The Ultimate 101 Prompt Guide for IB Mathematics: Analysis and Approaches (Latest Update 2025)

Introduction

This guide is designed to help educators and students harness the power of Generative AI to master the IB Diploma Programme Mathematics: Analysis and Approaches (MAA) course. The prompts below are engineered to be clear, actionable, and directly aligned with the latest IB curriculum (first assessment 2021), covering topics for both Standard Level (SL) and Higher Level (HL).

How to Use These Prompts:

Think of AI as your academic co-pilot. It can accelerate your workflow, provide new perspectives, and generate tailored resources on demand. The key to unlocking this potential lies in the art of effective prompting.

Copy and Paste: Select a prompt that fits your needs.
Specify Your Context: The more detail you provide, the better the output. Replace bracketed text like [topic] or [HL/SL] with your specific details. For example, changing [calculus topic] to the chain rule is good, but the chain rule for trigonometric functions is even better.
Refine and Iterate: Treat the AI’s first response as a draft, not a final product. Use follow-up prompts to hone the output. For example, after getting a worksheet, you could ask: “Make question 5 more challenging by requiring two different concepts to be combined,” or “Rephrase the explanation in prompt 16 using a sports analogy.” Your expertise is crucial in guiding the AI toward the perfect result.

Section 1 – Educator Prompts (50)

This section provides prompts to assist with the entire teaching lifecycle, from initial course architecture to creating enriching extension activities.

Group A: Planning & Structuring (15 Prompts)

Syllabus Outline: Act as an experienced IB Math AA department head. Create a detailed year-long syllabus outline for my [HL/SL] class. Break down the 5 core topics into a weekly schedule, and for each week, suggest a key ATL (Approaches to Learning) skill to focus on and a potential TOK (Theory of Knowledge) link.
Unit Plan: Generate a comprehensive unit plan for the topic of [Functions]. The plan should include: specific learning objectives for [HL/SL], key vocabulary, a list of common student misconceptions with pre-emptive teaching strategies, ideas for formative and summative assessments, and at least two activities that integrate technology.
Lesson Objectives: I’m teaching [the binomial theorem] to my [SL] class tomorrow. List 3-4 specific, measurable, achievable, relevant, and time-bound (SMART) learning objectives for a 60-minute lesson. Then, for each objective, suggest one activity or question that would directly assess its achievement.
Connecting Topics: Create a detailed concept map showing how the topic of [Trigonometric Functions] links to other areas of the Math AA syllabus, such as [Calculus, Complex Numbers, and Vectors]. For each link, provide a brief explanation and a sample problem that exemplifies the connection.
HL vs. SL Comparison: Generate a three-column markdown table comparing the [Calculus] topic for SL and HL. The columns should be: “Shared Concept,” “SL Application,” and “HL Extension.” This will help clarify the progression of knowledge and skills required.
IA Timeline: Design a detailed and student-friendly timeline for the Internal Assessment (IA) process for an [HL/SL] class. Break it down into key stages (e.g., brainstorming, proposal, research, drafting, peer review, final submission) with suggested deadlines and deliverables for each stage.
Tech Integration Plan: For the unit on [Statistics and Probability], suggest specific ways to integrate a graphing display calculator (GDC) and a spreadsheet program (like Excel or Google Sheets) to enhance student understanding of [e.g., regression analysis or probability distributions].
Prior Knowledge Check: Create a short diagnostic quiz (5-7 questions) to assess students’ prior knowledge of [Algebraic manipulation] before starting the [Calculus] topic. Ensure questions range from simple recall to more complex application. Provide a detailed answer key that explains the reasoning for each answer.
Interdisciplinary Links: Suggest 3 potential interdisciplinary project ideas that connect the Math AA topic of [Kinematics] with [IB Physics or IB Economics]. For each idea, outline a potential research question and the key mathematical techniques that would be used.
Theory of Knowledge (TOK) Integration: Generate three TOK discussion prompts related to the [Number and Algebra] topic. The prompts should explore concepts like the nature of proof, axioms, and mathematical certainty by linking them to specific Ways of Knowing (e.g., Reason, Intuition) and Areas of Knowledge (e.g., The Natural Sciences).
Command Term Focus: Create a lesson plan for an [HL/SL] class focused on differentiating between the IB command terms “Calculate,” “Determine,” and “Show that.” Use examples from the [Geometry and Trigonometry] topic to illustrate how the required response changes for each term. Include a student activity where they must write a response for each command term given the same initial problem.
Paper 3 (HL) Strategy: Outline a comprehensive teaching strategy for preparing HL students for Paper 3. The plan should include a series of workshops on mathematical conjecture, formal proof techniques, and effective communication of complex mathematical ideas. Suggest a structure for in-class practice sessions.
Resource Curation: Act as a curriculum specialist. Curate a list of 5 high-quality online resources (simulations, videos, articles, GeoGebra applets) for teaching the [HL topic of complex numbers]. For each resource, provide a brief description and suggest how it could be used in a lesson.
Pacing Guide Adjustment: My [SL] class is falling behind in the [Calculus] unit. Analyze a standard pacing guide for this topic and suggest adjustments to consolidate key concepts and catch up. Offer two alternative plans: one that trims less essential content, and another that integrates review into the start of subsequent lessons.
Differentiated Planning: I have a mixed-ability [HL] class. For the topic of [Sequences and Series], provide a three-tiered set of learning objectives and corresponding activities (foundational, proficient, advanced). For the advanced tier, include an extension that hints at a university-level concept.

