AP Calculus AB
Our AP Calculus AB course covers all eight units: limits and continuity, differentiation definitions and rules, composite, implicit and inverse functions, contextual applications of differentiation, analytical applications, integration and accumulation of change, differential equations, and applications of integration. You practise both calculator and non-calculator sections. Lessons are live and one-to-one with a verified tutor, who uses College Board style multiple-choice and free-response questions and scores practice answers against the published rubrics. Suitable for students in the US and at international schools sitting the May exams.
Reviewed by M. Wazid, Master's in Mathematics, Jamia Millia IslamiaLast updated
$14 – $42
per hour
Free demo class · pay only if you continue
What you will learn
Learning outcomes
- Evaluate limits and analyze continuity
- Apply derivative rules accurately
- Interpret derivatives graphically and contextually
- Solve related rates problems
- Analyze functions using derivatives
- Solve optimization problems
- Evaluate definite and indefinite integrals
- Apply the Fundamental Theorem of Calculus
- Use integration techniques
- Solve separable differential equations
- Apply integrals to area and volume problems
- Analyze slope fields
- Interpret accumulation functions
- Solve AP-style free-response questions
- Prepare effectively for the AP Calculus AB exam
Prerequisites
- Algebra
- Geometry
- Trigonometry
- Functions and graphs
- Exponential and logarithmic functions
- Polynomial and rational functions
- Precalculus
- Basic mathematical modeling
Tags
Course structure
Syllabus(8 modules)
- Introducing Calculus
- Defining Limits and Limit Notation
- Estimating Limits from Graphs
- Estimating Limits from Tables
- Determining Limits Using Algebraic Properties
- Limits Using Algebraic Manipulation
- Squeeze Theorem
- Types of Discontinuities
- Continuity at a Point
- Continuity over an Interval
- Removing Discontinuities
- Infinite Limits and Vertical Asymptotes
- Limits at Infinity and Horizontal Asymptotes
- Intermediate Value Theorem
What is AP Calculus AB?
In short: this course gives one-to-one online tutoring for AP Calculus AB. A verified maths tutor teaches limits, derivatives, integrals and differential equations, calculator and non-calculator technique, and free-response justification, using College Board-style practice.
AP Calculus AB is a College Board Advanced Placement course equivalent to a first-semester college calculus course, covering limits, derivatives, integrals and differential equations. The AP exam is taken in May and scored 1 to 5, and many colleges award credit or placement for a qualifying score.
This course covers all eight AB units one to one with a verified calculus tutor.
Official specification: AP Calculus AB exam (College Board).
For wider support, see our maths tutoring page, or the AP Calculus BC course if you are ready for series and parametric topics.
What is the AP Calculus AB exam format?
The AP Calculus AB exam is a hybrid digital exam lasting 3 hours 10 minutes: you answer multiple-choice questions in the Bluebook app and handwrite free-response answers in a paper booklet. Calculators are permitted. You can't take both AP Calculus AB and BC in the same year.
| Section | Questions | Time | Weighting |
|---|---|---|---|
| I: Multiple choice | 42 | 1 hour 40 minutes | 50% |
| II: Free response | 6 | 1 hour 30 minutes | 50% |
AP exams are scored on a 1 to 5 scale. Exam details from AP Students (College Board).
Which units does AP Calculus AB cover?
| Unit | Topic |
|---|---|
| 1 | Limits and continuity |
| 2 | Differentiation: definition and fundamental properties |
| 3 | Differentiation: composite, implicit and inverse functions |
| 4 | Contextual applications of differentiation |
| 5 | Analytical applications of differentiation |
| 6 | Integration and accumulation of change |
| 7 | Differential equations |
| 8 | Applications of integration |
How do you answer AP Calculus free-response questions?
Free-response questions reward clear reasoning as much as the answer.
- Show the set-up: the derivative or integral you are evaluating.
- Use correct notation, including units in context.
- Justify conclusions with theorems such as the Mean Value Theorem or the first derivative test.
- Write answers in context, such as rate of change per hour.
- Don't round intermediate values; give three decimal places where required.
What does a worked AP Calculus AB question look like?
Here is a typical question: find and classify the critical points of f(x) = x³ − 6x² + 9x.
| Step | Working |
|---|---|
| Derivative | f′(x) = 3x² − 12x + 9 = 3(x − 1)(x − 3) |
| Critical points | x = 1 and x = 3 |
| Second derivative | f″(x) = 6x − 12 |
| Classify | f″(1) = −6 < 0: local maximum; f″(3) = 6 > 0: local minimum |
Where do students lose marks in AP Calculus AB?
Students most often lose free-response points by not answering exactly what the task verb asks, skipping units or justification, leaving work unlabelled and running out of time on long questions.
| Mark-loser | What to do instead |
|---|---|
| Ignoring the task verb | Answer exactly what "justify", "explain" or "calculate" asks |
| Missing units or justification | Show units and reasoning for every answer |
| Unlabelled work | Label graphs, diagrams and steps |
| Time pressure | Practise timed free-response sets |
| Guessing patterns in multiple choice | Eliminate options using reasoning |
AB or BC: which should I take?
