AP Calculus AB
AP Calculus AB
Course Overview:
AP Calculus AB is a college-level course that introduces students to the fundamental concepts of differential and integral calculus. The course emphasizes a multi-representational approach, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Students develop an understanding of the concepts of calculus and experience its methods and applications.(College Board)
Course Content:
The AP Calculus AB curriculum is organized into eight units:
- Limits and Continuity (10%–12%)
- Understanding the behavior of functions as inputs approach certain values.
- Differentiation: Definition and Fundamental Properties (10%–12%)
- Exploring the derivative concept and its foundational rules.
- Differentiation: Composite, Implicit, and Inverse Functions (9%–13%)
- Applying differentiation techniques to complex functions.
- Contextual Applications of Differentiation (10%–15%)
- Using derivatives to solve real-world problems involving rates of change.
- Analytical Applications of Differentiation (15%–18%)
- Analyzing functions for extrema, concavity, and inflection points.
- Integration and Accumulation of Change (17%–20%)
- Understanding antiderivatives and definite integrals as accumulation functions.
- Differential Equations (6%–12%)
- Solving basic differential equations and modeling situations with them.
- Applications of Integration (10%–15%)
- Applying integration techniques to compute areas, volumes, and other quantities.
Exam Structure:
The AP Calculus AB exam assesses students’ understanding through two sections:
- Section I: Multiple Choice (50%)
- 45 questions divided into:
- Part A: 30 questions; 60 minutes (calculator not permitted).
- Part B: 15 questions; 45 minutes (graphing calculator required).
- 45 questions divided into:
- Section II: Free Response (50%)
- 6 questions divided into:
- Part A: 2 questions; 30 minutes (graphing calculator required).
- Part B: 4 questions; 60 minutes (calculator not permitted).
- 6 questions divided into:
Tutoring Services:
To support students in mastering AP Calculus AB, we offer personalized tutoring options:
- Private In-Home Tutoring:
- One-on-one sessions tailored to individual learning styles and schedules.
- Focused instruction on challenging topics and exam strategies.
- Online Tutoring:
- Interactive virtual sessions with experienced tutors.
- Flexible scheduling to accommodate students’ availability.
Program Highlights:
- Comprehensive coverage of all AP Calculus AB topics.
- Emphasis on conceptual understanding and problem-solving skills.
- Practice with real exam questions and mock tests.
- Development of effective study plans and time management strategies.
Getting Started:
Students can begin their tutoring journey at any time. Our programs are customized to fit individual needs, whether aiming for a thorough course review or targeted assistance in specific areas.
For more information or to schedule a free consultation, please contact us.
AP Calculus BC
AP Calculus BC
Course Overview:
AP Calculus BC is a college-level course that extends the content learned in AP Calculus AB to different types of equations and introduces additional topics. It is equivalent to both first and second semester college calculus courses. Students will explore concepts such as parametric, polar, and vector functions, and will be introduced to advanced integration techniques, sequences and series, and differential equations. The course emphasizes a multi-representational approach, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally.(College Board)
Course Content:
The AP Calculus BC curriculum is organized into ten units:
- Limits and Continuity (4%–7%)
- Understanding the behavior of functions as inputs approach certain values.
- Differentiation: Definition and Fundamental Properties (4%–7%)
- Exploring the derivative concept and its foundational rules.(AP Central)
- Differentiation: Composite, Implicit, and Inverse Functions (4%–7%)
- Applying differentiation techniques to complex functions.
- Contextual Applications of Differentiation (6%–9%)
- Using derivatives to solve real-world problems involving rates of change.
- Analytical Applications of Differentiation (10%–15%)
- Analyzing functions for extrema, concavity, and inflection points.
- Integration and Accumulation of Change (17%–20%)
- Understanding antiderivatives and definite integrals as accumulation functions.
- Differential Equations (6%–12%)
- Solving basic differential equations and modeling situations with them.
- Applications of Integration (10%–15%)
- Applying integration techniques to compute areas, volumes, and other quantities.
- Parametric, Polar, and Vector Functions (10%–15%)
- Analyzing and interpreting functions represented in parametric, polar, and vector forms.(College Board)
- Infinite Sequences and Series (17%–18%)
- Exploring convergence and divergence of sequences and series, including Taylor and Maclaurin series.
Exam Structure:
The AP Calculus BC exam assesses students’ understanding through two sections:
- Section I: Multiple Choice (50%)
- 45 questions divided into:
- Part A: 30 questions; 60 minutes (calculator not permitted).
- Part B: 15 questions; 45 minutes (graphing calculator required).
- 45 questions divided into:
- Section II: Free Response (50%)
- 6 questions divided into:
- Part A: 2 questions; 30 minutes (graphing calculator required).
- Part B: 4 questions; 60 minutes (calculator not permitted).
- 6 questions divided into:
Tutoring Services:
To support students in mastering AP Calculus BC, we offer personalized tutoring options:
- Private In-Home Tutoring:
- One-on-one sessions tailored to individual learning styles and schedules.
- Focused instruction on challenging topics and exam strategies.(AP Central, AP Central)
- Online Tutoring:
- Interactive virtual sessions with experienced tutors.
- Flexible scheduling to accommodate students’ availability.
Program Highlights:
- Comprehensive coverage of all AP Calculus BC topics.
- Emphasis on conceptual understanding and problem-solving skills.
- Practice with real exam questions and mock tests.
- Development of effective study plans and time management strategies.
Getting Started:
Students can begin their tutoring journey at any time. Our programs are customized to fit individual needs, whether aiming for a thorough course review or targeted assistance in specific areas.(en.wikipedia.org)
For more information or to schedule a free consultation, please contact us.