Group B: Delivery & Resource Creation (15 Prompts)

Concept Analogy: Explain the concept of [a limit in calculus] using two different analogies: one related to sports or a physical journey, and another related to digital technology (like zooming in on a pixelated image).
Real-World Application: Provide three detailed, real-world examples where [logarithms] are applied (e.g., finance, seismology, chemistry). For each, explain the context, the specific formula used, and create a sample problem based on that application.
Worksheet Generation: Create a worksheet with 10 practice questions on [solving trigonometric equations] for an [HL/SL] class. Structure the worksheet with increasing difficulty: 3 foundational, 4 proficiency-level, and 3 challenging/multi-step problems. Provide a detailed answer key that shows the full worked solution.
GDC Tutorial Script: Write a step-by-step script for a short video tutorial on how to use a TI-84/Casio GDC to [find the numerical derivative and integral of a function]. Include on-screen text callouts for key button presses and common errors to avoid.
Common Misconceptions: For the topic of [conditional probability], list the top 5 common student misconceptions. For each misconception, provide a clear explanation to address it and design a specific counter-example problem that exposes the flawed logic.
Guided Inquiry Activity: Design a guided inquiry-based activity for students to discover [the relationship between the graphs of f(x), f'(x), and f”(x)] on their own using graphing software like Desmos or GeoGebra. Provide a structured worksheet with leading questions to guide their exploration.
Worked Example: Provide a detailed, step-by-step worked example for a challenging [HL integration by parts] problem that requires applying the technique twice. Annotate each step with clear explanations, including the strategic choice for ‘u’ and ‘dv’.
Presentation Slides: Generate a 10-slide presentation outline on [Vectors and their applications] for an HL class. Include a title slide, learning objectives, key definitions, diagrams, formulas for dot and cross product with their geometric interpretations, and three example problems (one geometric, one physics-based, one abstract).
Starter Activity: Create a 5-minute “Do Now” or starter activity to review [the laws of exponents]. The activity should have three parts: a quick calculation, an algebraic simplification, and a “find the error” problem.
Plenary/Exit Ticket: Design a quick “exit ticket” to assess student understanding at the end of a lesson on [the fundamental theorem of calculus]. The ticket should have three prompts: “Define the concept in your own words,” “Calculate a simple definite integral,” and “What question do you still have?”
Visual Aid Idea: Suggest a physical or digital visual aid I could create to help students understand the concept of [the unit circle and its relationship to sine and cosine graphs]. Describe how to create a dynamic model using GeoGebra where moving a point on the circle traces the corresponding trig graphs.
Debate Prompt: Formulate a debate prompt for HL students: “Is mathematics discovered or invented?” Use [the development of complex numbers] as a case study. Assign one side to argue it was a necessary discovery to solve existing problems and the other to argue it was a purely abstract invention. Provide starting points for both arguments.
Scaffolded Problem: Create a scaffolded version of a complex [optimization problem in calculus involving a 3D shape]. Break it down into 4-5 smaller, manageable parts: defining variables, writing the primary equation, writing the secondary constraint, expressing the primary in one variable, and finally, finding the derivative to optimize.
Formula Derivation: Explain the derivation of the [quadratic formula] by completing the square. Provide a clear, step-by-step walkthrough, and then explain why this derivation is a powerful illustration of algebraic proof techniques.
Jigsaw Activity: Design a jigsaw activity for the topic [applications of integration]. Divide the topic into four expert groups: area between curves, volume of revolution (disc method), volume of revolution (washer method), and kinematics. Create a short “expert guide” and a practice problem for each group.

