Indiana High School Calculus Topics
StudyPug covers every major Calculus topic taught in Indiana high schools, from introductory limits all the way through integral applications. Whether your student is taking a standard Calculus course or preparing for AP Calculus AB or BC, every concept is covered with clear video lessons and practice problems.
Limits and Continuity
Calculus begins with limits — understanding how functions behave as inputs approach a value. Indiana students learn to evaluate limits graphically, numerically, and using substitution. From there, they study continuity at a point, identify types of discontinuities, and explore limits at infinity to describe end behavior of functions.
Derivatives and Differentiation Rules
The derivative is one of the most important ideas in Calculus. Students learn to interpret the derivative as a rate of change and the slope of a tangent line. StudyPug covers all core differentiation rules:
- Power rule, product rule, quotient rule, and chain rule
- Derivatives of trigonometric, exponential, and logarithmic functions
- Implicit differentiation for functions not written explicitly in terms of x
Applications of Derivatives
Derivatives aren't just a calculation — they describe real-world behavior. Indiana Calculus students apply derivatives to find equations of tangent lines, use linear approximation, identify critical points, and solve optimization problems. Curve sketching brings together increasing/decreasing analysis and concavity. Related rates and motion problems connect Calculus to physics and everyday contexts.
Integrals and the Fundamental Theorem of Calculus
The second half of Calculus focuses on integration. Students start with antiderivatives and basic integration rules, then move to Riemann sums for approximating definite integrals. The Fundamental Theorem of Calculus connects differentiation and integration — a central idea in all of Calculus. StudyPug also covers the substitution method for evaluating integrals.
Applications of Integrals
Indiana students apply integrals to find area under curves, area between curves, displacement and distance from velocity functions, and the average value of a function over an interval. These topics show up in science, engineering, and economics — making them essential for students planning to study STEM fields.
StudyPug's Calculus content aligns to Indiana Academic Standards for Math and is designed to help Indiana high school students succeed in class, on tests, and beyond.
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