act as an experienced AP Calculus AB teacher. Generate a detailed, 180-day syllabus based on the 2024-2025 College Board curriculum. The syllabus should be structured by unit, allocating a specific number of 45-minute class periods to each topic and subtopic within the course framework. Include suggested timings for quizzes, unit tests, and midterm/final exam review.”
Unit 1 Plan (Limits & Continuity): “Create a comprehensive lesson plan for Unit 1: Limits and Continuity. For each topic (e.g., ‘Estimating limits from graphs and tables,’ ‘Determining limits using algebraic properties,’ ‘Continuity’), provide a learning objective, a 15-minute ‘hook’ or warm-up activity, key vocabulary terms, a list of example problems (ranging from easy to hard), and a 10-minute exit ticket question.”
Big Ideas Explained: “Explain the three ‘Big Ideas’ of AP Calculus AB (Change, Limits, and Analysis of Functions) in simple, accessible language suitable for a high school student. For each Big Idea, provide three concrete examples of how it applies to real-world scenarios (e.g., physics, economics, engineering).”
Essential Knowledge Map: “Generate a concept map that visually outlines the ‘Essential Knowledge’ statements for Unit 3: Differentiation: Composite, Implicit, and Inverse Functions. The map should show the logical connections between topics like the Chain Rule, implicit differentiation, and derivatives of inverse functions.”
Pacing Guide Adjustment: “I have a 4-day school week. Adapt the standard AP Calculus AB pacing guide for a block schedule with 90-minute classes that meet twice a week. Provide a semester-long plan that covers all 10 units before the AP exam in May, building in time for review.”
Lab/Activity Ideas: “Brainstorm three hands-on, inquiry-based lab activities for Unit 6: Integration and Accumulation of Change. One activity should use physical materials (e.g., water, containers), one should use a digital tool like Desmos or GeoGebra, and one should involve analyzing real-world data.”
FRQ Strategy Plan: “Develop a year-long plan for integrating Free-Response Questions (FRQs) into my curriculum. The plan should start with single-concept FRQs early in the year and gradually build to multi-part, multi-concept questions. Specify which FRQ types to introduce in each unit.”
Common Misconceptions: “For Unit 4: Contextual Applications of Differentiation, list the top 5 most common student misconceptions. For each misconception, explain the flawed thinking and provide a targeted teaching strategy and a specific example problem to correct it.”
Technology Integration: “Suggest five ways to effectively integrate a graphing calculator (like a TI-84) into lessons for Unit 8: Applications of Integration. The suggestions should go beyond simple graphing and focus on features that enhance conceptual understanding (e.g., numerical integration, slope fields).”
Vocabulary List: “Create a comprehensive vocabulary list for the entire AP Calculus AB course. Group the terms by unit. For each term, provide a student-friendly definition and an example.”
Parent Communication: “Draft a letter to parents at the beginning of the school year. The letter should introduce AP Calculus AB, outline the course expectations, explain the importance of the AP exam, and suggest ways parents can support their students.”
Substitute Teacher Plan: “Create an emergency substitute plan for a 50-minute class period covering the topic ‘The Fundamental Theorem of Calculus.’ The plan should include a brief review, a worksheet with 10 practice problems (with an answer key), and an extension activity for students who finish early.”
Project-Based Learning: “Design a project-based learning (PBL) assignment for Unit 5: Analytical Applications of Differentiation. The project should require students to analyze a function of their choosing, finding its critical points, intervals of increase/decrease, concavity, and inflection points, and then create a detailed report and presentation of their findings.”
Interdisciplinary Connections: “Generate a list of 5 interdisciplinary connections between AP Calculus AB and AP Physics 1. For each connection (e.g., derivatives and velocity/acceleration), suggest a mini-project or problem set that could be co-taught.”
Pre-Calculus Review Packet: “Create a 25-question ‘Are You Ready for Calculus?’ diagnostic packet that covers essential pre-calculus skills needed for success in AP Calculus AB. Topics should include functions (domain, range, composition), trigonometry (unit circle, identities), and advanced algebra (logarithms, rational functions).”
Stage 2: Delivery & Instruction (15 Prompts)
Real-World Analogy: “Explain the concept of a ‘limit’ using three different real-world analogies. One analogy should be sports-related, one food-related, and one technology-related.”
Socratic Seminar Questions: “Generate 10 thought-provoking, open-ended questions to facilitate a Socratic seminar on the Mean Value Theorem. The questions should encourage students to explore its conditions, conclusions, and graphical interpretations.”