Group C: Assessment & Feedback (15 Prompts)

Quiz Creation: Act as an IB examiner. Create a 25-mark quiz on [Sequences and Series] for an [SL] class. Ensure the questions map to Assessment Objectives 1, 2, and 3, including a question that requires students to “justify” their choice of formula. Provide a detailed mark scheme.
Paper 1 Style Questions: Generate 3 short-response, non-calculator questions in the style of IB Math AA Paper 1 on the topic of [differentiation rules]. One question should test the product rule, one the quotient rule, and one the chain rule with trigonometric functions.
Paper 2 Style Questions: Generate 1 extended-response, calculator-based question in the style of IB Math AA Paper 2 on the topic of [normal distribution]. The question should have multiple parts, requiring students to find a probability, then work backward to find a value given a probability (inverse normal), and finally, set up and solve an algebraic equation involving the mean or standard deviation.
Paper 3 Style Task (HL): Generate a two-part investigation task in the style of IB Math AA HL Paper 3. Start with a specific case of [a Maclaurin series for e^x], ask students to investigate its accuracy for different values of x, and then challenge them to generalize their findings and explore the series for a related function like [e^(2x)].
IA Topic Brainstorm: Provide 5 potential IA topics related to the [Functions] unit that would be appropriate for an [SL] student. For each, suggest a possible research question, the type of data that would be needed, and a key mathematical process that would be central to the exploration.
Rubric Creation: Create a simplified, student-friendly rubric for the “Mathematical Communication” and “Personal Engagement” criteria of the IA. Use examples relevant to a project on [modeling population growth with logistic functions] to illustrate what each level of achievement looks like in practice.
Feedback Generation: A student submitted this incorrect solution to [a related rates problem]: [paste student’s incorrect work]. Provide constructive feedback that identifies the conceptual error (e.g., differentiating with respect to the wrong variable) and the mechanical error. Guide the student with two probing questions and suggest a similar problem for them to try.
Distractor Analysis: Here is a multiple-choice question: [paste question]. The correct answer is B. The other options are A, C, and D. For each incorrect option (distractor), explain the likely mathematical error or misconception a student would have that would lead them to choose that option.
Mark Scheme Development: Create a detailed, point-by-point mark scheme for this exam question: [paste a multi-part exam question]. The mark scheme should include allocation for Method (M), Answer (A), and Reasoning (R) marks, and note any acceptable alternative methods.
Peer Assessment Sheet: Design a peer assessment checklist for students to use when reviewing each other’s IA first drafts. The checklist should be structured around the five IA criteria and use “I can see…” and “I suggest…” sentence starters to encourage constructive feedback.
Test Review Sheet: Create a comprehensive test review sheet for the upcoming unit test on [Geometry and Trigonometry]. The sheet should list all key topics, all relevant formulas (and specify which are in the formula booklet), and provide 5 practice problems, one for each major concept.
Error Analysis Task: Create a worksheet that contains 5 solved problems on [integration], each with a common but subtle error (e.g., mishandling the negative sign in a u-substitution, incorrect integration bounds). Ask students to act as the teacher, find the error, explain the flawed logic, and provide the fully corrected solution.
Portfolio Question: Design a portfolio-style question that requires students to apply concepts from [vectors and calculus] to solve a multi-stage problem involving the collision course of two moving objects. The question should require both calculation and a written explanation of their results.
IA Reflection Prompts: Provide 5 guiding questions to help a student write a deep and meaningful “Reflection” section of their IA. The prompts should move beyond “what I did” to “what it means,” encouraging them to consider the significance, limitations, and potential extensions of their work.
Predictive Question: Based on past IB exam trends and the emphasis on linking topics, what type of question combining [trigonometry and complex numbers] is likely to appear on the HL exam? Generate an example question that requires using De Moivre’s theorem to derive a multiple angle identity.

