High School Calculus Topics Covered
StudyPug's High School Calculus course covers all major topics Nebraska students encounter in their calculus classes. From understanding limits graphically and numerically to evaluating definite integrals using the Fundamental Theorem of Calculus, every concept is broken down into clear, step-by-step video lessons.
Limits and Continuity
Students start by understanding limits graphically and numerically, then learn to evaluate limits using substitution. The course covers continuity at a point, types of discontinuities, limits at infinity, and end behavior of functions — giving students a strong foundation before moving into derivatives.
Derivatives
The derivative unit teaches students the power rule, product rule, quotient rule, and chain rule. Students also learn to differentiate trigonometric, exponential, and logarithmic functions, as well as implicitly defined functions. Practical applications include finding tangent line equations and using linear approximation.
Applications of Derivatives
Students apply derivatives to real-world problems, including finding critical points, local maxima and minima, and solving optimization problems. The course also covers curve sketching using increasing/decreasing behavior and concavity, related rates problems, and motion problems involving velocity and acceleration.
Integrals
The integral unit introduces antiderivatives of basic functions, Riemann sums for approximating definite integrals, and the Fundamental Theorem of Calculus. Students learn the substitution method, how to find area under and between curves, displacement and distance from velocity functions, and average value of a function over an interval.
- Limits: graphical, numerical, and algebraic approaches
- Derivatives: all major rules and special functions
- Applications: optimization, curve sketching, related rates
- Integrals: antiderivatives, Riemann sums, FTC, substitution
- Real-world applications: motion, area, average value
Nebraska