Differentiated Instruction: “I have a student who excels at algebra but struggles with geometric and graphical concepts. Provide three differentiated activities for Unit 2: Differentiation: Definition and Fundamental Properties, tailored to this student’s strengths and weaknesses.”
Scaffolded Worksheet: “Create a scaffolded worksheet for ‘Related Rates’ problems. The worksheet should start with a fully worked-out example, followed by problems with decreasing levels of guidance (e.g., given equations, then given diagrams, then just a word problem).”
Interactive Notebook Entry: “Design an interactive notebook entry for the ‘Product Rule’ and ‘Quotient Rule.’ It should include foldable elements for the formulas, a space for students to write their own mnemonic devices, and several practice problems.”
Role-Playing Script: “Write a short script for a role-playing activity where one student is the ‘Derivative’ and another is the ‘Integral.’ The script should have them debate which one is more important, highlighting their relationship as inverse operations (FTC).”
Guided Notes: “Generate a set of guided (fill-in-the-blank) notes for a lesson on ‘Solving Differential Equations using Separation of Variables.’ Include key definitions, step-by-step procedures, and two worked-out examples.”
Error Analysis Task: “Create an error analysis task for ‘Implicit Differentiation.’ Provide 5 problems that have been solved incorrectly. For each problem, students must identify the error, explain why it’s wrong, and provide the correct solution.”
Think-Pair-Share: “Develop a ‘Think-Pair-Share’ activity for the topic ‘Connecting a Function, its First Derivative, and its Second Derivative.’ Provide a graph of f'(x) and ask students to first think individually, then discuss with a partner, and finally share with the class their conclusions about the properties of f(x) and f”(x).”
Jigsaw Activity: “Design a jigsaw activity for ‘Applications of Integration.’ Divide the topic into four sub-topics: 1) Finding the area between curves, 2) Finding volume with the disk/washer method, 3) Finding volume with the shell method, 4) Finding volume with known cross-sections. Create an ‘expert sheet’ for each group.”
Lecture Script: “Write a 10-minute mini-lecture script explaining the formal definition of the derivative. The script should be engaging, use clear language, and include cues for when to draw specific diagrams on the board.”
Concept Comparison: “Create a Venn diagram or a comparison table that highlights the similarities and differences between the ‘Mean Value Theorem’ and the ‘Intermediate Value Theorem’.”
Exit Ticket Variations: “Generate three different exit ticket questions for a lesson on the Chain Rule. One should be a calculation, one a conceptual question, and one asking students to create their own problem.”
Graphic Organizer: “Create a graphic organizer to help students remember the different integration techniques covered in the course (e.g., u-substitution, integration by parts, long division).”
Classroom Debate: “Frame a debate topic for Unit 7: Differential Equations. Topic: ‘Is it more useful to find an exact analytical solution to a differential equation or to approximate a solution using Euler’s Method?’ Provide opening statements for both the ‘pro-analytical’ and ‘pro-approximation’ sides.”
Stage 3: Assessment & Feedback (10 Prompts)
Quiz Generator: “Generate a 5-question multiple-choice quiz on Unit 1: Limits and Continuity. The questions should be modeled after AP-style questions, including at least one question that requires analysis of a graph and one that requires analysis of a table.”
FRQ Creation: “Create an original, 2-part Free-Response Question (FRQ) on the topic of ‘Accumulation Functions.’ The question should provide a rate function (e.g., in gallons per hour) and ask students to interpret the meaning of a definite integral in context and find the total amount accumulated over an interval.”
Rubric Design: “Design a detailed, 9-point scoring rubric for the FRQ you created in the previous prompt. The rubric should clearly define how points are awarded for setup, calculation, and interpretation, mirroring the College Board’s scoring guidelines.”
Test Blueprint: “Create a test blueprint for a Unit 5 exam on ‘Analytical Applications of Differentiation.’ The blueprint should specify the number of multiple-choice and free-response questions, the specific topics covered by each question, and the corresponding learning objectives from the course framework.”
Feedback Comments: “Generate a bank of constructive feedback comments for common errors on a ‘Related Rates’ FRQ. Include comments for mistakes like forgetting to differentiate with respect to time, incorrect geometric formulas, and substitution errors.”
Multiple Choice Distractors: “Take the following question: ‘What is the derivative of f(x) = ln(x^2)?’ The correct answer is 2/x. Generate three plausible distractors (incorrect multiple-choice options) and explain the likely student error that would lead to each distractor.”
