AP Calculus Topics Covered
StudyPug's AP Calculus course covers every major topic Mississippi students need, from understanding limits graphically and numerically to evaluating definite integrals using the Fundamental Theorem of Calculus. Whether your student is just starting with limits or working through optimization and related rates, every concept is explained with clear video lessons and practice problems.
Limits and Continuity
Students start by understanding limits graphically and numerically, evaluating basic limits using substitution, and determining continuity at a point. Lessons also cover identifying types of discontinuities and finding limits at infinity to describe end behavior of functions.
Derivatives
The derivatives unit covers the derivative as a rate of change and slope of a tangent line. Students learn to apply the power rule, product rule, quotient rule, and chain rule. Lessons also include derivatives of trigonometric, exponential, and logarithmic functions, as well as implicit differentiation.
Applications of Derivatives
Students apply derivatives to find equations of tangent lines, perform linear approximation, locate critical points, and solve optimization problems. Lessons on curve sketching help students analyze increasing and decreasing behavior and concavity. Related rates and motion problems give students practice with real-world applications.
Integrals and Applications
- Finding antiderivatives of basic functions using initial conditions
- Approximating definite integrals with left, right, and midpoint Riemann sums
- Using the Fundamental Theorem of Calculus to evaluate definite integrals
- Evaluating integrals using substitution
- Finding area under curves and between curves
- Using integrals for displacement, distance, and average value of functions
These topics align to MS College Career Ready Standards and prepare Mississippi students for the AP Calculus exam and college-level mathematics.
Mississippi