Group D: Enrichment & Differentiation (5 Prompts)

Extension Problem: Create a challenging extension problem for an HL student who has mastered [L’Hôpital’s Rule]. The problem should require them to first manipulate an expression into an indeterminate form or connect the rule to the definition of the derivative.
Scaffolding for Struggling Students: I have a student struggling to understand [the chain rule]. Provide a series of 3 scaffolding questions that use the “onion layer” analogy. Start with a very simple outer function, then add a simple inner function, and finally use a composition of three functions.
University-Level Connection: How does the IB Math AA HL topic of [Maclaurin and Taylor series] directly lead to concepts studied in a first-year university engineering or mathematics course, such as [differential equations or Fourier analysis]? Provide a brief but clear explanation of the link.
Olympiad-Style Problem: Create a Math Olympiad-style problem that uses concepts from the [Number and Algebra] section of the AA course, such as the properties of modular arithmetic or Diophantine equations, but requires a clever insight beyond standard algorithmic solutions.
Historical Context: Provide a brief historical context for the development of [calculus]. Explain the distinct approaches of Newton (fluxions, physics-based) and Leibniz (notation, formalism) and discuss how their combined contributions created the powerful tool we use today.

Section 2 – Student Prompts (50)

This section is for learners to take control of their studies, from clarifying confusing ideas to stress-testing their knowledge before an exam.

Group E: Understanding Concepts (15 Prompts)

Simple Explanation: Explain [the fundamental theorem of calculus] in simple terms. Then, create a simple diagram or visual metaphor to help me remember the connection between differentiation and integration.
Analogy Request: Give me an analogy to help me understand the difference between a [sequence and a series]. Then, create another analogy for the difference between a [convergent and divergent series].
Concept Comparison: What is the difference between [permutations and combinations]? Give me a clear example of a situation for each and explain why the order does or does not matter in each case.
Visualizing a Concept: Can you describe a way to visualize [complex number multiplication on the Argand diagram]? Explain how the magnitudes multiply and the arguments add, using a specific example.
Why Does This Work?: Why does [L’Hôpital’s Rule] work for finding limits of indeterminate forms? Explain the intuition behind it by relating it to the local linear approximation of the functions involved.
Key Vocabulary: I’m starting the [Statistics] topic. Define the key terms [mean, median, mode, and standard deviation]. For each term, explain what it tells us about a data set and describe a situation where it would be the most appropriate measure of central tendency.
Step-by-Step Process: What are the exact steps to follow when proving a statement using [mathematical induction]? Break it down into the base case, inductive hypothesis, and inductive step, and explain the purpose of each part.
Common Mistakes: What are the three most common mistakes students make when applying [the chain rule in differentiation]? For each mistake, show an example of the error and the correct version side-by-side.
GDC Function: How do I use my [TI-84/Casio] calculator to [solve a system of linear equations using matrices]? Provide the exact key presses and explain how to interpret the output.
Formula Breakdown: Break down the formula for [the volume of a solid of revolution] (V = π ∫ y² dx). Explain what each part of the formula represents geometrically, especially why the y is squared and why the dx is included.
“Teach Me” Prompt: Teach me the basics of [vector dot and cross products] at an HL level. Start with the algebraic formulas, then explain the geometric interpretations (projection for dot, orthogonal vector and area for cross) with clear diagrams.
Real-Life Relevance: When would I ever use [the sine rule or cosine rule] in real life? Give me a practical, step-by-step example from a field like surveying, navigation, or construction.
Connecting Ideas: How is [e^ix = cos(x) + i sin(x)] (Euler’s formula) related to [trigonometric identities like the angle sum formulas]? Show me how to derive one from the other.
Unpacking a Definition: The formal epsilon-delta definition of a [limit] is confusing. Can you unpack it for me using the specific example of lim (x->2) of 3x = 6?
Graphical Interpretation: Show me graphically what it means for a function to be [continuous but not differentiable] at a point. Provide a well-known example like f(x) = |x| and explain why the derivative is undefined at the sharp corner.