Peer Review Checklist: “Create a peer review checklist for students to use when grading each other’s work on a ‘Disk and Washer Method’ volume problem. The checklist should prompt them to check for correct setup of the integral, correct bounds, and accurate calculation.”
Retake Policy: “Draft a fair and effective test retake policy. The policy should require students to complete test corrections and a relevant review assignment before being eligible for a retake that covers the same concepts with different problems.”
Portfolio Assignment: “Design a cumulative portfolio assignment for the end of the semester. The portfolio should require students to select one problem they struggled with from each unit, rework it correctly, and write a one-paragraph reflection on their initial mistake and new understanding.”
AP Exam Review Kahoot: “Generate 15 engaging questions for a Kahoot! review game covering the entire AP Calculus AB curriculum. The questions should be fast-paced and cover a wide range of topics.”
Stage 4: Enrichment & Extension (10 Prompts)
Calculus in Careers: “Describe how calculus is used in the career of a) a video game designer, b) a financial analyst, and c) an architect. Provide a sample problem for each career that would require calculus to solve.”
Historical Context: “Write a short biography of either Isaac Newton or Gottfried Wilhelm Leibniz, focusing on their contributions to the development of calculus. Explain the nature of their famous priority dispute in simple terms.”
Calculus BC Preview: “My top students are considering taking AP Calculus BC next year. Create a ‘sneak peek’ worksheet that introduces one topic from the BC curriculum (e.g., parametric equations or polar coordinates) and shows how it builds on AB concepts.”
Math Competition Problems: “Generate three challenging, math competition-style problems that extend concepts from AP Calculus AB. For example, a complex optimization problem or a non-standard solids of revolution problem.”
Connection to Statistics: “Explain the relationship between a probability density function (a concept from statistics) and integration. Create a simple problem where students have to find the probability of an event by calculating the area under a curve.”
L’Hôpital’s Rule Introduction: “Create a discovery-based lesson to introduce L’Hôpital’s Rule for evaluating indeterminate forms. The lesson should have students investigate limits like sin(x)/x as x approaches 0 numerically and graphically before introducing the rule itself.”
Cryptography Connection: “Briefly explain how calculus concepts, particularly derivatives and optimization, can play a role in modern cryptography and data security, for instance, in optimizing algorithms.”
Explore a Paradox: “Explain Zeno’s ‘Dichotomy Paradox’ and how the concept of a limit and infinite series can be used to resolve it. Create a simple version of the paradox for students to analyze.”
Independent Research Topics: “Generate a list of 10 potential topics for an independent research project for a student who wants to go beyond the AP curriculum. Topics should be accessible but challenging (e.g., ‘Introduction to Fourier Series,’ ‘The Calculus of Variations’).”
‘Why Calculus?’ Essay: “Write a persuasive essay (500 words) arguing for the importance of learning calculus, even for students who do not plan to major in a STEM field. The essay should focus on the development of logical reasoning and problem-solving skills.”
Section 2: Student Prompts (50)
These prompts are designed to help students master concepts, practice effectively, and prepare for all assessments.
Stage 1: Understanding Concepts (15 Prompts)
Explain It To Me Like I’m 10: “Explain the concept of the ‘Chain Rule’ as if you were talking to a 10-year-old. Use a simple analogy, like Russian nesting dolls or gears on a bike.”
Concept Visualizer: “Describe a visual or a diagram that would help me remember the difference between the ‘Disk Method’ and the ‘Washer Method’ for finding volumes of revolution.”
Key Differences: “What is the key difference between the ‘average rate of change’ and the ‘instantaneous rate of change’? Provide a real-world example that clearly illustrates this difference.”
Why Does It Work?: “Explain the intuition behind the ‘First Fundamental Theorem of Calculus.’ Why does taking the derivative of an accumulation function give you back the original function?”
Connect the Concepts: “How is the ‘Mean Value Theorem for Derivatives’ related to the ‘Rolle’s Theorem’? Explain how Rolle’s Theorem is just a special case of the MVT.”
Study Guide Creator: “Act as my study partner. Create a one-page study guide for Unit 3: Differentiation. The guide should include the most important formulas (Product, Quotient, Chain Rules), key concepts in simple terms, and one worked-out example for each rule.”
Identify the Conditions: “What are the three conditions that must be met for the ‘Intermediate Value Theorem’ to apply? For each condition, give an example of a function that fails to meet it and show why the theorem doesn’t work.”
Vocabulary Flashcards: “Generate a set of 10 digital flashcards for Unit 7: Differential Equations. On the front of each card, put a key term (e.g., ‘Slope Field,’ ‘Separation of Variables,’ ‘Initial Condition’). On the back, provide a simple definition and a hint for how to use it.”
