AP Courses

AP Calculus AB

AP Calculus AB focuses on topics such as limits, derivatives, and integrals.

90%

of students score

4 and above

78%

students get a top score of

5 in

AP Calculus AB

80%

students showed exceptional
performance in their first semester of

AP Calculus AB

Course Concept

AP Calculus AB is a college-level course that introduces students to the fundamental concepts and techniques of calculus. It is designed to provide a strong foundation in differential and integral calculus, preparing students for further studies in mathematics, engineering, sciences, and other related fields.

The course covers topics such as limits, derivatives, and integrals, focusing on both algebraic and graphical representations. Students learn to analyze functions, determine their rates of change, and calculate areas under curves. They develop skills in solving problems using calculus methods and apply their understanding to real-life situations.

  • Understanding of limits and continuity: Students learn about the concept of limits, which describes the behavior of functions as the input approaches a certain value. They explore the continuity of functions and the relationship between limits and continuity.
  • Differentiation: The course introduces students to the concept of derivative, which measures the rate of change of a function. They learn various differentiation techniques, including the power rule, product rule, chain rule, and implicit differentiation. Students apply derivatives to analyze the behavior of functions, determine critical points, and solve optimization problems.
  • Integration: Students study the concept of integration, which involves finding the area under a curve. They learn different integration techniques, such as the power rule, substitution, and integration by parts. Students apply integration to calculate areas, solve problems involving accumulation, and find the antiderivative of functions.
  • Applications of calculus: Calculus AB emphasizes the application of calculus in various contexts. Students solve real-world problems involving rates of change, optimization, and area calculations. They also analyze the behavior of functions using calculus concepts and techniques.
  • Mathematical reasoning and communication: Students develop skills in mathematical reasoning and communication. They learn to justify mathematical statements, explain their problem-solving strategies, and effectively communicate their solutions using mathematical language, symbols, and notation.
  • Graphical representation: The course emphasizes graphical representations of functions and their derivatives. Students learn to interpret and analyze graphs, identify key features such as extrema and inflection points, and make connections between the graphical and algebraic representations of functions.

AP Calculus AB

Course Details:

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Syllabus

Best-in-class content by leading faculty and industry leaders in the form of videos, cases and projects, assignments and live sessions

COURSE SYLLABUS PDF
1. Limits and Continuity
  • Concept of Instantaneous rate of change 
  • Understanding the Limit 
  • Proper Limits 
  • Finding Limits Analytically 
  • Limits of transcendental functions 
  • Limits and Continuity 
  • Infinite Limits and Limits at Infinity 
  • Intermediate Value Theorem
2. Differentiation - Basic Derivative Rules
  • Rate of change and tangent line 
  • Tangent line and the derivatives 
  • Understanding the Derivatives 
  • Differentiability and Continuity 
  • Basic Differentiation  Rule 
  • The Product and Quotient Rule 
  • Velocity and Other Rate of Change
3. Differentiation - Part 2 Composite Implicit and Inverse Functions
  • The Chain Rule 
  • Differentiation from Tables and Symbolically 
  • Implicit Differentiation 
  • Inverse Functions 
  • Derivatives of Inverse Trigonometric Functions
4. Contextual Applications of Differentiations
  • The Interpretation of the Derivative 
  • Straight Line Motion- Connecting Position Velocity and Acceleration 
  • Rate of change in other application 
  • Related rates 
  • Local Linearity 
  • L' Hospital's Rule 
  • Indeterminate Form
5. Analytic Applications of Differentiations
  • Mean Value Theorem 
  • Extrema  on an Interval 
  • First Derivative Test 
  • Curve Sketching 
  • Optimization
6. Integration - Accumulation of Change
  • Approximating Area with Riemann Sums 
  • Sigma Notation and Riemann Sums '
  • Accumulation Functions 
  • Properties of Definite Integrals 
  • Antiderivatives and Indefinite Integrals 
  • Fundamental theorem of Calculus 
  • Integration by Substitution 
  • Integration of Transcendental Functions
7. Differential Equations
  • Introduction to Differential Equations
  • Slope Fields 
  • Separation of variables 
  • Differential Equations Growth and decay
8. Applications of Integration
  • Finding Average value of Integrals 
  • Another Look at Particle Motion 
  • Accumulation Functions In context 
  • Area Between Two curves 
  • Volumes By Cross Sections
  • Volumes by Disc and Washer Methods
  • Volume About a Line 

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AP Guru offers highly customised and personalised SAT Prep delivered live online.

