Math can be the bane of many students’ existences. Even mentioning the words ‘AP® Calculus exam’ can send a shock of terror through any student’s heart. But don’t worry, we’ve got the tools that you’ll need to succeed. We have developed a 30-day study plan that will help you solve problems, experiment, interpret results, and support your conclusions. We’re here to sharpen your math skills and make you an AP® Calculus AB/BC pro in no time. This AP® study guide will give you everything you need to review, learn, and maintain for the AP® Calculus AB/BC Exam. If you stick to the daily regimen we have laid out for you here, we will sharpen your calculus skills like never before and get you that much closer to that 5 on the AP® exam.

Key Things to Remember While Using this AP® Study Guide

• This is a guide, you don’t have to follow every step if it’s not working for you. Everybody learns differently and it’s ok if some steps are not quite working for you. Change things up and mix our recommendations around. Just find whatever will work best for you.
• This may seem like an impossible statement, but make studying fun! Try not to get too stressed out when studying for the exam. True, math and calculus can seem a bit daunting, but don’t get too caught up in you work. You will be doing a lot of work over the next 30 days, but stress and freaking out never helped anyone ace a test. Nothing is so important that it should make you miserable, so enjoy and feel pride in each of your accomplishments as we move forward. We’re rooting for you too!
• On that note, stay healthy! Maintain a healthy eating and sleeping schedule. You can study all you want, but if you don’t take care of your body, you will not be doing yourself any favors on test day. A healthy mind remembers things better. Also, if you ever feel yourself getting tired following this study plan, get up and do a couple of quick stretches, or go for a short walk. Your brain will appreciate the extra blood flow.

What You Will Need

• Access to Albert.io’s AP® Calculus AB/BC homepage. The best way to study for the Calculus exam is to practice, practice, and practice. And Albert.io has the questions you need. You will be getting very familiar with these practice questions over the next month.
• A flashcard site such as Quizlet. Or you just use regular notecards. These are going to help you get all of those math terms down, so make sure that you keep on top of your daily flashcards.
• Note taking materials. These can be done on your computer, tablet, etc. but you’re also going to need plenty of paper and countless sharpened pencils. Just like the flashcards, you’re going to be taking a lot of notes and practicing those equations on a daily basis, so make sure that you’re comfortable using whichever version you choose.
• The College Board homepage for Calculus AB and/or BC. Make sure you thoroughly read the AP® Calculus information provided by the College Board’s website. Just like any other exam, it is necessary to understand the expectations of the people testing you.
• Your own Calculus Textbook or an online source of that will provide you with the same amount of detail.

Optional (but helpful) Stuff:

• Any AP-style workbooks or study guides your teacher provides, or any supplemental material you find helps your study of the main materials. As we’ve stated before, the more the merrier when it comes to studying for the AP® exams.
• Albert.io has some excellent recommendations on the how to approach the AP® Calculus AB/BC exams and other great recommendations on readings, study tips, etc. Take a look at everything the site has to offer and make your own decisions on what will work best for you.
• A dictionary, which can be in print or online. Some math concepts get a little tricky, so this might help in the long run.
• You are also going to want a graphing calculator for certain questions. Look at our FRQs for help on which ones to choose.

How to Use the Study Plan

Day 1: Getting Started

Familiarize yourself with the structure of the AP® Calculus AB or BC exam by visiting the College Board’s official course description. Gather your resources: your textbook, a graphing calculator, and reliable online practice (like Albert.io). Organize a notebook or digital document for daily notes, plus a system for flashcards (physical or digital) where you’ll store definitions, formulas, and theorems. Take a quick baseline quiz (such as a few random multiple-choice questions from any past exam or from Albert.io) to assess where you stand. Don’t worry about the score—this is purely to see which areas feel comfortable and which areas need extra focus.

Days 2–4: Unit 1 – Limits and Continuity

Unit 1 Topics to Cover:

• 1.1–1.4: Introducing Calculus, Defining Limits, Estimating Limits from Graphs and Tables
• 1.5–1.9: Algebraic properties for limits, Squeeze Theorem, various approaches to finding limits
• 1.10–1.16: Discontinuities, Continuity at a point and over intervals, IVT, infinite limits, and horizontal/vertical asymptotes

Suggested Daily Breakdown:

Day 2:

Read and take notes on subtopics 1.1–1.4.

