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AP Calculus AB

AP Calculus AB – Summit College Preparatory

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)

UnitTitleCore Topics
Unit 1Limits and ContinuityUnderstanding limits graphically, numerically, and algebraically; continuity and asymptotic behavior
Unit 2Differentiation: Definition and Fundamental PropertiesDerivatives from first principles, interpreting the derivative, basic rules of differentiation
Unit 3Differentiation: Composite, Implicit, and Inverse FunctionsChain rule, implicit differentiation, inverse functions
Unit 4Contextual Applications of DifferentiationMotion, related rates, optimization, graphing with derivatives
Unit 5Analytical Applications of DifferentiationMean Value Theorem, extrema, concavity, curve sketching
Unit 6Integration and Accumulation of ChangeDefinite and indefinite integrals, Riemann sums, Fundamental Theorem of Calculus
Unit 7Differential EquationsSeparation of variables, slope fields, modeling with differential equations
Unit 8Applications of IntegrationArea 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

CategoryWeight
AP Practice Tests and FRQs35%
Homework and Problem Sets20%
Projects and Labs15%
Quizzes15%
Participation & Collaboration15%

College Board – SAT/AP Crosswalk

DomainCalculus AB Connection
Problem Solving and Data AnalysisModeling real-world change with calculus
Algebra and FunctionsFunctions, graph behavior, and algebraic manipulation
Passport to Advanced MathJustifying procedures, analyzing models, working with expressions and equations

Academic Vocabulary Matrix

CategoryKey TermsUse
LimitsLimit, Continuity, AsymptoteUnderstanding behavior of functions
DifferentiationDerivative, Chain Rule, ImplicitAnalyzing change and slope
IntegrationDefinite Integral, Riemann Sum, FTCAccumulation and area
ApplicationsOptimization, Related Rates, VolumesReal-world problem solving