AB covers Units 1 to 8. BC covers the same content plus Units 9 and 10 (parametric, polar and vector functions, and infinite series), so it moves faster. Choose BC if you are confident with precalculus and want the full two-semester equivalent; see our AP Calculus BC course.
How the lessons work
Lessons are live and one to one on video with a shared whiteboard. Your tutor uses released College Board free-response questions and scoring guidelines. See also A-Level Mathematics and our Mathematics subject page.
AP Calculus AB tutor online: who this course is for, prerequisites and study plan
An AP Calculus AB tutor online gives you live 1-to-1 lessons on limits, derivatives and integrals, with multiple-choice and free-response practice for the exam.
This course suits high school students taking AP Calculus AB at school or self-studying, in the US and abroad.
Prerequisites: algebra, geometry, trigonometry, functions and graphs, and precalculus.
Course length: 55 one-hour lessons across 8 units.
| Stage | Topics | What you can do afterwards |
|---|---|---|
| 1 | Limits and continuity | Evaluate limits and test continuity |
| 2 | Differentiation: definition, rules, composite, implicit and inverse functions | Differentiate any standard function |
| 3 | Contextual and analytical applications of differentiation | Solve rates and optimisation problems |
| 4 | Integration; differential equations; applications of integration | Integrate and find areas and volumes |
Where it leads: see the AP Calculus BC course if you are moving on, or our maths tutoring page.
AP Calculus AB: frequently asked questions
How long is the AP Calculus AB exam?
3 hours 10 minutes: 42 multiple-choice and 6 free-response questions.
Is a calculator allowed on AP Calculus AB?
Calculators are permitted for the exam; check the College Board AP Calculus exam page and calculator policy for exactly where they can be used.
How is AP Calculus AB scored?
On a scale of 1 to 5.
When is the AP Calculus AB exam?
In May each year.
What is the hardest AP Calculus AB unit?
Many students find applications of differentiation and integration, and related rates, the hardest.
Do I need to justify answers?
Yes. Free-response questions often require justification using calculus theorems.
How do I get a 5 in AP Calculus AB?
Master the core techniques, practise released free-response questions and learn from scoring guidelines.
Do you use College Board materials?
Yes. Tutors use released free-response questions and scoring guidelines. FLN Tutors is not affiliated with the College Board.
How much does an AP Calculus tutor cost?
The price depends on the tutor and session length. You see the hourly rate before booking, with no subscription.
Can I study online from any country?
Yes. Lessons are online and scheduled around your time zone.
How many multiple-choice questions are on the AP Calculus AB exam?
42 questions, worth 50% of the score.
How many free-response questions are there?
6 questions, worth 50% of the score.
Is the AP Calculus AB exam digital?
It is a hybrid digital exam: multiple choice in the Bluebook app and handwritten free-response answers in a paper booklet.
Is AP Calculus AB hard?
AP Calculus AB is challenging but very manageable for students with solid algebra and precalculus skills. Most difficulty comes from applying derivatives and integrals in context and justifying answers clearly in free-response questions. Regular practice with released free-response questions and careful feedback on reasoning make a 4 or 5 realistic.
Is AP Calculus AB or BC harder?
AP Calculus BC is harder because it covers all of AB plus further topics such as series, parametric and polar functions, and more integration techniques, at a faster pace. AB suits most students taking calculus for the first time. Strong students with good algebra often take BC directly, and BC exams also report an AB subscore.
Do you offer lessons in my time zone?
Yes. Lessons are online, so you can book times that suit your time zone.
Can I take AP Calculus AB and BC in the same year?
No. College Board does not allow both exams in the same year.
How do I classify critical points?
Use the sign change of f′ or the second derivative: negative means a maximum, positive a minimum.
What do I need to justify in AP Calculus free response?
State the theorem or reasoning, such as a sign change of f′, not just the answer.
Where can I find AP Calculus AB past exam questions?
College Board publishes past AP Calculus AB free-response questions with scoring guidelines on its AP Central website. Work through them under timed conditions, then mark your answers with the guidelines. Your tutor uses the results to choose which units to revisit before the exam.
Can I get an AP Calculus AB tutor online?
Yes. You can learn with a 1-to-1 AP Calculus AB tutor online through live video lessons from any country. Your tutor explains each unit step by step, shows you how to justify free-response answers and practises calculator and non-calculator questions under exam timing.
Keep learning
Related courses
Student reviews
What students say about AP Calculus AB
Used FLN Tutors? Be one of the first to share how it went, in writing or in a short video.
Money-Back Guarantee
Full refund if we miss the agreed deadline, can't find a suitable expert, or major errors can't be fixed by revision.
Learn more →100% Confidential
Your identity, order details and institution are never shared with any third party.
Learn more →Deadline-Backed Delivery
Every order has an agreed deadline. If we don't deliver by it, you can claim a full refund.
Learn more →Get started today
Ready to get expert help?
Tell us what you need and get matched with a tutor who teaches your subject. Delivered on time, every time.