• Practice limit questions (e.g., “1.2 | Defining Limits,” “1.3 | Estimating Limit Values from Graphs” on Albert).
• Create flashcards for key limit definitions (e.g., formal definition of a limit, continuity criteria).

Day 3:

Dive into subtopics 1.5–1.9. Focus on algebraic manipulations, Squeeze Theorem, and how to handle tricky limit setups.

• Complete more practice using multiple choice or short free-response regarding limit computation.
• Keep updating flashcards with key theorems (Intermediate Value Theorem, continuity definitions).

Day 4:

Finish subtopics 1.10–1.16, focusing on types of discontinuities, infinite limits, and asymptotes.

• Tackle the “Miscellaneous (AB/BC) | Continuity and Differentiability” free response set.
• Attempt the “AP® Calculus | Unit 1 Assessment” (Part A: No Calculator; then Part B: Calculator Allowed).
• Reflect in your notebook: Which limit techniques feel strongest? Where do you need a refresher?

Days 5–7: Unit 2 – Differentiation: Definition and Fundamental Properties

Unit 2 Topics to Cover:

• 2.1–2.4: Definitions of the derivative at a point, relationship to continuity, average rate of change vs. instantaneous rate of change
• 2.5–2.10: Rules of differentiation (Power Rule, constant multiples, sums, products, quotients, derivatives of sin/cos/exponential/log, trig derivatives)

Suggested Daily Breakdown:

Day 5:

Study subtopics 2.1–2.4. Understand how derivative and continuity intersect, plus best ways to interpret derivative notation.

• Practice short problem sets on the derivative limit definition and reading derivative estimates from data/graphs.

Day 6:

Work through subtopics 2.5–2.7 (Power Rule and derivatives of basic trig/exponential/log).

• Complete practice sets labeled “2.5 | Applying the Power Rule,” “2.7 | Derivatives of cos(x), sin(x), e^x, ln(x)” on Albert.
• Update flashcards with derivative formulas.

Day 7:

Wrap the unit with subtopics 2.8–2.10 (Product Rule, Quotient Rule, derivatives of tangent/cotangent/secant/cosecant).

• Take the “AP® Calculus | Unit 2 Assessment” (Part A: No Calculator, Part B: Calculator).
• Check your work carefully, noting mistakes and creating a “trouble spot” list.

Days 8–10: Unit 3 – Differentiation: Composite, Implicit, and Inverse Functions

Unit 3 Topics to Cover:

• 3.1–3.6: Chain Rule, implicit differentiation, derivatives of inverse functions, inverse trig, higher-order derivatives

Suggested Daily Breakdown:

Day 8:

Learn/review the Chain Rule thoroughly (3.1). Practice with composite functions. Start investigating implicit differentiation (3.2) with example problems that involve xy terms.

Day 9:

Dive into 3.3–3.4: Differentiating inverse functions (including inverse trig).

• Update flashcards with arc-sin, arc-cos, arc-tan derivative formulas.
• Work relevant practice sets on chain rule, implicit derivatives, and inverse derivatives.

Day 10:

Review 3.5–3.6 (selecting derivative procedures and higher-order derivatives).

• Take the “AP® Calculus | Unit 3 Assessment.”
• Review your performance and note anything that felt tricky (like implicit steps or chain rule pitfalls).

Days 11–13: Unit 4 – Contextual Applications of Differentiation

Unit 4 Topics to Cover:

• 4.1–4.7: Interpreting derivative in context (motion, rates of change), related rates, linearization, L’Hôpital’s Rule

Suggested Daily Breakdown:

Day 11:

Cover 4.1–4.3: Derivatives in real-world contexts (position, velocity, acceleration), rates of change in non-motion scenarios.

• Practice “Straight-Line Motion,” focusing on position-velocity-acceleration relationships.
• Do a few free-response questions from “Particle Motion (AB and BC)” to see how these show up in the exam.

Day 12:

Explore 4.4–4.5: Related rates. Work both basic and multi-step problems.

• Practice L’Hôpital’s Rule for indeterminate forms (4.7).
• Make sure to test yourself with short timed practice sets.