Group F: Practicing Skills (15 Prompts)

Practice Problems: Give me 5 practice problems on [finding the derivative of trigonometric functions], in increasing order of difficulty. Include the answers so I can check my work.
Problem Walkthrough: Walk me through solving this problem step-by-step: [paste a specific problem from your textbook]. Adopt the persona of an encouraging tutor and explain not just what to do, but why you’re doing it at each stage.
Create a Similar Problem: I’m struggling with this type of problem: [paste a problem]. Can you create a similar problem for me to practice, but change the context or the numbers? Also, create a slightly easier version and a slightly harder version.
Check My Work: I solved this problem on [integration by substitution]. Is my answer correct? Here is my work: [paste your full solution]. If it’s wrong, please identify the exact line where I made a mistake and explain my error.
Non-Calculator Practice: Give me 5 questions on [logarithms] that I should be able to solve without a calculator, similar to Paper 1. The questions should test log laws, change of base, and solving log equations.
Calculator Practice: Give me 3 challenging questions on [binomial distribution] where a GDC is necessary, similar to Paper 2. One question should require finding P(X=x), one P(X<=x), and one finding the smallest n for a probability to exceed a certain value.
Mixed Problems: Create a mixed set of 5 problems covering all the different [differentiation rules (product, quotient, chain)]. Make sure at least two problems require combining multiple rules in one question.
Application Problem: Create a word problem that requires me to use [optimization with derivatives] to solve it. Use a realistic context, like minimizing the material for a container or maximizing revenue for a company.
From Scratch: I need to find the [angle between two vectors]. What formula do I use? Explain the components of the formula and then walk me through applying it to a specific example.
Reverse Problem: The derivative of a function is [f'(x) = 3x² + 4x] and the function passes through the point (1, 5). What is the original function f(x)? Explain the role of the constant of integration and how to find it using the given point.
Justify the Method: For the integral of [x * ln(x)], why is [integration by parts] the correct method to use over [u-substitution]? Explain the strategic thinking involved in choosing a method.
Multi-Step Problem: Give me a multi-step problem that starts with [finding the roots of a quadratic function], then asks me to [find the coordinates of its vertex], and finally asks me to [calculate the area enclosed by the function and the x-axis between its roots].
Proof Practice: Give me a simple statement related to [the sum of an arithmetic series] that I can try to prove by mathematical induction. Provide the statement and let me try it on my own.
Show That: Give me a problem where I have to “Show that” a specific [trigonometric identity] is true. Provide the identity and I will attempt the proof.
HL Challenge: Give me a challenging HL-level problem that combines [complex numbers in polar form and De Moivre’s theorem] to find the roots of a complex number.

Group G: Revising & Preparing for Assessment (20 Prompts)

