Advanced Placements Mathematics

Course details

An accelerated AP Mathematics course that focuses on core concepts, foundational skills, and exam preparation. This outline covers essential topics in either AP Calculus AB or AP Statistics, condensed for a quicker pace. Each session is 2 hours long, totalling 20 sessions.
 


Part 1: Foundations and Core Concepts (12 Hours)
Session 1: Introduction and Essential Skills Review

• Core Algebra and Functions Review
• Understanding Functions and Graphs
• Key Trigonometric Identities (for Calculus)

 
Session 2: Limits and Continuity

• Introduction to Limits and Notation
• Calculating Limits: Analytical and Graphical Approaches
• Continuity and Types of Discontinuities

 
Session 3: Derivatives (AP Calculus) or Descriptive Statistics (AP Stats)

• Calculus: Definition of Derivatives, Power Rule
• Statistics: Summarizing Data, Measures of Central Tendency and Spread

 
Session 4: Derivative Applications or Probability Basics

• Calculus: Differentiation Rules (Product, Quotient, Chain)
• Statistics: Probability Rules, Conditional Probability

 
Session 5: Integrals (AP Calculus) or Probability Distributions (AP Stats)

• Calculus: Antiderivatives, Basic Integration Rules
• Statistics: Binomial and Normal Distributions, Expected Value

 


Part 2: Applications and Advanced Topics (14 Hours)
Session 6: Applications of Derivatives or Sampling Distributions

• Calculus: Optimization, Related Rates
• Statistics: Central Limit Theorem, Sampling Distributions

 
Session 7: Fundamental Theorem of Calculus / Hypothesis Testing Basics

• Calculus: Connecting Derivatives and Integrals, Basic Applications
• Statistics: Introduction to Hypothesis Testing, z-scores, and p-values

 
Session 8: Advanced Integration Techniques or Confidence Intervals

• Calculus: Definite Integrals, Area Under Curves
• Statistics: Confidence Intervals for Proportions and Means

 
 
Session 9: Applications of Integrals or Inference Testing for Proportions

• Calculus: Volume of Solids of Revolution
• Statistics: 1-Sample and 2-Sample Proportion Testing

 
Session 10: Sequences & Series (BC) or Regression Analysis

• Calculus (BC Only): Intro to Sequences, Series, Convergence
• Statistics: Linear Regression, Correlation, Residual Analysis

Part 3: Review and Exam Preparation (14 Hours)
Session 11: AP Exam Structure and Strategies

• Understanding AP Exam Format and Scoring
• Time Management and Common Pitfalls

 
Session 12-14: Practice with Multiple Choice and Free Response Questions

• Focused Practice on Core Topics (2 Hours Each)
• Practice with Calculus Problems / Statistical Inference

 
Session 15: Mock Exam and Immediate Feedback

• Full-Length Practice Exam in Timed Conditions
• Immediate Review and Discussion of Results

 
Session 16-17: Problem-Solving Sessions

• Tackling Challenging Questions in Small Groups
• Strategies for Complex Calculus Applications / Statistical Analysis

 
Session 18: Key Formula and Concept Review

• Review of Critical Formulas and Theorems
• Key Concepts in Calculus / Major Statistical Tests

 
Session 19: Final Practice Exam and Review

• Simulated Exam with Mixed Question Types
• Final Q&A for Clarifications

 
Session 20: Final Recap and Tips for Exam Day

• Summary of Major Topics and Last-Minute Tips
• Test-Taking Tips, Managing Time, and Building Confidence

Total: 40 Hours


Key Takeaways:

• Core Mastery: Understanding of major AP Calculus or AP Statistics concepts
• Exam Strategy: Focused practice and strategies to tackle the AP exam confidently
• Foundation for Further Study: A strong grasp of foundational topics for continued math education

 
This plan is an intensive course, ideal for students who need a thorough review of AP Math essentials.
  Updated on 27 November, 2024