Real-World Application: “Give me a step-by-step explanation of how a police officer could use calculus (specifically, related rates) to determine a car’s speed using a radar gun.”
The ‘So What?’ Question: “I understand how to find the second derivative of a function. But what does it actually tell me about the original function’s graph? Explain the concept of concavity and points of inflection.”
Formula Proof: “Provide a simple, intuitive proof or derivation of the ‘Product Rule.’ You can use the limit definition of the derivative to show where the formula comes from.”
Common Mistakes: “What are the most common algebraic mistakes students make when finding limits? List the top 3 and show an example of each.”
Graphical Interpretation: “I have the graph of f'(x), the derivative of a function. Create a checklist of questions I should ask myself to determine the properties of the original function f(x) (e.g., where is f(x) increasing/decreasing? where are the local max/min?)”
Concept Story: “Tell me a short story or create a narrative that explains the entire process of solving an optimization problem, from reading the problem to verifying the result.”
Translate the Math: “Translate the formal definition of continuity at a point,
lim(x->c) f(x) = f(c), into plain English. Break down what each part of the equation means.”
Stage 2: Practicing & Applying (15 Prompts)
Problem Generator: “Generate 5 practice problems on ‘u-substitution.’ Make 2 of them easy, 2 medium, and 1 hard. Provide the final answers so I can check my work.”
Step-by-Step Solution: “I’m stuck on this problem: ‘Find the volume of the solid generated by revolving the region bounded by y = sqrt(x), y = 0, and x = 4 about the x-axis.’ Provide a detailed, step-by-step solution, explaining the reasoning for each step.”
Work Checker: “I tried to solve the following related rates problem and got a specific answer. Can you check my work? [Paste your full solution here]. If I made a mistake, please identify it and explain how to correct it.”
Create a Similar Problem: “Here is a problem I understand: [Paste a problem you’ve already solved]. Can you create a new problem that uses the same concepts but with different numbers and a different context?”
FRQ Practice: “Give me a past AP Calculus AB Free-Response Question that deals with a table of values and asks for approximations of derivatives and integrals (e.g., using Riemann sums).”
Multiple-Choice Drills: “Create 10 AP-style multiple-choice questions focusing specifically on the ‘Chain Rule.’ Include a mix of functions (trigonometric, logarithmic, exponential).”
Targeted Practice: “I always get confused between the ‘Disk Method’ and the ‘Washer Method.’ Give me two practice problems, one that must be solved with the Disk Method and one that must be solved with the Washer Method. Explain why each method is appropriate for that problem.”
Build My Own Problem: “Help me create my own ‘optimization’ problem. Guide me through choosing a scenario (e.g., fencing a yard, making a box), defining the variables, and setting up the primary and secondary equations.”
‘What’s the Next Step?’: “I’ve started this implicit differentiation problem: x^2 + y^2 = 25. I’ve taken the derivative of both sides to get 2x + 2y(dy/dx) = 0. What is the very next algebraic step I should take to solve for dy/dx?”
Justification Practice: “For the function f(x) = x^3 – 6x^2 + 5, I found that there is a critical point at x = 4. How do I properly justify that this is a local minimum using the Second Derivative Test? Write out the sentence I should use on the AP exam.”
Calculator Skills: “Explain, step-by-step, how to use a TI-84 graphing calculator to find the numerical value of the definite integral of
sin(x^2)from x=1 to x=2.”Contextual Problem: “Write a word problem about the rate of water leaking from a tank that requires me to use the Fundamental Theorem of Calculus to find the total amount of water that has leaked out over a specific time interval.”
Mixed Review Set: “Create a mixed review problem set with 5 questions. It should include one limit problem, one derivative problem, one integral problem, one related rates problem, and one differential equation problem.”
Mental Math: “Give me 5 simple derivative problems that I should be able to solve in my head to build speed and accuracy (e.g., d/dx of 5x^4, sin(x), e^x).”
Analyze a Solution: “Here is a worked-out solution to an FRQ from the College Board website. [Paste link or text]. Can you explain the scoring for Part (c)? Why did the student earn the point for the answer but not the justification?”
Stage 3: Revising & Self-Assessment (10 Prompts)
Custom Quiz: “Create a 5-question quiz for me. The quiz should have 2 questions on the Product Rule, 2 on the Quotient Rule, and 1 that requires both. Provide an answer key with explanations.”
Identify My Weakness: “I’ve done these 5 practice problems [paste your work or describe the problems]. Based on my answers, what topic do you think is my biggest weakness? Suggest a plan for how I can improve on this topic.”
