Advanced Placement (AP)

Understanding AP Mathematics

Advanced Placement courses offer high school students the opportunity to complete college-level coursework and earn university credit before graduation. Strong AP scores demonstrate academic readiness and can significantly strengthen university applications, both in the United States and internationally.

AP Calculus AB

AP Calculus AB covers the equivalent of a first-semester college calculus course. This is the most popular AP mathematics exam worldwide.

Core Topics:

• Limits and Continuity: Formal definitions, properties, and the squeeze theorem
• Derivatives: Rules of differentiation, implicit differentiation, and related rates
• Applications of Derivatives: Optimization, curve analysis, and motion problems
• Integrals: Riemann sums, the Fundamental Theorem of Calculus, and antiderivatives
• Differential Equations: Slope fields, separation of variables, and exponential models
• Applications of Integration: Area, volume, and accumulation functions

Exam Format:

• Section I: 45 multiple choice questions (1 hour 45 minutes)
• Section II: 6 free response questions (1 hour 30 minutes)

---

AP Calculus BC

AP Calculus BC includes all AB content plus additional topics equivalent to a full year of college calculus. Students who score well on BC receive both a BC score and an AB subscore, demonstrating competency in both areas.

Additional Topics Beyond AB:

• Parametric and Polar Functions: Derivatives, integrals, and arc length in alternate coordinate systems
• Advanced Integration: Integration by parts, partial fractions, and improper integrals
• Sequences and Series: Convergence tests, power series, and error bounds
• Taylor and Maclaurin Series: Polynomial approximations and Lagrange error analysis

---

AP Statistics

AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. This course is an excellent complement to calculus and is highly valued for students pursuing social sciences, business, or pre-medical studies.

Core Areas:

• Exploring Data: Describing patterns, distributions, and departures from expected behavior
• Sampling and Experimentation: Planning and conducting well-designed studies
• Probability and Simulation: Anticipating patterns using theoretical and empirical methods
• Statistical Inference: Estimating population parameters and testing hypotheses with confidence

---

The AP Exam Advantage

Score	College Credit	Qualification Level
5	Accepted at most universities	Extremely well qualified
4	Accepted at many universities	Well qualified
3	Accepted at some universities	Qualified

My students consistently achieve scores of 4 and 5, securing college credit and demonstrating their mathematical capabilities to admissions committees worldwide.

---

Preparation for AP examinations requires more than content knowledge. Success depends on mastering the specific question formats, understanding how the College Board awards points on free response questions, and building the calculator fluency that saves valuable time under exam conditions. Every session is designed to build both deep understanding and the strategic exam skills that lead to top scores.