647-568-0258
AP Calculus AB
$999.00
All course prices are in CAD – Canadian Dollars
Course Description For AP Calculus AB
AP Calculus AB is a college-level Advanced Placement course that introduces students to differential and integral calculus. First, students study limits, derivatives, integrals, differential equations, and key uses of calculus. In addition, they use graphs, equations, tables, and math models to solve problems. For example, students use calculus to study rates of change, motion, and areas. They also build strong math and problem-solving skills through regular practice. As a result, students learn to apply calculus ideas with greater confidence. Overall, the course prepares students for the AP Calculus AB Exam and future studies in mathematics, engineering, computer science, economics, and other STEM fields.
Skills You'll Learn
Course Content
| Unit | Title | Expectations Summary | Focus |
|---|---|---|---|
| 1 | Limits and Continuity | First, students study limits as a foundation for calculus. They use tables, graphs, and equations to explore one-sided limits, continuity, breaks in graphs, asymptotes, and the Intermediate Value Theorem. | Limits |
| 2 | Differentiation: Definition and Fundamental Properties | Next, students study derivatives as rates of change and slopes of tangent lines. In addition, they estimate derivatives, use derivative notation, and apply basic derivative rules. | Derivative Foundations |
| 3 | Differentiation: Composite, Implicit, and Inverse Functions | Then, students extend their skills by using the chain rule and implicit differentiation. They also study inverse functions, inverse trigonometric functions, and higher-order derivatives. | Advanced Differentiation |
| 4 | Contextual Applications of Differentiation | For example, students use derivatives to study motion, related rates, local linearity, linearization, and L'Hospital's Rule. They also explain their answers using appropriate units. | Applied Rates |
| 5 | Analytical Applications of Differentiation | In addition, students use derivatives to study how functions behave. They explore extrema, increasing and decreasing intervals, concavity, graphing, optimization, and the Mean Value Theorem. | Function Analysis |
| 6 | Integration and Accumulation of Change | Next, students learn how integration represents accumulation and connects with differentiation. They study Riemann sums, definite integrals, accumulation functions, the Fundamental Theorem of Calculus, antiderivatives, and substitution. | Integration |
| 7 | Differential Equations | Then, students use differential equations to model change. In particular, they study slope fields, separable equations, solutions, and models for exponential growth and decay. | Differential Equations |
| 8 | Applications of Integration | Furthermore, students use definite integrals to solve different types of problems. For example, they study average value, motion, net change, area between curves, cross sections, and volumes of revolution. | Integral Applications |
| Final | AP Review and Calculus Modeling Portfolio | Finally, students complete AP-style multiple-choice and free-response practice. As a result, they review key calculus skills and complete a modeling task using graphs, numbers, equations, and written explanations. | AP Preparation |
Frequently Asked Questions
Replace the first FAQ answer with:
AP Calculus AB is an introductory, college-level calculus course. In particular, students study limits, derivatives, integrals, and the Fundamental Theorem of Calculus. For example, they use these ideas to solve math and real-world problems.
AP Calculus AB is a good choice for students who enjoy math. In particular, it can help students who plan to study engineering, computer science, physics, economics, business, or other STEM fields.
Students build strong math, problem-solving, and communication skills. For example, they learn to explain and support their solutions using graphs, equations, tables, and written explanations.
Students should have a strong foundation in algebra, geometry, trigonometry, analytic geometry, and elementary functions before beginning the course.
The course is usually completed over one academic year. As a result, students have time to build their calculus skills, prepare for the AP Calculus AB Exam, and get ready for college-level calculus.
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