AP Courses

AP Calculus AB

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


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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:

Dedicated Test Prep Manager to Oversee Your Program

Physical & Digital Copies of the AP Guru Strategy Guides & Classroom Books

Test Reports With Detailed Analytics

Personalized Lesson Notes And Assignments








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







Live Sessions

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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Our team of teachers boasts the top 1% scores for the sections they teach.

All of our teachers have demonstrated an exceptional ability to convey material in a fun, personalized, and results-driven way.

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

Our programs are one-on-one to ensure each student receives personalized attention.

Amazing Curriculum

Our curriculum includes strategy guides, classroom books, homework sets, and full-length tests.

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

Mentoring & Support

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

Our mentors are someone students can always talk to about anything related to their SAT Prep.

The AP Guru Advantage

Private Tutoring

AP Guru specializes in one-on-one teaching, empowering students with online personalized exam prep

With AP Guru, each student gets...
  • their instructor’s undivided attention and a guided exploration of their subject with both theory and applications taught live in class.
  • 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
  • This subject specialist will convey essential concepts in a clear and easily understandable manner
  • 99th percentile scorer in the subject he or she teaches

Graded Assessments

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

School-Aligned Curriculum

Our comprehensive curriculum is school-aligned and follows the structure of the International Specification (Edexcel / CIE / AQA / OCR) in order to ensure improvement on both internal tests and external exams.

Our curriculum includes...
  • A conceptual foundation of the subject with the help of the latest textbooks, revision guides and workbooks
  • Special focus on school assignments and projects
  • Class notes to help you recall concepts tested on the exam

Practice Papers

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

With AP Guru, you will get...
  • detailed progress reports with feedback and suggestions for improvement
  • video recordings and 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 (IGCSE/ Edexcel / CIE / AQA / OCR)
  • 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

Admission Process

Complete Application

Step 1 of the APGuru process is the application phase. We'll ask for basic information such as your name, contact details, current educational level, and your specific goals or challenges. Once you've filled out the application, your application will be promptly reviewed by our admissions team.

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Step 2 is the trial class, where applicants receive an invitation to experience our teaching methods and interact with instructors. During this session, students engage in discussions, ask questions, and evaluate whether APGuru aligns with their learning preferences and goals, helping them make an informed decision.

Join AP Guru

Step 3 involves officially joining the program after a successful trial class. Students confirm their enrollment, select their desired course or program, and gain access to comprehensive study resources. They begin attending regular classes, receiving guidance from experienced instructors making progress towards academic excellence.

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