AP Calculus AB
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Calculus AB – Master the Mathematics of Change
Build Your Foundations in Differential and Integral Calculus
Calculus AB is where algebra, geometry, and trigonometry come together to help you understand
how things change—instantaneous rates, area under curves, and everything in between. At Guru
Tutorials, our Calculus AB course breaks down these big ideas into clear, logical steps. You’ll
learn not just how to compute derivatives and integrals, but why the Fundamental Theorem of
Calculus connects them so powerfully.
Why Choose Calculus AB with Guru Tutorials?
Concept-Driven Learning
We go beyond rote formulas—every rule and procedure is motivated by real problems
(motion, optimization, area).
Small-Group, Live Instruction
Capped at 8–10 students on Zoom, ensuring you get personalized feedback and plenty of
problem-solving practice.
AP-Aligned Curriculum
Tailored to the College Board framework: limits, continuity, derivatives, applications,
integrals, and differential equations.
Frequent Checks & Support
Weekly quizzes and on-demand help sessions keep you on track and exam-ready.
Real-World Applications
From physics to economics, see how calculus models anything that moves or grows.
What You’ll Learn in Calculus AB
Course aligned to the College Board AP® Calculus AB framework
Limits & Continuity
• Formal definition of a limit (graphical, numerical, analytical) • Continuity at a point and over an interval • Asymptotes and infinite limits • Intermediate Value Theorem
Differentiation: Definition & Fundamental Properties
• Derivative as a limit (difference quotient) • Basic derivative rules (power, constant, sum, difference) • Derivatives of sine, cosine, exponential, and logarithmic functions
Differentiation: Composite, Implicit & Inverse Functions
• Chain Rule for composite functions
• Implicit differentiation
• Derivatives of inverse and inverse trigonometric functions
Contextual Applications of Differentiation
• Interpreting the derivative as a rate of change
• Motion along a line (position, velocity, acceleration)
• Related rates problems
• Linear approximation & L’Hôpital’s Rule for indeterminate forms
Analytical Applications of Differentiation
• Mean Value Theorem & Extreme Value Theorem
• First and second derivative tests for extrema
• Sketching curves using f, f′, and f″
• Optimization problems in context
Integration & Accumulation of Change
• Riemann sums and definite integral notation • Fundamental Theorem of Calculus (parts 1 & 2) • Properties of integrals; substitution method • Antiderivatives and indefinite integrals
Differential Equations
• Modeling with separable differential equations • Slope fields and Euler’s method • Exponential growth & decay applications
Applications of Integration
• Average value of a function • Areas between curves • Volumes of solids of revolution (disks and washers) • Net change and accumulated change interpretations
Course Format
- Duration: Weekly 90-minute live Zoom sessions
- Practice: Homework, quizzes, and AP-style free-response questions
- Extras: Unlimited extra-help office hours included
- Class Size: Maximum 10 students for individualized attention
First two sessions free (no obligation)
The course begins with a free trial (first two sessions) and run in small, interactive classes designed to build mastery, confidence, and top AP scores. Ready to go beyond the basics? Enroll now in Calculus BC—spaces fill quickly!
Call Rajesh at
443-863-0752
rajesh@gurututorial.com
Testimonials
Available Online
Yes
Hours of Classes
42
Level
Advanced
Certificate
Yes
Lifetime Access
Yes
Duration (Days)
120
Community Access
Yes