Day 13:

Summarize linearization and approximations (4.6)

• Combine it all: “AP® Calculus | Unit 4 Assessment.”
• Revisit additional free-response questions on “Particle Motion” or “Modeling with Rate Functions.”
• Evaluate your weaknesses; schedule extra time if related rates or L’Hôpital still feels shaky.

Days 14–16: Unit 5 – Analytical Applications of Differentiation

Unit 5 Topics to Cover:

• 5.1–5.12: Mean Value Theorem, Extreme Value Theorem, critical points, intervals of increase/decrease, concavity, first and second derivative tests, optimization, implicit expressions.
• Also includes “Comparing and Analyzing f, f’, and f’’” – perfect for second derivative connections.

Suggested Daily Breakdown:

Day 14:

Review 5.1–5.3: Mean Value Theorem, Extreme Value Theorem, identifying critical points.

• Practice short multiple-choice sets (like “Extreme Value Theorem,” “Mean Value Theorem”).

Day 15:

Read through 5.4–5.7: Analyzing concavity and the first/second derivative tests for extrema.

• Incorporate “Comparing and Analyzing f, f’, and f’’” free-response items.
• Sketch graphs from derivative information and vice versa.

Day 16:

Review and practice 5.8–5.12: Optimization problems and exploring implicit relations deeper.

• Complete “AP® Calculus | Unit 5 Assessment.”
• Reflect on how multiple derivatives link to shape and behavior of functions.

Days 17–19: Unit 6 – Integration and Accumulation of Change

Unit 6 Topics to Cover:

• 6.1–6.14: Riemann sums, definite integrals, Fundamental Theorem of Calculus, indefinite integrals (basic rules, substitution, partial fractions, integration by parts for BC), improper integrals
• Include “Charts and Riemann Sums” free-response practice here.

Suggested Daily Breakdown:

Day 17:

Start with 6.1–6.4: Accumulation of change, Riemann sums, understanding the Fundamental Theorem of Calculus.

• Practice “Charts and Riemann Sums” free-response and short multiple-choice.

Day 18:

Next, read through 6.5–6.10: Properties of definite integrals, advanced antiderivative techniques (u-substitution, partial fraction if you’re BC).

• Tackle more problem sets focusing on the variety of integration scenarios.

Day 19:

Wrap up unit 6 with 6.11–6.14: Integration by parts (BC), linear partial fractions (BC), and improper integrals.

• Complete “AP® Calculus | Unit 6 Assessment.”
• Review which integration technique is used when—this is crucial for test day.

Days 20–22: Unit 7 – Differential Equations

Unit 7 Topics to Cover:

• 7.1–7.9: Modeling with differential equations, slope fields, Euler’s method (BC), separation of variables, logistic growth (BC)

Suggested Daily Breakdown:

Day 20:

Start unit 7 with 7.1–7.4: What differential equations are, verifying solutions, slope fields basics.

• Work “Slope Fields and Differential Equations (AB and BC)” free-response examples.

Day 21:

Then, review 7.5–7.7: Euler’s method (BC focus), separation of variables, initial conditions.

• Practice problem sets on separation of variables for typical dy/dx = k×f(y) forms.

Day 22:

Finish with 7.8–7.9: Exponential models, logistic growth for BC.

• Complete “AP® Calculus | Unit 7 Assessment.”
• Revisit slope fields or logistic problems as needed.

Days 23–24: Unit 8 – Applications of Integration

Unit 8 Topics to Cover:

• 8.1–8.13: Average value, displacement/velocity integrals, area between curves, volumes of revolution (disk, washer, cross-sections), arc length (BC)
• Tie in the “Volume and Area” free-response set here.

Suggested Daily Breakdown:

Day 23:

Review 8.1–8.6: Average value of a function, area between curves, including ones that intersect more than twice.

• Practice AB-level volume or area FRQs (like “Volume and Area (AB and BC)”) to strengthen geometry integration.

Day 24:

Read through 8.7–8.13: Cross-sections, disk/washer methods, arc length (BC).

• Take “AP® Calculus | Unit 8 Assessment.”
• Double-check conceptual understanding of rotational solids: set up integrals carefully to avoid sign/limit mistakes.

Days 25–26: Unit 9 – Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC)

Unit 9 Topics to Cover:

• 9.1–9.9: Differentiating parametric equations, polar derivatives, area in polar coordinates, vector-valued functions, motion analysis

Suggested Daily Breakdown:

Day 25:

Review 9.1–9.5: Basic definitions, parametric x(t), y(t), derivative formulas, and second derivatives. Intro to vector-valued function differentiation.