Summary Sheet: Create a one-page summary sheet for the topic of [Vectors] for [HL/SL]. Include all key formulas, concepts, diagrams, and a small section on “Common Pitfalls” and another on “Calculator Tips.”
Flashcards: Generate a set of 15 flashcards for the [Calculus] unit. Each card should have a key term, formula, or concept on one side and a concise definition, explanation, or example on the other. Present it in a two-column markdown table.
Mind Map: Create a detailed mind map structure for the topic [Functions]. The central idea should be “Functions,” with main branches for types of functions, transformations, key characteristics (domain, range, asymptotes), and inverse functions. Add sub-branches for each.
Revision Plan: Create an adaptive 7-day revision plan for my final exam in IB Math AA [SL/HL]. For each day, specify a major and minor topic, a ‘core’ set of tasks (e.g., “review summary sheet and do 5 practice problems”), and an ‘extension’ task (e.g., “try a Paper 3 style investigation”).
Self-Quiz: Create a 10-question multiple-choice quiz covering the entire [Statistics and Probability] topic. Make sure the distractors for each question correspond to common errors. Provide an answer key with explanations for why the correct answer is right and the others are wrong.
IA Brainstorm: I’m interested in [financial markets]. Can you suggest 3 possible IA research questions related to this interest for Math AA [HL]? For each, suggest a mathematical model I could use (e.g., regression, time series analysis) and a potential challenge I might face.
IA Outline: Help me create a detailed outline for my IA with the research question: [paste your research question]. Structure it according to the IB criteria: Introduction, Main Body (methods and results), Conclusion, and Reflection. Suggest key points to include in each section.
Exam Strategy: What are the best strategies for managing my time during Paper 1 (the non-calculator paper)? Provide tips on question selection, time allocation per mark, and when to move on from a difficult question.
Command Term Glossary: Create a glossary of the top 10 most important IB command terms (e.g., “Hence,” “Write down,” “Determine,” “Justify”). For each term, explain what it requires me to do and provide a sample question from the [Calculus] topic.
Explain a Mark Scheme: Here is an IB mark scheme for a question: [paste mark scheme]. Explain what the M1, A1, R1, and AG marks mean. Then, rewrite the mark scheme in plain English, as if a teacher were explaining how I would earn each point.
Compare/Contrast Concepts: Create a Venn diagram or table to compare and contrast [differentiation and integration]. Include their purpose, rules, geometric meaning, and their relationship via the Fundamental Theorem of Calculus.
Topic Test: Generate a 45-minute topic test for [Geometry and Trigonometry] at the [HL] level, with a mix of Paper 1 and Paper 2 style questions, weighted according to typical exam structure.
Key Formulas List: List all the essential formulas for the [Number and Algebra] topic that are NOT in the IB formula booklet. For each one, provide a brief explanation of when to use it.
Mistake Journal: I made these 3 mistakes on my last test: [list your mistakes, e.g., “forgot the constant of integration,” “mixed up sine and cosine derivatives,” “algebra error in simplification”]. Create 2 practice problems for each mistake that specifically target these weaknesses.
“Explain it Back” Prompt: I’m going to try and explain [the binomial theorem] to you. [Student writes their explanation]. Please review my explanation for accuracy, clarity, and use of correct terminology. Give me feedback as if you were my teacher.
Paper 3 Practice (HL): I am preparing for Paper 3. Give me a starting point for an investigation on the properties of [the Gamma function as an extension of the factorial]. Suggest some possible patterns to look for and conjectures to explore.
Reflection on Learning: I just finished the [Calculus] unit. Give me three questions to help me reflect on my learning. The questions should be: “What concept was most difficult and why?”, “Which concept did I find most interesting and why?”, and “How does this unit connect to another area of mathematics I’ve studied?”
Study Buddy Simulation: Act as my study buddy. Let’s do a rapid-fire review of [probability distributions]. Ask me 10 quick questions, give me immediate feedback on my answers, and keep track of my score.
IA Personal Engagement: How can I demonstrate “personal engagement” in my IA on [modeling the spread of a virus]? Give me 3 specific, creative ideas beyond just saying “I’m interested in it.”
Exam Day Checklist: Create a practical checklist of things I should do the day before and the morning of my IB Math exam, covering materials, mindset, and last-minute review strategy.

Section 3 – Bonus: Advanced & Interdisciplinary Prompts (3 Prompts)

The Interdisciplinary Challenge: Act as a panel of experts from the fields of [e.g., Music, Biology, and Architecture]. Analyze the mathematical concept of [e.g., Logarithmic Spirals or Sequences and Series]. Each expert should provide a short paragraph from their discipline’s perspective on the significance or application of this concept. Finally, synthesize these views to propose a novel IA topic that an IB student could pursue.
The Modeling Challenge: Act as a data scientist. Here is a real-world dataset: [paste a small, clean dataset, e.g., historical population data, temperature records, or stock prices]. Guide me through the process of creating a mathematical model for this data. Prompt me to: choose an appropriate function type (linear, exponential, logistic), justify my choice, perform a regression, and critically evaluate the model’s limitations and predictive power.
The Future-Focused Connection: How might the mathematical concepts in [IB topic, e.g., vectors and matrices] be applied in an emerging technology like [e.g., machine learning for image recognition or quantum computing]? Explain the connection in a clear, conceptual way that an ambitious HL student could understand, bridging the gap between their current knowledge and future applications.