AP Calculus AB
AP Calculus AB focuses on topics such as limits, derivatives, and integrals.
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students get a top score of 7 in
AP Courses
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students showed exceptional
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AP Courses
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 PDF18
Months
108
Assignments
18
Live Sessions
2
Hours
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1
Assignment
- 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
5
Hours
1
Assignment
- 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
1
Hours
1
Assignment
- The Chain Rule
- Differentiation from Tables and Symbolically
- Implicit Differentiation
- Inverse Functions
- Derivatives of Inverse Trigonometric Functions
3
Hours
1
Assignment
- 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
1
Hours
1
Assignment
- Mean Value Theorem
- Extrema on an Interval
- First Derivative Test
- Curve Sketching
- Optimization
4
Hours
1
Assignment
- 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
1
Hours
1
Assignment
- Introduction to Differential Equations
- Slope Fields
- Separation of variables
- Differential Equations Growth and decay
2
Hours
1
Assignment
- 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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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...
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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...
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Test Prep Manager
All of our students are paired with an experienced mentor to guide the student through his or her prep
Doubt Classes
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Mock Tests
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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.
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, click the submit button. Your application will be promptly reviewed by our admissions team.
Take a Trial Class
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 of the APGuru process 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, and tracking their progress towards academic excellence.
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