• Practice “Parametric Equations” free-response, focusing on motion problems.

Day 26:

Read through your notes on 9.6–9.9: Integrating vector-valued functions, area in polar form, advanced polar/parametric motion.

• Complete “AP® Calculus | Unit 9 Assessment.”
• Revisit any tricky parametric or polar FRQs to ensure you’re comfortable with setting up integrals and derivatives.

Days 27–28: Unit 10 – Infinite Sequences and Series (BC)

Unit 10 Topics to Cover:

• 10.1–10.15: Convergence/divergence tests, geometric/p-series, comparison tests, alternating series, ratio test, power series, Taylor/Maclaurin expansions, Lagrange error bound
• Include “Convergent and Divergent Functions” and “Taylor Polynomials and Maclaurin Series” free-response here.

Suggested Daily Breakdown:

Day 27:

Start with 10.1–10.9: Fundamentals of convergence, nth term test, integral test, comparison tests, ratio tests, absolute vs. conditional convergence.

• Practice “Convergent and Divergent Functions” FRQs.

Day 28:

Finally, review 10.10–10.15: Taylor polynomials, Lagrange error, radius of convergence, Maclaurin expansions.

• Complete “AP® Calculus | Unit 10 Assessment.”
• Work “Taylor Polynomials and Maclaurin Series” free-response problems.

Day 29: Full AP® Practice Exam #1

Simulate the actual test environment as closely as possible. Gather pencils, a calculator (if allowed), scratch paper, and a timer.

If you’re AB: Use “AP® Calculus AB | Practice Exam #1.” If you’re BC: Use “AP® Calculus BC | Practice Exam #1.”

Stick to the official timing:

• Section 1A (no calculator) → 30 multiple choice in 60 minutes,
• Section 1B (calculator allowed) → 15 multiple choice in 45 minutes,
• Section 2A (calculator allowed) → 2 FRQs in 30 minutes,
• Section 2B (no calculator) → 4 FRQs in 60 minutes.

Score it using the provided keys or guidelines. Note what felt tough or slow—these become your final refreshers tomorrow.

Day 30: Full AP® Practice Exam #2 and Conclusion

Repeat the test simulation with the second full-length exam: “AP® Calculus AB | Practice Exam #2” or “AP® Calculus BC | Practice Exam #2.” Check your results carefully. Compare them with Day 29’s performance. Review any lingering trouble spots, focusing on small clarifications or formula refreshers. As final steps before the real exam, make sure you:

• Gather all materials (calculator, extra batteries, pencils, ID).
• Eat well, drink plenty of water, and get a full night’s rest.

Conclusion

You did it! Awesome job! Don’t stress out. Feel good about your work. And be proud that you made it through our 30-day study guide.

You’re going to want to focus on being prepared for the exam itself. Get your stuff ready. Just like the preparation for your last couple of practice exams, do you have your pencils? Water? Snacks? Calculator? Get all that together the day before the exam, so you’re spending the day thinking only about Calculus.

Probably most important, get your sleep! Don’t throw the last 30 days away by being tired and brain-fogged during the exam.

If you have kept up with this daily study guide, you will have:

• Notes, key terms, and flashcards on the four central themes of AP® Calculus.
• Gained the skills to graphically, numerically, analytically, and verbally explain how calculus works in both theory and in applied mathematical equations.
• Completed a broad range of example Free Response Questions and practiced with hundreds multiple choice questions!
• Applied tried and true test-taking tips to your AP® Calculus study regiment.

If you have any extra time between the end of this 30-day study guide and your actual test, stay on top of our work. You are going to want to go over all of the material provided by Albert.io as often as possible.

Finally, maintain that feeling of confidence. Desire and discipline pave the road to success. The fact that you have shown your dedication and resilience in completing this 30-day study guide shows that you are a strong learner. Work with your strengths and always feel proud!

For information on other AP® exams and the other study guides we offer, head to Albert.io or read more of our other blog posts.

Start your AP® Calculus Prep today

Looking for AP® Calculus practice?

Kickstart your AP® Calculus prep with Albert. Start your AP® exam prep today.