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Geometry+
Primary Math - Reasoning | Cogat+
Pre-Elementary+
Aos-Aet-Acl-Tj Prep+
Algebra+
Computer Science+
College Board+
Sat (Scholastic Assessment Test)+
Math Contests | Sols+
Acsl (American Computer Science League)+
Course TOCCourse DescriptionCourse Slider
1. Limits and Continuity
A. How limits help us to handle change at an instant
B. Definition and properties of limits in various representations
C. Definitions of continuity of a function at a point and over a domain
D. Asymptotes and limits at infinity
E. Reasoning using the Squeeze theorem and the Intermediate Value Theorem
2. Differentiation- Definition and Fundamental Properties
A. Defining the derivative of a function at a point and as a function
B. Connecting differentiability and continuity
C. Determining derivatives for elementary functions
D. Applying differentiation rules
3. Differentiation- Composite, Implicit, and Inverse Functions
A. The chain rule for differentiating composite functions functions
B. Implicit differentiation
C. Differentiation of general and particular inverse functions
D. Determining higher-order derivatives of functions
4. Contextual Applications of Differentiation
A. Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change
B. Applying understandings of differentiation to problems involving motion
C. Generalizing understandings of motion problems to other situations involving rates of change
D. Solving related rates problems
E. Local linearity and approximation
5. Analytical Applications of Differentiation
A. Mean Value Theorem and Extreme Value Theorem
B. Derivatives and properties of functions
C. How to use the first derivative test, second derivative test, and candidates test
D. Sketching graphs of functions and their derivatives
E. How to solve optimization problems
F. Behaviors of Implicit relations
6. Integration and Accumulation of Change
A. Using definite integrals to determine accumulated change over an interval
B. Approximating integrals using Riemann Sums
C. Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
D. Antiderivatives and indefinite integrals
E. Properties of integrals and integration techniques
7. Differential Equations
A. Sketching slope fields and families of solution curves
B. Solving separable differential equations to find general and particular solutions
C. Deriving and applying a model for exponential growth and decay
8. Applications of Integration
A. Determining the average value of a function using definite integrals
B. Modeling particle motion
C. Solving accumulation problems
D. Finding the area between curves
E. Determining volume with cross-sections, the disc method, and the washer method