Two-Minute Review: “Summarize the entire topic of ‘Limits’ in a way that I could read and understand in two minutes. Focus on the most critical ideas I need to remember for the exam.”
‘Cheat Sheet’ Creator: “Help me create a one-page ‘cheat sheet’ for my final exam. It should be organized by unit and contain only the most essential formulas, theorems (with conditions), and derivative/integral rules. Use a compact, two-column format.”
Predict the FRQ: “Based on the topics covered in recent years’ AP Calculus AB exams, what are three likely types of Free-Response Questions that could appear this year? For each type, list the key skills I would need to demonstrate.”
Self-Grading Rubric: “I’m about to attempt an FRQ on my own. Give me a simplified, student-friendly rubric I can use to grade my own response. The rubric should be in the form of a checklist.”
Mnemonic Device: “Create a memorable mnemonic device, acronym, or rhyme to help me remember the rules for finding derivatives of the six trigonometric functions.”
Concept Map Review: “Generate a text-based concept map that links the following ideas: ‘critical points,’ ‘local extrema,’ ‘intervals of increasing/decreasing,’ ‘first derivative test,’ and ‘concavity.’ Use indentation to show the relationships.”
Explain It Back: “I’m going to try to explain the ‘Mean Value Theorem’ to you. [Student writes their explanation]. Now, critique my explanation. Is it accurate? Is it clear? What could I improve?”
Top 5 Mistakes to Avoid: “What are the top 5 ‘rookie mistakes’ students make on the AP Calculus AB exam that are easy to avoid? For each mistake, tell me how to prevent it.”
Stage 4: Exam Preparation (10 Prompts)
Study Plan Generator: “It’s 4 weeks before the AP exam. Create a detailed, week-by-week study plan for me. The plan should balance reviewing old content with practicing full-length multiple-choice and FRQ sections. Allocate specific topics for each day.”
FRQ Time Management: “The FRQ section is 90 minutes for 6 questions. Give me a time management strategy. How much time should I spend on each question? What should I do if I get stuck?”
‘Calculator Active’ Strategy: “What are the key things I should remember for the ‘calculator active’ portion of the exam? What types of problems should I immediately use my calculator for?”
Justification Keywords: “List the key ‘justification’ phrases the AP readers look for. For example, ‘f(x) has a local minimum at x=c because f'(x) changes from negative to positive at x=c.’ Give me 5 more examples for different scenarios (concavity, points of inflection, etc.).”
Full Practice Exam: “Generate a complete, simulated AP Calculus AB practice exam, including a 30-question ‘no calculator’ multiple-choice section, a 15-question ‘calculator active’ multiple-choice section, and a 6-question FRQ section. Ensure the questions cover the full range of course topics.”
‘Brain Dump’ Sheet: “On exam day, I get a few minutes before the test starts. What are the top 10 things I should immediately write down on my scratch paper (a ‘brain dump’)? Include formulas, theorems, and the unit circle.”
Exam Day Checklist: “Create a checklist for the 24 hours leading up to the AP exam. Include what to study, what to eat, what to pack (pencils, calculator, etc.), and tips for staying calm.”
Analyze an FRQ Prompt: “Take this FRQ prompt: [Paste an official FRQ prompt]. Break down the prompt part by part. What calculus skill is each part testing? What are the keywords I should pay attention to?”
Post-Exam Reflection: “The exam is over. Create a list of 5 reflection questions to help me think about my performance. The questions should help me identify what I did well and what I might do differently if I were to take it again.”
Common ‘Trap’ Questions: “Describe 3 types of ‘trap’ questions that often appear on the multiple-choice section. For each one, explain what the trap is and how to recognize and avoid it.”
Section 3: Bonus Universal Prompt (1)
This prompt is designed to foster creativity and interdisciplinary thinking for both educators and students.
Calculus Art Project: “Act as a creative director. Design a project where calculus is used to create a piece of visual art. The project must use concepts from the AP Calculus AB curriculum. Provide a detailed prompt that explains the requirements. The prompt should specify that the final submission must include: a) The artwork itself (this could be a digital plot, a physical drawing, or a 3D model). b) A 500-word written explanation detailing the mathematical processes used. This explanation must correctly use calculus vocabulary and notation to describe how functions, derivatives (for shape and form), and integrals (for area or volume) were used to generate the art. c) A scoring rubric for an educator to grade the project, with points allocated for artistic creativity, mathematical accuracy, and the clarity of the written explanation.”
