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AP Calculus include two parts, AP Calculus AB and AP Calculus BC. AP Calculus AB is traditionally taken after precalculus. AP Calculus BC is a full-year course in the calculus of functions of a single variable. It includes all topics covered in Calculus AB plus additional topics, such as parametric, polar, vector functions, and series.
AP Calculus AB/BC – Key Exam Details
The AP Calculus AB and BC exams both consist of two 1-hour 45-minute sections (3 hours 15 minutes total):
- Section I: 45 multiple-choice questions (50% of score)
- Section II: 6 free-response questions (50% of score)
Core Topics (AB & BC):
- Limits & Continuity: Evaluate limits algebraically and graphically
- Differentiation: Rules, applications (rates, optimization), and implicit differentiation
- Integration: Definite/indefinite integrals, FTC, u-substitution
- Applications: Area/volume, particle motion, differential equations (AB: basic; BC: advanced)
BC-Only Topics:
- Series: Convergence tests, Taylor/Maclaurin series
- Parametric/Polar: Derivatives and integrals
- Vector-Valued Functions: Derivatives and motion analysis
Exam Tips:
- MCQ Strategy:
- AB: Focus on derivative/integral applications (60% of exam)
- BC: Master series (25-30% of exam)
- FRQ Strategy:
- Show all steps (even if messy)—partial credit saves scores!
- Label answers clearly (e.g., "Part (a):")
AP Calculus AB/BC Key Formulas to Know (Not on Formula Sheet)
1. Differentiation
- ln(u):
d/dx[ln(u)] = u'/u
- aᵘ:
d/dx[aᵘ] = aᵘ · ln(a) · u'
- arctan(u):
d/dx[arctan(u)] = u'/(1 + u²)
- arcsin(u):
d/dx[arcsin(u)] = u'/√(1 - u²)
2. Integration
- tan(x):
∫tan(x) dx = -ln|cos(x)| + C
- sec(x):
∫sec(x) dx = ln|sec(x) + tan(x)| + C
- By Parts:
∫u dv = uv - ∫v du
3. Series (BC Only)
- Taylor Series:
∑[fⁿ(a)/n!] (x-a)ⁿ
- eˣ:
eˣ = 1 + x + x²/2! + x³/3! + ...
- sin(x):
sin(x) = x - x³/3! + x⁵/5! - ...
- Lagrange Error:
|Rₙ(x)| ≤ M|x-a|ⁿ⁺¹/(n+1)!
4. Polar/Parametric (BC Only)
- Polar Area:
A = ½∫r² dθ
- Parametric Derivative:
dy/dx = (dy/dt)/(dx/dt)
5. Miscellaneous
- Average Value:
1/(b-a) ∫f(x) dx
- Logistic Growth:
dP/dt = kP(1 - P/L)
- Arc Length:
L = ∫√(1 + (dy/dx)²) dx
AP Calculus AB Syllabus
AP Calculus AB Syllabus
AP Calculus AB Syllabus
AP Calculus BC Syllabus
AP Calculus BC Syllabus
Exam Schedule and Fees
AP exams are held in April each year. For the next exam schedule and the associated fees, please visit at:
Exam Calendar and Fees.
Exam Enrollment
The registration procedures depends on if your school offers AP courses or not, or if you enroll as an international student. Follow the guidelines at:
Registering for Exam.
Online Math Tutoring
If you are looking for online Calculus or other Math related tutoring, please send a message at Contact.
AP Calculus AB 2019 Free Response Questions.
AP Calculus AB 2018 Free Response Questions.
AP Calculus AB 2017 Free Response Questions.
AP Calculus AB 2016 Free Response Questions .
AP Calculus AB 2015 Free Response Questions .
AP Calculus AB 2014 Free Response Questions .
AP Calculus AB 2013 Free Response Questions .
AP Calculus AB Practice Exam from 2015 administration.
AP Calculus BC Practice Exam from 2016 administration .
AP Calculus BC Practice Exam from 2015 administration.
AP Calculus Problem Book.
AP Calculus AB Study Guide .
AP Calculus BC Parametric, Polar, Vector Test.
AP Calculus AB & BC Final Notes.