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  • expert guidance at every step that involves interactive sessions, class notes, worksheets, class recordings, and access to past papers.
  • specialist subject tutors who have graduated from top universities with a passion for teaching and a dedicated program manager to track your progress.

Experienced Tutors

Our team of teachers boast top 1% scores for the subjects they teach. All of our teachers have demonstrated an exceptional ability to convey material in a fun, personalized, and results-driven way.

With AP Guru, each student gets...
  • an experienced and certified online tutor
  • a subject specialist that will convey essential concepts in a clear and easily understandable manner
  • a teacher who is 99th percentile scorer in the subject he or she teaches

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Between each class, you'll get personalized assignments so you master what you learned

With AP Guru, you will get...
  • Topic-wise worksheets and graded assessments (with marking schemes) to ensure mastery of each topic tested on the school exams
  • Doubt sessions after every couple of classes to review incorrect questions
  • Additional worksheets on topic areas of concern

Practice Papers

Practice for the exam with our library of Topic-wise Tests and Past Papers.

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  • detailed progress reports
  • study materials for easy revision
  • full-length mock papers, graded as per the grade boundaries and marking schemes.

Mentoring & Support

At AP Guru, we pair you with an experienced mentor to guide you through the exam prep process.

With AP Guru, you will get...
  • a Program Manager to help you at every step
  • dedicated support to resolve doubts, convenient class schedules and reminders for important sessions
  • Parents Teacher Meetings - We set up monthly parent teacher meetings for your to interact with the tutors

Grade Improvement: Exam Ready

The AP Guru course ensures that each student is exam ready regardless of the initial academic level at which they stand.

Exam Ready
  • Track your progress including topic, class and homework discussion
  • 10 Months of exhaustive exam prep to get you ready
  • Last 2 months of Exam Improvement Pointers and Strategies for writing high-scoring answers.
One-to-One Classes

AP Guru offers highly customised and personalised SAT Prep delivered live online

Experienced Tutor

You will be paired with an experienced English and an experienced Math Tutor

Targeted Assessments

Between each class, you'll get personalized assignments so you master what you learned

Test Prep Manager

All of our students are paired with an experienced mentor to guide the student through his or her prep

Doubt Classes

We will conduct regular one-on-one feedback and doubt classes to go through your errors in mock tests and weekly assessments

Mock Tests

We offer more than 30 full length tests for our programs to our students with detailed explanations. 

Test Analytics

For each test you take, you will receive detailed reports of your performance as well as question explanations

Study Plan

The program manager will set test schedules, create reminders, set up doubt sessions, etc.

Strategy Guides

Our AP Guru SAT Strategy Guides cover every concept and strategy tested on the SAT

Weekly Progress Reports

Our curriculum is written by our tutors and founders based on their years of teaching experience.

Web Portal

The AP Guru online portal contain 100+ hours of SAT content - detailed lesson notes, and additional practice

Parent Teacher Meetings

Parents Teacher Meeting - We set up monthly parent teacher meetings for your to interact with the tutors

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FAQs

Frequently Asked Questions

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    We conduct our programs online.

    Is this a live class? Will it be a group or private class?
    All our classes are live instructor lead classes. All our academic tutoring are only one-on-one.

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    All our classes are live instructor lead classes. All our academic tutoring are only one-on-one.

  • When is the best time to get started?
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    The earlier the better! When students come to us right before it is time to apply to college, there is only so much we can do. We can certainly help these students with score improvements and craft as compelling an application as possible, but we are given experiences and data points that cannot be altered.

    When students come to us early in their educational careers, we pair them with a counselor to help them develop as applicants, students, and people early on. We help students strategize early, build their profiles, and stand out from their peers. We help students explore and develop their academic interests, engage in unique and meaningful extracurricular activities, strengthen their personal qualities and leadership skills, and ultimately, position them to get into the best schools possible.

    It takes A LOT of hard work, strategy, determination, and self-reflection to get into the school of your dreams. At AP Guru, we are here, every step of the way, to help you get there.

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    No. We know that each student is different and has unique goals and aspirations. Our focus is to help each student excel in the tests and exams they are preparing towards.

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    In terms of academic scores, for students not already at the top of the range, we typically want to see at least a 20 percentile rank improvement (the actual raw score this translates to varies across the scale). Going from the 50th to 70th percentile or from the 70th to 90th typically opens up a whole new range of schools for students.