About High School Illinois Calculus
Illinois high school calculus follows the Illinois Learning Standards, built around the study of limits, derivatives, and integrals. This course covers limits and continuity, differentiation rules including product, quotient, and chain rules, derivatives of trigonometric and exponential functions, optimization and curve sketching, antiderivatives, Riemann sums, the Fundamental Theorem of Calculus, and integral applications. StudyPug provides video lessons and practice problems for every strand in this course.
- Strands covered: limits and continuity, differentiation, applications of derivatives, integration, and applications of integrals
- Video lessons taught by certified teachers for every topic in the Illinois Learning Standards
- Practice problems and step-by-step explanations to reinforce each concept
- Content aligned to Illinois Learning Standards for high school calculus
Curriculum topics by strand
Browse lessons and practice problems organized by strand and aligned to Illinois Learning Standards for high school calculus.
Illinois High School Calculus Topics
- Limits and continuity: Understand limits graphically and numerically, evaluate limits using substitution, determine continuity at a point, identify types of discontinuities, and find limits at infinity to describe end behavior.
- 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.
- Applications of derivatives: Find equations of tangent lines and use linear approximation; locate critical points, local maxima and minima; solve optimization problems; analyze increasing and decreasing behavior and concavity; sketch curves; solve related rates problems; and apply derivatives to velocity, acceleration, and other rate problems.
- Integration and antiderivatives: Find antiderivatives of basic functions using initial conditions; approximate definite integrals using left, right, and midpoint Riemann sums; apply the Fundamental Theorem of Calculus; and use substitution to evaluate integrals.
- Applications of integrals: Find area under curves and between curves; use integrals to find displacement and distance from velocity functions; and calculate the average value of a function over an interval.
How StudyPug Helps Illinois High School Calculus Students
When a student gets stuck on a related rates problem or loses track of which differentiation rule to use, StudyPug lets them go back to the exact concept causing trouble. Each video lesson focuses on one idea, followed by practice problems with step-by-step explanations, so gaps are addressed before they become bigger obstacles.
Students preparing for AP Calculus or college readiness can work through every strand at their own pace, revisiting limits, integration techniques, or curve analysis as many times as needed without waiting for the next class session.
Aligned to Illinois High School Calculus Curriculum
Every lesson and practice problem on StudyPug is built around the Illinois Learning Standards, so the topics students see on the platform match what their teachers cover in class. Families can feel confident that the support their student gets at home is directly relevant to the work happening in the Illinois classroom.
Written by the StudyPug Math Team
Last updated June 5, 2026
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