AP Calculus AB
Welcome to AP Calculus AB at Summit College Preparatory. This is a rigorous, college-level mathematics course aligned with the College Board framework. It prepares students to explore the foundational principles of calculus, develop conceptual understanding, and apply mathematical models to real-world and theoretical problems.
Course Overview
AP Calculus AB is designed for advanced high school students in 11th or 12th grade who have successfully completed Pre-Calculus or an equivalent course. The curriculum emphasizes both differential and integral calculus, focusing on concepts, procedures, and applications. Students engage with limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. The course includes real-world problem solving, graphical interpretation, and analytical reasoning.
College Board Units (8 Units)
| Unit | Title | Core Topics |
|---|---|---|
| Unit 1 | Limits and Continuity | Understanding limits graphically, numerically, and algebraically; continuity and asymptotic behavior |
| Unit 2 | Differentiation: Definition and Fundamental Properties | Derivatives from first principles, interpreting the derivative, basic rules of differentiation |
| Unit 3 | Differentiation: Composite, Implicit, and Inverse Functions | Chain rule, implicit differentiation, inverse functions |
| Unit 4 | Contextual Applications of Differentiation | Motion, related rates, optimization, graphing with derivatives |
| Unit 5 | Analytical Applications of Differentiation | Mean Value Theorem, extrema, concavity, curve sketching |
| Unit 6 | Integration and Accumulation of Change | Definite and indefinite integrals, Riemann sums, Fundamental Theorem of Calculus |
| Unit 7 | Differential Equations | Separation of variables, slope fields, modeling with differential equations |
| Unit 8 | Applications of Integration | Area between curves, volume of solids of revolution |
Learning Outcomes by Quarter (34 Weeks)
- Quarter 1: Understand limits, continuity, and foundational derivative rules (Units 1–2).
- Quarter 2: Apply derivative techniques, use implicit differentiation, solve real-world rate problems (Units 3–4).
- Quarter 3: Analyze function behavior using derivatives, solve optimization and related problems, explore integrals (Units 5–6).
- Quarter 4: Solve differential equations, apply integration to area/volume, and review for the AP exam (Units 7–8).
Instructional Methods
Students participate in lectures, exploratory labs, AP-style problem sets, collaborative group work, and digital simulations. Instruction blends conceptual understanding with procedural fluency and encourages mathematical communication. Practice includes both calculator and non-calculator approaches.
Assessment and Grading
| Category | Weight |
|---|---|
| AP Practice Tests and FRQs | 35% |
| Homework and Problem Sets | 20% |
| Projects and Labs | 15% |
| Quizzes | 15% |
| Participation & Collaboration | 15% |
College Board – SAT/AP Crosswalk
| Domain | Calculus AB Connection |
|---|---|
| Problem Solving and Data Analysis | Modeling real-world change with calculus |
| Algebra and Functions | Functions, graph behavior, and algebraic manipulation |
| Passport to Advanced Math | Justifying procedures, analyzing models, working with expressions and equations |
Academic Vocabulary Matrix
| Category | Key Terms | Use |
|---|---|---|
| Limits | Limit, Continuity, Asymptote | Understanding behavior of functions |
| Differentiation | Derivative, Chain Rule, Implicit | Analyzing change and slope |
| Integration | Definite Integral, Riemann Sum, FTC | Accumulation and area |
| Applications | Optimization, Related Rates, Volumes | Real-world problem solving |