IN High School Calculus Curriculum

Indiana High School Calculus Topics

• Limits and Continuity: Understand limits graphically and numerically, evaluate basic limits using substitution, determine continuity at a point, identify types of discontinuities, and find limits at infinity to describe end behavior of functions.
• Derivatives and Differentiation Rules: Understand the derivative as rate of change and slope of a tangent line; apply the power rule, product rule, quotient rule, and chain rule; differentiate trigonometric, exponential, and logarithmic functions; and find derivatives of implicitly defined functions.
• Tangent Lines and Linear Approximation: Find equations of tangent lines and use them for linear approximation of function values.
• Curve Analysis and Optimization: Find critical points, local maxima and minima, and solve optimization problems; analyze increasing and decreasing behavior and concavity; and sketch curves using derivative information.
• Rates of Change Applications: Solve related rates problems in real-world contexts and apply derivatives to velocity, acceleration, and other rate problems.
• Antiderivatives and Integration: Find antiderivatives of basic functions using initial conditions, approximate definite integrals using left, right, and midpoint Riemann sums, and apply the Fundamental Theorem of Calculus to evaluate definite integrals and find antiderivatives.
• Integration Techniques and Applications: Use the substitution method to evaluate integrals, find area under curves and between curves using definite integrals, determine displacement and distance from velocity functions, and calculate the average value of functions over intervals.

How StudyPug Helps Indiana High School Calculus Students

When a student gets stuck on a problem - whether it is applying the chain rule or setting up a Riemann sum - StudyPug lets them go straight to the lesson for that specific topic. Each lesson walks through the concept step by step, followed by practice problems so the student can check their understanding before the next class.

Parents can track which strands their student has visited and where they are spending the most time. That visibility makes it easier to decide whether a student needs more practice on derivatives or is ready to move on to integral applications.

Aligned to Indiana High School Calculus Curriculum

Every lesson and practice problem on StudyPug is organized to match the strands and learning expectations of the Indiana Academic Standards for high school math. Students work through the same sequence their class follows - from limits and continuity through differentiation rules and on to integral calculus - so what they learn on StudyPug directly supports what they are doing in school.